CSparse: a Concise Sparse Matrix package.
CSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
SPDX-License-Identifier: LGPL-2.1+

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.

The algorithms contained in CSparse have been chosen with five goals in mind:
(1) they must embody much of the theory behind sparse matrix algorithms,
(2) they must be either asymptotically optimal in their run time and memory
    usage or be fast in practice,
(3) they must be concise so as to be easily understood and short enough to
    print in the book,
(4) they must cover a wide spectrum of matrix operations, and
(5) they must be accurate and robust.
The focus is on direct methods; iterative methods and solvers for
eigenvalue problems are beyond the scope of this package.

No detailed user guide is included in this package; the user guide is the
book itself.  Some indication of how to call the CSparse C routines is given
by the M-files in the MATLAB/CSparse directory.

Complex matrices are not supported, except for methods that operate only
on the nonzero pattern of a matrix.  A complex version of CSparse appears
as a separate package, CXSparse ("Concise Extended Sparse matrix package").

The performance of the sparse factorization methods in CSparse will not be
competitive with UMFPACK or CHOLMOD, but the codes are much more concise and
easy to understand (see the above goals).  Other methods are competitive.

Some of the MATLAB tests require the AMD package.
See http://www.suitesparse.com for CSparse and the AMD ordering
package.  See the Doc/License.txt file for the license.

To compile the C-library (./Source) and C demo programs (./Demo) just type
"make" in this directory, or import the CMakeLists.txt into your build system
(such as Microsoft Visual Studio).  To install, use "sudo make install".
Run the demos with "make demos".  To clean up, do "make clean".

To run the exhaustive tests, type "make" in the Tcov directory (Linux is
assumed).  To remove all files not in the original distribution, type "make
distclean".

While in MATLAB, type "cs_install" while in the CSparse/MATLAB directory to
compile and install CSparse for use in MATLAB.  For more details, see
CSparse/MATLAB/README.txt.

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Contents:
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Demo/           demo C programs that use CSparse
Doc/            license and change log
Makefile        Makefile for the whole package
MATLAB/         MATLAB interface, demos, and tests for CSparse
Matrix/         sample matrices
README.txt      this file
Source/         primary CSparse source files (C only, no MATLAB)
Tcov/           CSparse tests
Config/         source for Include/cs.h
build/          compiled files

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./Doc:          license and change log
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ChangeLog       changes in CSparse since first release
License.txt     license

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./Source:       Primary source code for CSparse
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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 triplet form to compressed-column form
cs_counts.c     column counts for Cholesky and QR
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 CSparse
cs_happly.c     apply Householder reflection
cs_house.c      compute Householder reflection
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=G\b where G, x, and b are sparse, and G 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
README.txt      README file for CSparse

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./Config:
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cs.h.in         source for cs.h

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./Demo:         C program demos
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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
README.txt      Demo README file

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./MATLAB:       MATLAB interface, demos, and tests
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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
ssget/          MATLAB interface to SuiteSparse Matrix Collection

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./MATLAB/CSparse:   MATLAB interface for CSparse
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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


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./MATLAB/Demo:      MATLAB demos for CSparse
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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


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./MATLAB/Demo/private: private functions for MATLAB demos
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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


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./MATLAB/Test:      Extensive test of CSparse, in MATLAB
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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


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./MATLAB/ssget:     MATLAB interface for the SuiteSparse Matrix Collection
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See MATLAB/ssget/README.txt for details

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./Matrix:           Sample matrices, most from Rutherford/Boeing collection
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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)

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./Tcov:             Exhaustive test coverage of CSparse
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covall              run test coverage (requires Linux)
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
README.txt          README file for Tcov directory

