--- The Folders MATLAB/ and Matrix/ have been removed from the original project in order to save space --- CXSparse: Copyright (c) 2006-2012, Timothy A. Davis. http://www.suitesparse.com Derived from CSparse. Conversion originally by David Bateman, Motorola, and then modified by Tim Davis. ANSI C99 is required, with support for the _Complex data type. (if you use a C++ compiler, the C++ complex type is used instead). CXSparse is a version of CSparse that operates on both real and complex matrices, using either int or SuiteSparse_long integers. A SuiteSparse_long is normally just a long on most platforms, but becomes __int64 on WIN64. It now includes a MATLAB interface, enabling the use of CXSparse functions on both 32-bit and 64-bit platforms. To install for use in MATLAB, simply type "cs_install" in the MATLAB Command Window, while in the CXSparse/MATLAB directory. (NOTE: Windows users cannot use the "lcc" command; run "mex -setup" first, and select a different compiler). If you use the Unix "make" command in that directory instead and are using a 64-bit platform, then you must edit the CXSparse/MATLAB/Makefile first. Refer to the instructions in that file. Refer to "Direct Methods for Sparse Linear Systems," Timothy A. Davis, SIAM, Philadelphia, 2006. No detailed user guide is included in this package; the user guide is the book itself. To compile the C-library (./Source), C demo programs (./Demo) just type "make" in this directory. To run the exhaustive statement coverage tests, type "make" in the Tcov directory; the Tcov tests assume you are using Linux. To remove all files not in the original distribution, type "make distclean". I recommend that you use a different level of optimization than "cc -O", which was chosen so that the Makefile is portable. See Source/Makefile. If your C compiler does not support the ANSI C99 complex type, the #include <complex.h> statement will fail. If this happens, compile the code with the -DNCOMPLEX flag (the MATLAB cs_install will do this for you). This package is backward compatible with CSparse. That is, user code that uses CSparse may switch to using CXSparse without any changes to the user code. Each CXSparse function has a generic version with the same name as the CSparse function, and four type-specific versions. For example: cs_add same as cs_add_di by default, but can be changed to use SuiteSparse_long integers if user code is compiled with -DCS_LONG, and/or can be changed to operate on complex matrices with -DCS_COMPLEX. cs_di_add double/int version of cs_add cs_dl_add double/SuiteSparse_long version of cs_add cs_ci_add complex/int version of cs_add cs_cl_add complex/SuiteSparse_long version of cs_add The sparse matrix data structures are treated in the same way: cs, css, csn, and csd become cs_di, cs_dis, cs_din, and cs_did for the double/int case, cs_cl, cs_cls, cs_cln, and cs_cld for the complex/SuiteSparse_long case, and so on. See cs_demo.c for a type-generic user program, and cs_cl_demo.c for a type-specific version of the same program (complex/SuiteSparse_long). Several macros are available in CXSparse (but not in CSparse) to allow user code to be written in a type-generic manner: CS_INT int by default, SuiteSparse_long if -DCS_LONG compiler flag is used CS_ENTRY double by default, double complex if -DCS_COMPLEX flag is used. CS_ID "%d" or "%ld", for printf and scanf of the CS_INT type. CS_INT_MAX INT_MAX or LONG_MAX, the largest possible value of CS_INT. CS_REAL(x) x or creal(x) CS_IMAG(x) 0 or cimag(x) CS_CONJ(x) x or conj(x) CS_ABS(x) fabs(x) or cabs(x) Even the name of the include file (cs.h) is the same. To use CXSparse instead of CSparse, simply compile with -ICXSparse/Source instead of -ICSparse/Source, and link against libcxsparse.a instead of the CSparse libcsparse.a library. To determine at compile time if CXSparse or CSparse is being used: #ifdef CXSPARSE CXSparse is in use. The generic functions equivalent to CSparse may be used (cs_add, etc). These generic functions can use different types, depending on the -DCS_LONG and -DCS_COMPLEX compile flags, with the default being double/int. The type-specific functions and data types (cs_di_add, cs_di, CS_INT, etc.) can be used. #else CSparse is in use. Only the generic functions "cs_add", etc., are available, and they are of type double/int. #endif See cs.h for the prototypes of each function, and the book "Direct Methods for Sparse Linear Systems" for full documentation of CSparse and CXSparse. Other changes from CSparse: cs_transpose performs the complex conjugate transpose if values>0 (C=A'), the pattern-only transpose if values=0 (C=spones(A') in MATLAB), and the array transpose if values<0 (C=A.' in MATLAB notation). A set of four conversion routines are included in CXSparse, to convert real matrices to/from complex matrices. The Householder reflection constructed by cs_house.c also differs slightly, to accomodate both the real and complex cases properly. CXSparse is generated automatically from CSparse. Refer to http://www.suitesparse.com for details. -------------------------------------------------------------------------------- Contents: -------------------------------------------------------------------------------- Demo/ demo C programs that use CXSparse Doc/ license and change log Makefile Makefile for the whole package MATLAB/ MATLAB interface, demos, and tests for CXSparse Matrix/ sample matrices (with extra complex matrices for CXSparse) README.txt this file Source/ primary CXSparse source files Tcov/ CXSparse tests -------------------------------------------------------------------------------- ./Doc: license and change log -------------------------------------------------------------------------------- ChangeLog changes in CSparse since first release lesser.txt the GNU LGPL License.txt license (GNU LGPL) -------------------------------------------------------------------------------- ./Source: Primary source code for CXSparse -------------------------------------------------------------------------------- cs_add.c add sparse matrices cs_amd.c approximate minimum degree cs_chol.c sparse Cholesky cs_cholsol.c x=A\b using sparse Cholesky cs_compress.c convert a compress form to compressed-column form cs_counts.c column counts for Cholesky and QR cs_convert.c convert real to complex and complex to real (not in CSparse) cs_cumsum.c cumulative sum cs_dfs.c depth-first-search cs_dmperm.c Dulmage-Mendelsohn permutation cs_droptol.c drop small entries from a sparse matrix cs_dropzeros.c drop zeros from a sparse matrix cs_dupl.c remove (and sum) duplicates cs_entry.c add an entry to a triplet matrix cs_ereach.c nonzero pattern of Cholesky L(k,:) from etree and triu(A(:,k)) cs_etree.c find elimination tree cs_fkeep.c drop entries from a sparse matrix cs_gaxpy.c sparse matrix times dense matrix cs.h include file for CXSparse cs_happly.c apply Householder reflection cs_house.c Householder reflection (*** NOTE: different algo. from CSparse) cs_ipvec.c x(p)=b cs_leaf.c determine if j is a leaf of the skeleton matrix and find lca cs_load.c load a sparse matrix from a file cs_lsolve.c x=L\b cs_ltsolve.c x=L'\b cs_lu.c sparse LU factorization cs_lusol.c x=A\b using sparse LU factorization cs_malloc.c memory manager cs_maxtrans.c maximum transveral (permutation for zero-free diagonal) cs_multiply.c sparse matrix multiply cs_norm.c sparse matrix norm cs_permute.c permute a sparse matrix cs_pinv.c invert a permutation vector cs_post.c postorder an elimination tree cs_print.c print a sparse matrix cs_pvec.c x=b(p) cs_qr.c sparse QR cs_qrsol.c solve a least-squares problem cs_randperm.c random permutation cs_reach.c find nonzero pattern of x=L\b for sparse L and b cs_scatter.c scatter a sparse vector cs_scc.c strongly-connected components cs_schol.c symbolic Cholesky cs_spsolve.c x=Z\b where Z, x, and b are sparse, and Z upper/lower triangular cs_sqr.c symbolic QR (also can be used for LU) cs_symperm.c symmetric permutation of a sparse matrix cs_tdfs.c depth-first-search of a tree cs_transpose.c transpose a sparse matrix cs_updown.c sparse rank-1 Cholesky update/downate cs_usolve.c x=U\b cs_util.c various utilities (allocate/free matrices, workspace, etc) cs_utsolve.c x=U'\b Makefile Makefile for CXSparse README.txt README file for CXSparse -------------------------------------------------------------------------------- ./Demo: C program demos -------------------------------------------------------------------------------- cs_ci_demo1.c complex/int version of cs_demo1.c cs_ci_demo2.c complex/int version of cs_demo2.c cs_ci_demo3.c complex/int version of cs_demo3.c cs_ci_demo.c complex/int version of cs_demo.c cs_ci_demo.h complex/int version of cs_demo.h cs_cl_demo1.c complex/SuiteSparse_long version of cs_demo1.c cs_cl_demo2.c complex/SuiteSparse_long version of cs_demo2.c cs_cl_demo3.c complex/SuiteSparse_long version of cs_demo3.c cs_cl_demo.c complex/SuiteSparse_long version of cs_demo.c cs_cl_demo.h complex/SuiteSparse_long version of cs_demo.h cs_demo1.c read a matrix from a file and perform basic matrix operations cs_demo2.c read a matrix from a file and solve a linear system cs_demo3.c read a matrix, solve a linear system, update/downdate cs_demo.c support routines for cs_demo*.c cs_demo.h include file for demo programs cs_demo.out output of "make", which runs the demos on some matrices cs_di_demo1.c double/int version of cs_demo1.c cs_di_demo2.c double/int version of cs_demo2.c cs_di_demo3.c double/int version of cs_demo3.c cs_di_demo.c double/int version of cs_demo.c cs_di_demo.h double/int version of cs_demo.h cs_dl_demo1.c double/SuiteSparse_long version of cs_demo1.c cs_dl_demo2.c double/SuiteSparse_long version of cs_demo2.c cs_dl_demo3.c double/SuiteSparse_long version of cs_demo3.c cs_dl_demo.c double/SuiteSparse_long version of cs_demo.c cs_dl_demo.h double/SuiteSparse_long version of cs_demo.h cs_idemo.c convert real matrices to/from complex (int version) cs_ldemo.c convert real matrices to/from complex (SuiteSparse_long version) Makefile Makefile for Demo programs readhb.f read a Rutherford-Boeing matrix (real matrices only) README.txt Demo README file -------------------------------------------------------------------------------- ./MATLAB: MATLAB interface, demos, and tests -------------------------------------------------------------------------------- cs_install.m MATLAB function for compiling and installing CSparse for MATLAB CSparse/ MATLAB interface for CSparse Demo/ MATLAB demos for CSparse Makefile MATLAB interface Makefile README.txt MATLAB README file Test/ MATLAB test for CSparse, and "textbook" routines UFget/ MATLAB interface to UF Sparse Matrix Collection -------------------------------------------------------------------------------- ./MATLAB/CSparse: MATLAB interface for CSparse -------------------------------------------------------------------------------- Contents.m Contents of MATLAB interface to CSparse cs_add.m add two sparse matrices cs_add_mex.c cs_amd.m approximate minimum degree cs_amd_mex.c cs_chol.m sparse Cholesky cs_chol_mex.c cs_cholsol.m x=A\b using a sparse Cholesky cs_cholsol_mex.c cs_counts.m column counts for Cholesky or QR (like "symbfact" in MATLAB) cs_counts_mex.c cs_dmperm.m Dulmage-Mendelsohn permutation cs_dmperm_mex.c cs_dmsol.m x=A\b using dmperm cs_dmspy.m plot a picture of a dmperm-permuted matrix cs_droptol.m drop small entries cs_droptol_mex.c cs_esep.m find edge separator cs_etree.m compute elimination tree cs_etree_mex.c cs_gaxpy.m sparse matrix times dense vector cs_gaxpy_mex.c cs_lsolve.m x=L\b where L is lower triangular cs_lsolve_mex.c cs_ltsolve.m x=L'\b where L is lower triangular cs_ltsolve_mex.c cs_lu.m sparse LU factorization cs_lu_mex.c cs_lusol.m x=A\b using sparse LU factorization cs_lusol_mex.c cs_make.m compiles CSparse for use in MATLAB cs_mex.c support routines for CSparse mexFunctions cs_mex.h cs_multiply.m sparse matrix multiply cs_multiply_mex.c cs_must_compile.m determine if a source file needs to be compiled with mex cs_nd.m nested dissection cs_nsep.m find node separator cs_permute.m permute a sparse matrix cs_permute_mex.c cs_print.m print a sparse matrix cs_print_mex.c cs_qleft.m apply Householder vectors to the left cs_qright.m apply Householder vectors to the right cs_qr.m sparse QR factorization cs_qr_mex.c cs_qrsol.m solve a sparse least squares problem cs_qrsol_mex.c cs_randperm.m randdom permutation cs_randperm_mex.c cs_scc.m strongly-connected components cs_scc_mex.c cs_sep.m convert an edge separator into a node separator cs_sparse.m convert a triplet form matrix to a compress-column form cs_sparse_mex.c cs_symperm.m symmetric permutation of a sparse matrix cs_symperm_mex.c cs_sqr.m symbolic QR ordering and analysis cs_sqr_mex.c cs_thumb_mex.c compute small "thumbnail" of a sparse matrix (for cspy). cs_transpose.m transpose a sparse matrix cs_transpose_mex.c cs_updown.m sparse Cholesky update/downdate cs_updown_mex.c cs_usolve.m x=U\b where U is upper triangular cs_usolve_mex.c cs_utsolve.m x=U'\b where U is upper triangular cs_utsolve_mex.c cspy.m a color "spy" Makefile Makefile for CSparse MATLAB interface README.txt README file for CSparse MATLAB interface -------------------------------------------------------------------------------- ./MATLAB/Demo: MATLAB demos for CSparse -------------------------------------------------------------------------------- Contents.m Contents of MATLAB demo for CSparse cs_demo.m run all MATLAB demos for CSparse cs_demo1.m MATLAB version of Demo/cs_demo1.c cs_demo2.m MATLAB version of Demo/cs_demo2.c cs_demo3.m MATLAB version of Demo/cs_demo3.c private/ private functions for MATLAB demos README.txt README file for CSparse MATLAB demo -------------------------------------------------------------------------------- ./MATLAB/Demo/private: private functions for MATLAB demos -------------------------------------------------------------------------------- demo2.m demo 2 demo3.m demo 3 ex_1.m example 1 ex2.m example 2 ex3.m example 3 frand.m generate a random finite-element matrix get_problem.m get a matrix is_sym.m determine if a matrix is symmetric mesh2d1.m construct a 2D mesh (method 1) mesh2d2.m construct a 2D mesh (method 2) mesh3d1.m construct a 3D mesh (method 1) mesh3d2.m construct a 3D mesh (method 2) print_order.m print the ordering method used resid.m compute residual rhs.m create right-hand-side -------------------------------------------------------------------------------- ./MATLAB/Test: Extensive test of CSparse, in MATLAB -------------------------------------------------------------------------------- Makefile Makefile for MATLAB Test directory README.txt README file for MATLAB/Test Contents.m Contents of MATLAB/Test, "textbook" files only chol_downdate.m downdate a Cholesky factorization. chol_left.m left-looking Cholesky factorization. chol_left2.m left-looking Cholesky factorization, more details. chol_right.m right-looking Cholesky factorization. chol_super.m left-looking "supernodal" Cholesky factorization. chol_up.m up-looking Cholesky factorization. chol_update.m update a Cholesky factorization. chol_updown.m update or downdate a Cholesky factorization. cond1est.m 1-norm condition estimate. cs_fiedler.m the Fiedler vector of a connected graph. givens2.m find a Givens rotation. house.m find a Householder reflection. lu_left.m left-looking LU factorization. lu_right.m right-looking LU factorization. lu_rightp.m right-looking LU factorization, with partial pivoting. lu_rightpr.m recursive right-looking LU, with partial pivoting. lu_rightr.m recursive right-looking LU. norm1est.m 1-norm estimate. qr_givens.m Givens-rotation QR factorization. qr_givens_full.m Givens-rotation QR factorization, for full matrices. qr_left.m left-looking Householder QR factorization. qr_right.m right-looking Householder QR factorization. cs_fiedler.m Fiedler vector cs_frand.m generate a random finite-element matrix cs_frand_mex.c cs_ipvec.m x(p)=b cs_ipvec_mex.c cs_maxtransr.m recursive maximum matching algorithm cs_maxtransr_mex.c cs_pvec.m x=b(p) cs_pvec_mex.c interface for cs_pvec cs_reach.m non-recursive reach (interface to CSparse cs_reach) cs_reach_mex.c non-recursive x=spones(L\sparse(b)) cs_reachr.m recursive reach (interface to CSparse cs_reachr) cs_reachr_mex.c cs_rowcnt.m row counts for sparse Cholesky cs_rowcnt_mex.c row counts for sparse Cholesky cs_sparse2.m same as cs_sparse, to test cs_entry function cs_sparse2_mex.c like cs_sparse, but for testing cs_entry cs_test_make.m compiles MATLAB tests check_if_same.m check if two inputs are identical or not choldn.m Cholesky downdate cholup.m Cholesky update, using Given's rotations cholupdown.m Cholesky update/downdate (Bischof, Pan, and Tang method) cs_q1.m construct Q from Householder vectors cs_test_make.m compiles the CSparse, Demo, and Test mexFunctions. dmperm_test.m test cs_dmperm chol_example.m simple Cholesky factorization example etree_sample.m construct a sample etree and symbolic factorization gqr3.m QR factorization, based on Givens rotations happly.m apply Householder reflection to a vector hmake1.m construct a Householder reflection mynormest1.m estimate norm(A,1), using LU factorization (L*U = P*A*Q). myqr.m QR factorization using Householder reflections another_colormap.m try another color map cspy_test.m test cspy and cs_dmspy qr2.m QR factorization based on Householder reflections sample_colormap.m try a colormap for use in cspy signum.m compute and display the sign of a column vector x sqr_example.m test cs_sqr dmspy_test.m test cspy, cs_dmspy, and cs_dmperm test_qr.m test various QR factorization methods test_randperms.m test random permutations testh.m test Householder reflections test_qr1.m test QR factorizations test_qrsol.m test cs_qrsol test_sep.m test cs_sep, and compare with Gilbert's meshpart vtxsep testall.m test all CSparse functions (run tests 1 to 28 below) test1.m test cs_transpose test2.m test cs_sparse test3.m test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol test4.m test cs_multiply test5.m test cs_add test6.m test cs_reach, cs_reachr, cs_lsolve, cs_usolve test7.m test cs_lu test8.m test cs_cholsol, cs_lusol test9.m test cs_qr test10.m test cs_qr test11.m test cs_rowcnt test12.m test cs_qr and compare with svd test13.m test cs_counts, cs_etree test14.m test cs_droptol test15.m test cs_amd test16.m test cs_amd test17.m test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol test18.m test iterative refinement after backslash test19.m test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc test20.m test cholupdown test21.m test cs_updown test22.m test cond1est test23.m test cs_dmspy test24.m test cs_fielder test25.m test cs_nd test26.m test cs_dmsol and cs_dmspy test27.m test cs_qr, cs_utsolve, cs_qrsol test28.m test cs_randperm, cs_dmperm -------------------------------------------------------------------------------- ./MATLAB/UFget: MATLAB interface for the UF Sparse Matrix Collection -------------------------------------------------------------------------------- Contents.m Contents of UFget mat/ default directory where downloaded matrices will be put README.txt README file for UFget UFget_defaults.m default parameter settings UFget_example.m example of use UFget_install.m installs UFget temporarily (for current session) UFget_java.class read a url and load it in into MATLAB (compiled Java code) UFget_java.java read a url and load it in into MATLAB (Java source code) UFget_lookup.m look up a matrix in the index UFget.m UFget itself (primary user interface) UFweb.m open url for a matrix or collection mat/UF_Index.mat index of matrices in UF Sparse Matrix Collection -------------------------------------------------------------------------------- ./Matrix: Sample matrices, most from Rutherford/Boeing collection -------------------------------------------------------------------------------- ash219 overdetermined pattern of Holland survey. Ashkenazi, 1974. bcsstk01 stiffness matrix for small generalized eigenvalue problem bcsstk16 stiffness matrix, Corp of Engineers dam fs_183_1 unsymmetric facsimile convergence matrix lp_afiro NETLIB afiro linear programming problem mbeacxc US economy, 1972. Dan Szyld, while at NYU t1 small example used in Chapter 2 west0067 Cavett problem with 5 components (chemical eng., Westerberg) c_mbeacxc complex version of mbeacxc c_west0067 complex version of west0067 mhd1280b Alfven spectra in magnetohydrodynamics (complex) neumann complex matrix qc324 model of H+ in an electromagnetic field (complex) t2 small complex matrix t3 small complex matrix t4 small complex matrix c4 small complex matrix young1c aeronautical problem (complex matrix) -------------------------------------------------------------------------------- ./Tcov: Exhaustive test coverage of CXSparse -------------------------------------------------------------------------------- covall same as covall.linux covall.linux find coverage (Linux) covall.sol find coverage (Solaris) cov.awk coverage summary cover print uncovered lines covs print uncovered lines cstcov_malloc_test.c malloc test cstcov_malloc_test.h cstcov_test.c main program for Tcov tests gcovs run gcov (Linux) Makefile Makefile for Tcov tests nil an empty matrix zero a 1-by-1 zero matrix czero a 1-by-1 complex zero matrix README.txt README file for Tcov directory -------------------------------------------------------------------------------- Change Log: -------------------------------------------------------------------------------- Refer to CSparse for changes in CSparse, which are immediately propagated into CXSparse (those Change Log entries are not repeated here). Jun 1, 2012. version 3.1.0 * now based on CSparse v3.1.0 * This version of CXSparse changes the 'long' integer from UF_long to cs_long_t. UF_long is still available to user codes, however, so this change is backward compatible with user codes. Future user codes should use cs_long_t instead of UF_long. * changed unsigned integer in cs_amd.c to signed, for hash code. * in Source, only changes are to cs_demo*.c, cs_print.c Nov 1, 2007. version 2.2.1 CXSparse/MATLAB/Test ported to Windows May 31, 2007. version 2.2.0 * back-port to MATLAB 7.2 and earlier (which does not have mwIndex). * more graceful failure in cs_make when attempting complex matrix support (Windows, in particular) * correction to CXSparse/Demo/Makefile * added sizeof(CS_INT) printout to cs_idemo.c, cs_ldemo.c Mar 14, 2007. Version 2.1.0. * MATLAB interface added for CXSparse. * cs_complex_t type added (a #define for "double _Complex", which is the complex type used in CXSparse 2.0.x). When compiling with a C++ compiler, the std::compex<double> type is used for the complex case. * bug fix in complex sparse Cholesky (cs_chol.c). * bug fix in complex sparse Cholesky update/downdate (cs_updown.c). * bug fix in cs_symperm for the complex case. * "beta" changed from complex to real, in sparse QR (cs_house.c, cs_happly.c, cs_qr.c), (a performance/memory improvement, not a bug fix). Similar change to "nz2" in cs_cumsum.c. May 5, 2006. Version 2.0.1 released. * long changed to UF_long, dependency in ../UFconfig/UFconfig.h added. "UF_long" is a #define'd term in UFconfig.h. It is normally defined as "long", but can be redefined as something else if desired. On Windows-64, it becomes __int64. Mar 6, 2006 "double complex" changed to "double _Complex", to avoid conflicts when CXSparse is compiled with a C++ compiler. Other minor changes to cs.h.