LINPLUS
Linear Algebra Utilities

LINPLUS is a MATLAB library of linear algebra routines, inspired by LINPACK and LAPACK.

The routines are primarily organized by the storage format of the matrix they operate on. Some of these formats were defined by LINPACK, while others are new; I just made them up when I had to solve problems involving such matrices. The formats include:

• C83 - Double complex tridiagonal;
• C8CI - Double complex circulant;
• C8GE - Double complex general;
• C8TO - Double complex Toeplitz;
• D3 - Double precision tridiagonal;
• D3P - Double precision tridiagonal periodic;
• D5 - Double precision pentadiagonal;
• DBB - Double precision border-banded;
• DBLT - Double precision banded lower triangular matrix;
• DBTO - Double precision block Toeplitz;
• DBUT - Double precision banded upper triangular matrix;
• DCB - Double precision compact band;
• DCBB - Double precision compact border-banded;
• DCC - Double precision compressed column sparse = Harwell Boeing Unsymmetric Assembled format = MATLAB sparse format;
• DCI - Double precision circulant;
• DGB - Double precision general band, used by LINPACK and LAPACK;
• DGD - Double precision general diagonal;
• DGE - Double precision general, used by LINPACK and LAPACK;
• DLT - Double precision lower triangular;
• DNCF - Double precision Nonsymmetric Coordinate Format (one of the formats used by NSPCG);
• DPBL - Double precision positive-definite symmetric band matrix, store diagonal and lower triangle;
• DPBU - Double precision positive-definite symmetric band matrix, store diagonal and upper triangle;
• DPO - Double precision positive-definite symmetric, used by LINPACK and LAPACK;
• DPP - Double precision positive-definite symmetric Packed, used by LINPACK and LAPACK;
• DS3 - Double precision sparse matrix stored by row, column, value (used by SLAP/DLAP, symmetric or nonsymmetric);
• DSD - Double precision symmetric diagonal;
• DSM - Double precision Sherman Morrison system A - u * v';
• DSP - Double precision sparse matrix stored by row, column, value (used by CSPARSE ("sparse triplet"), SLAP/DLAP (nonsymmetric SLAP triad format), MATLAB, and SPARSEKIT ("COO" format));
• DSR - Double precision sparse matrix stored by rows;
• DSS - Double precision symmetric skyline;
• DSTO - Double precision symmetric Toeplitz;
• DTO - Double precision Toeplitz;
• DUT - Double precision upper triangular;
• DVM - Double precision Vandermonde;
• R8VEC - Double precision vector, which in some cases is used to store a matrix;

Related Data and Programs:

BLAS1 is a library of MATLAB routines for vector operations, used by LINPACK.

CSPARSE is a C library of routines for the direct solution of sparse linear systems.

DLAP is a FORTRAN90 library of iterative linear algebra.routines for sparse systems.

DSP is a format used to store a DSP matrix in a file.

GSL is a C++ library, the Gnu Scientific Library, which includes many linear algebra routines.

LAPACK is a FORTRAN90 library, containing a modern linear algebra package.

LINPACK is a library of MATLAB routines forming a linear algebra package to solve linear systems for a variety of matrix storage formats.

LINPACK_BENCH is an executable FORTRAN90 benchmark program which measures the time taken by LINPACK to solve a particular linear system.

LINPLUS is also available in a C++ version and a FORTRAN90 version.

MGMRES is a MATLAB routine which applies the restarted GMRES algorithm to solve a sparse linear system.

NAG is a general purpose mathematical library, callable from FORTRAN90, which includes many linear algebra routines.

NSPCG is a FORTRAN90 library of routines for solving sparse systems of linear equations using the nonsymmetric sparse conjugate gradient method.

PETSC is a C++ library suitable for use in parallel programming, which includes linear algebra routines.

SPARSE_CC is a data directory which contains a description and examples of the CC format, ("compressed column") for storing a sparse matrix, including a way to write the matrix as a set of three files.

SPARSE_CR is a data directory which contains a description and examples of the CR format, ("compressed row") for storing a sparse matrix, including a way to write the matrix as a set of three files.

SPARSEKIT is a library of FORTRAN90 routines for operations on sparse matrices, including conversion between various formats.

SUPER_LU is a C library which implements some very fast solvers for systems of sparse linear equations.

TEMPLATES is a library of MATLAB routines that implement various iterative methods for solving a linear system.

TEST_MAT is a library of FORTRAN90 routines which define test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses and so on.

Reference:

1. Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford, James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Danny Sorensen,
   LAPACK User's Guide,
   Third Edition,
   SIAM, 1999,
   ISBN: 0898714478,
   LC: QA76.73.F25L36
2. Frank Beckman,
   The Solution of Linear Equations by the Conjugate Gradient Method,
   in Mathematical Methods for Digital Computers,
   edited by John Ralston, Herbert Wilf,
   Wiley, 1967,
   ISBN: 0471706892.
3. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Second Edition,
   Springer, 1987,
   ISBN: 0387964673.
4. Ward Cheney, David Kincaid,
   Numerical Mathematics and Computing,
   Brooks-Cole Publishing, 2004,
   ISBN: 0534201121.
5. Philip Davis,
   Circulant Matrices,
   Second Edition,
   Chelsea, 1994,
   ISBN: 0828403384,
   LC: QA188.D37.
6. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
7. Iain Duff, Roger Grimes, John Lewis,
   User's Guide for the Harwell-Boeing Sparse Matrix Collection,
   October 1992.
8. Bennett Fox,
   Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
   ACM Transactions on Mathematical Software,
   Volume 12, Number 4, December 1986, pages 362-376.
9. Gene Golub, Charles VanLoan,
   Matrix Computations, Third Edition,
   Johns Hopkins, 1996,
   ISBN: 0-8018-4513-X,
   LC: QA188.G65.
10. David Kahaner, Cleve Moler, Steven Nash,
    Numerical Methods and Software,
    Prentice Hall, 1989,
    ISBN: 0-13-627258-4,
    LC: TA345.K34.
11. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
    Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage,
    ACM Transactions on Mathematical Software,
    Volume 5, Number 3, September 1979, pages 308-323.
12. Albert Nijenhuis, Herbert Wilf,
    Combinatorial Algorithms for Computers and Calculators,
    Second Edition,
    Academic Press, 1978,
    ISBN: 0-12-519260-6,
    LC: QA164.N54.

Tar File:

A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.

• linplus_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• linplus_m_src.tar.gz the GZIP'ed TAR file.

Source Code:

• c8_le_l2.m, ( X <= Y ) for C8 values and the L2 norm;
• c8_swap.m, swaps two C8 values;
• c8vec_print.m, prints a C8 vector.
• c8vec_sort_a2.m, sorts a C8 vector by L2 norm;
• c8vec_unity.m, returns the N roots of unity;
• d3_cr_fa.m, factors a D3 system using cyclic reduction;
• d3_cr_sl.m, solves a D3 system factored by d3_cr_fa;
• d3_jac_sl.m, solves a D3 system using Gauss-Seidel iteration;
• d3_indicator.m, sets up a D3 indicator matrix;
• d3_jac_sl.m, solves a D3 system using Jacobi iteration;
• d3_mxv.m, multiplies a D3 matrix times a vector;
• d3_np_det.m, returns the determinant of a system factored by D3_NP_FA;
• d3_np_fa.m, factors a D3 linear system with no pivoting;
• d3_np_fs.m, factors and solves a D3 linear system with no pivoting;
• d3_np_ml.m, computes A * x or x * A, where A has been factored by D3_NP_FA;
• d3_np_sl.m, solves a D3 linear system factored by D3_NP_FA;
• d3_print.m, prints a D3 matrix;
• d3_print_some.m, prints some of a D3 matrix;
• d3_random.m, randomizes a D3 matrix;
• d3_to_dge.m, copies a D3 matrix to a DGE matrix;
• d3_vxm.m, multiplies a vector times a D3 matrix;
• d3p_det.m, computes the determinant of a D3P matrix factored by D3P_FA;
• d3p_fa.m, factors a D3P matrix;
• d3p_indicator.m, returns a D3P indicator matrix;
• d3p_ml.m, computes A*x or A'*x after A has been factored by D3P_FA;
• d3p_mxv.m, multiplies a D3P matrix times a vector;
• d3p_print.m, prints a D3P matrix;
• d3p_print_some.m, prints some of a D3P matrix;
• d3p_random.m, randomizes a D3P matrix;
• d3p_sl.m, solves a D3P linear system factored by D3P_FA;
• d3p_to_dge.m, copies a D3P matrix to a DGE matrix;
• d3p_vxm.m, multiplies a vector times a D3P matrix;
• d5_indicator.m, returns a D5 indicator matrix;
• d5_mxv.m, multiplies a D5 matrix times a vector;
• d5_np_fs.m, factors and solves a D5 linear system with no pivoting;
• d5_print.m, prints a D5 matrix;
• d5_print_some.m, prints some of a D5 matrix;
• d5_random.m, randomizes a D5 matrix;
• d5_to_dge.m, copies a D5 matrix to a DGE matrix;
• d5_vxm.m, multiplies a vector times a D5 matrix;
• dbb_add.m, adds a value to an entry in a DBB matrix;
• dbb_fa.m, factors a DBB matrix;
• dbb_get.m, gets the value of an entry in a DBB matrix;
• dbb_indicator.m, returns a DBB indicator matrix;
• dbb_mxv.m, multiplies a DBB matrix times a vector;
• dbb_print.m, prints a DBB matrix;
• dbb_print_some.m, prints some of a DBB matrix;
• dbb_random.m, returns a random DBB matrix;
• dbb_set.m, sets one entry of a DBB matrix;
• dbb_sl.m, solves a linear system that was factored by DBB_FA;
• dbb_to_dge.m, copies a DBB matrix to a DGE matrix;
• dbb_vxm.m, multiplies a vector times a DBB matrix;
• dblt_det.m, returns the determinant of a DBLT matrix;
• dblt_indicator.m, returns a DBLT indicator matrix;
• dblt_mxv.m, multiplies a DBLT matrix times a vector;
• dblt_print.m, prints a DBLT matrix;
• dblt_print_some.m, prints some of a DBLT matrix;
• dblt_random.m, randomizes a DBLT matrix;
• dblt_sl.m, solves a DBLT linear system;
• dblt_to_dge.m, copies a DBLT matrix to a DGE matrix;
• dblt_vxm.m, multiplies a vector times a DBLT matrix;
• dbto_indicator.m, returns a DBTO indicator matrix;
• dbto_mxv.m, multiplies a DBTO matrix times a vector;
• dbto_print.m, prints a DBTO matrix;
• dbto_print_some.m, prints some of a DBTO matrix;
• dbto_random.m, randomizes a DBTO matrix;
• (dbto_sl.m), solves a DBTO linear system (this routine is NOT available in a MATLAB version);
• dbto_vxm.m, multiplies a vector times a DBTO matrix;
• dbut_det.m, returns the determinant of a DBUT matrix;
• dbut_indicator.m, returns a DBUT indicator matrix;
• dbut_mxv.m, multiplies a DBUT matrix times a vector;
• dbut_print.m, prints a DBUT matrix;
• dbut_print_some.m, prints some of a DBUT matrix;
• dbut_random.m, randomizes a DBUT matrix;
• dbut_sl.m, solves a DBUT linear system;
• dbut_to_dge.m, copies a DBUT matrix to a DGE matrix;
• dbut_vxm.m, multiplies a vector times a DBUT matrix;
• dcb_det.m, returns the determinant of a DCB matrix;
• dcb_indicator.m, returns a DCB indicator matrix;
• dcb_ml.m, computes A*x or A'*x after A has been factored by DCB_NP_FA;
• dcb_mxv.m, multiplies a DCB matrix times a vector;
• dcb_np_fa.m, factors a DCB linear system with no pivoting;
• dcb_np_sl.m, solves a DCB linear system;
• dcb_print.m, prints a DCB matrix;
• dcb_print_some.m, prints some of a DCB matrix;
• dcb_random.m, randomizes a DCB matrix;
• dcb_to_dge.m, copies a DCB matrix to a DGE matrix;
• dcb_vxm.m, multiplies a vector times a DCB matrix;
• dcbb_to_dge.m, copies a DCBB matrix to a DGE matrix;
• dcbb_add.m, adds a value to an entry of a DCBB matrix;
• dcbb_fa.m, factors a DCBB matrix;
• dcbb_get.m, gets one entry of a DCBB matrix;
• dcbb_indicator.m, returns a DCBB indicator matrix;
• dcbb_mxv.m, multiplies a vector times a DCBB matrix;
• dcbb_print.m, print a DCBB matrix;
• dcbb_print_some.m, prints some of a DCBB matrix;
• dcbb_random.m, returns a random DCBB matrix;
• dcbb_set.m, sets one entry of a DCBB matrix;
• dcbb_sl.m, solves a linear system factored by DCBB_FA;
• dcbb_vxm.m, multiplies a vector times a DCBB matrix;
• dcc_get.m, gets an entry from a DCC matrix.
• dcc_ijk.m, gets the sparse index from the full indices in a DCC matrix.
• dcc_inc.m, increments an entry from a DCC matrix.
• dcc_indicator.m, returns a DCC indicator matrix;
• dcc_kij.m, gets the full indices from the sparse index in a DCC matrix.
• dcc_mxv.m, multiplies a DCC matrix times a vector;
• dcc_print.m, prints a DCC matrix;
• dcc_print_some.m, prints some of a DCC matrix;
• dcc_random.m, randomizes a DCC matrix;
• dcc_read.m, reads a DCC matrix from three files;
• dcc_read_size.m, reads the sizes associated with a DCC matrix stored in three files;
• dcc_set.m, sets an entry in a DCC matrix.
• dcc_to_dge.m, solves a DCC linear system;
• dcc_vxm.m, multiplies a vector times a DCC matrix;
• dcc_write.m, writes a DCC matrix to three files;
• dci_eval.m, returns the eigenvalues of a DCI matrix;
• dci_indicator.m, returns a DCI indicator matrix;
• dci_mxv.m, multiplies a DCI matrix times a vector;
• dci_print.m, prints a DCI matrix;
• dci_print_some.m, prints some of a DCI matrix;
• dci_random.m, randomizes a DCI matrix;
• dci_sl.m, solves a DCI linear system;
• dci_to_dge.m, copies a DCI matrix to a DGE matrix;
• dci_vxm.m, multiplies a vector times a DCI matrix;
• dgb_det.m, computes the determinant of a DGB matrix factored by DGB_FA or DGB_TRF;
• dgb_fa.m, performs a LINPACK style PLU factorization of a DGB matrix;
• dgb_indicator.m, returns a DGB indicator matrix;
• dgb_ml.m, computes A*x or A'*x after A has been factored by DGB_FA;
• dgb_mu.m, computes A*x or A'*x after A has been factored by DGB_TRF;
• dgb_mxv.m, multiplies a DGB matrix times a vector;
• dgb_nz_num.m, counts the nonzeroes in a DGB matrix;
• dgb_print.m, prints a DGB matrix.;
• dgb_print_some.m, prints some of a DGB matrix;
• dgb_random.m, randomizes a DGB matrix;
• dgb_sl.m, solves a system factored by DGB_FA;
• dgb_to_ds3.m, copies a DGB matrix to a DS3 matrix;
• dgb_to_dsp.m, copies a DGB matrix to a DSP matrix;
• dgb_to_r8vec.m, copies a DGB matrix to a R8VEC;
• dgb_to_dge.m, copies a DGB matrix to a DGE matrix;
• dgb_trf.m, performs a LAPACK style PLU factorization of a DGB matrix;
• dgb_trs.m, solves a linear system factored by DGB_TRS;
• dgb_vxm.m, multiplies a vector times a DGB matrix;
• dgd_indicator.m, returns a DGD indicator matrix;
• dgd_mxv.m, multiplies a DGD matrix times a vector;
• dgd_print.m, prints a DGD matrix;
• dgd_print_some.m, prints some of a DGD matrix;
• dgd_random.m, randomizes a DGD matrix;
• dgd_to_dge.m, copies a DGD matrix to a DGE matrix;
• dgd_vxm.m, multiplies a vector times a DGD matrix;
• dge_co.m, factors a DGE matrix and estimates its condition number;
• dge_det.m, computes the determinant of a factored DGE matrix;
• dge_dilu.m, produces the diagonal incomplete LU factor of a DGE matrix;
• dge_fa.m, factors a DGE matrix;
• dge_fs.m, factors and solves a DGE system;
• dge_identity.m, copies the identity matrix to a DGE matrix;
• dge_ilu.m, produces the incomplete LU factors of a DGE matrix;
• dge_indicator.m, returns a DGE indicator matrix;
• dge_inverse.m, returns the inverse of a DGE matrix;
• dge_ml.m, multiplies a DGE matrix factored by DGE_FA times a vector;
• dge_mu.m, multiplies a DGE matrix factored by DGE_TRF times a vector;
• dge_mxm.m, multiplies two DGE matrices;
• dge_mxv.m, multiplies a DGE matrix times a vector;
• dge_np_det.m, returns the determinant of a system factored by DGE_NP_FA;
• dge_np_fa.m, factors a DGE matrix by nonpivoting Gaussian elimination;
• dge_np_inverse.m, returns the inverse of a matrix factored by DGE_NP_FA;
• dge_np_ml.m, multiplies a matrix factored by DGE_NP_FA times a vector;
• dge_np_sl.m, solves a linear system factored by DGE_NP_FA;
• dge_np_trf.m, computes the LU factorization of a DGE matrix;
• dge_np_trm.m, multiplies a matrix factored by DGE_NP_TRF times a vector;
• dge_np_trs.m, solves a linear system factored by DGE_NP_TRF;
• dge_plu.m, produces the PLU factors of a DGE matrix;
• dge_poly.m, computes the characteristic polynomial of a DGE matrix;
• dge_print.m, prints a DGE matrix;
• dge_print_some.m, prints some of a DGE matrix;
• dge_random.m, returns a random DGE matrix;
• dge_res.m, computes the residual of a DGE linear system;
• dge_sl.m, solves a linear system factored by DGE_FA;
• dge_sl_it.m, applies one step of iterative refinement to a factored linear system;
• dge_to_dgb.m, converts a DGE matrix to a DGB matrix;
• dge_to_r8vec.m, converts a DGE matrix to a R8VEC;
• dge_trf.m, factors a DGE matrix;
• dge_trs.m, solves a system factored by DGE_TRF;
• dge_vxm.m, multiplies a vector times a DGE matrix;
• dlt_det.m, computes the determinant of a DLT matrix;
• dlt_indicator.m, returns a DLT indicator matrix;
• dlt_inverse.m, returns the inverse of a DLT indicator matrix;
• dlt_mxm.m, multiplies two DLT matrices;
• dlt_mxv.m, multiplies a DLT matrix times a vector;
• dlt_print.m, prints a DLT matrix;
• dlt_print_some.m, prints some of a DLT matrix;
• dlt_random.m, randomizes a DLT matrix;
• dlt_sl.m, solves a DLT linear system;
• dlt_vxm.m, multiplies a vector times a DLT matrix;
• dncf_indicator.m, returns a DNCF indicator matrix;
• dncf_print.m, prints a DNCF matrix.
• dncf_print_some.m, prints some of a DNCF matrix.
• dpbl_det.m, computes the determinant of a DPO matrix factored by DPBL_FA;
• dpbl_indicator.m, returns a DPBL indicator matrix;
• dpbl_print.m, prints a DPBL matrix;
• dpbl_print_some.m, prints some of a DPBL matrix;
• dpbl_random.m, randomizes a DPBL matrix;
• dpbl_to_dge.m, copies a DPBL matrix to a DGE matrix;
• dpbu_cg.m, uses the conjugate gradient method on a linear system with a DPBU matrix;
• dpbu_det.m, computes the determinant of a DPO matrix factored by DPBU_FA;
• dpbu_fa.m, factors a DPBU matrix;
• dpbu_indicator.m, returns a DPBU indicator matrix;
• dpbu_ml.m, computes A*x or A'*x after A has been factored by DPBU_FA;
• dpbu_mxv.m, multiplies a DPBU matrix times a vector;
• dpbu_print.m, prints a DPBU matrix;
• dpbu_print_some.m, prints some of a DPBU matrix;
• dpbu_random.m, randomizes a DPBU matrix;
• dpbu_sl.m, solves a DPBU linear system factored by D3P_FA;
• dpbu_sor.m, applies the SOR iterative method to solve a linear system with a DPBU matrix;
• dpbu_to_dge.m, copies a DPBU matrix to a DGE matrix;
• dpo_det.m, computes the determinant of a DPO matrix factored by DPO_FA;
• dpo_fa.m, factors a DPO matrix;
• dpo_indicator.m, returns a DPO indicator matrix;
• dpo_inverse.m, returns the inverse of a DPO matrix;
• dpo_ml.m, computes A*x or A'*x after A has been factored by DPO_FA;
• dpo_mxm.m, multiplies two DPO matrices;
• dpo_mxv.m, multiplies a DPO matrix times a vector;
• dpo_print.m, prints a DPO matrix;
• dpo_print_some.m, prints some of a DPO matrix;
• dpo_random.m, randomizes a DPO matrix;
• dpo_sl.m, solves a DPO linear system factored by D3P_FA;
• dpo_to_dge.m, copies a DPO matrix to a DGE matrix;
• dpp_det.m, returns the determinant of a DPP matrix;
• dpp_fa.m, computes the Cholesky factor of a DPP matrix;
• dpp_indicator.m, returns a DPP indicator matrix;
• dpp_mxv.m, multiplies a DPP matrix times a vector;
• dpp_print.m, prints a DPP matrix;
• dpp_print_some.m, prints some of a DPP matrix;
• dpp_random.m, randomizes a DPP matrix;
• dpp_sl.m, solves a DPP linear system;
• dpp_to_dge.m, copies a DPP matrix to a DGE matrix;
• ds3_indicator.m, returns a DS3 indicator matrix;
• ds3_print.m, prints a DS3 matrix;
• ds3_print_some.m, prints some of a DS3 matrix;
• ds3_read.m, reads a DS3 matrix from a file;
• ds3_read_size.m, reads the size of a DS3 matrix from a file;
• ds3_write.m, writes a DS3 matrix to a file;
• dsd_cg.m, uses the conjugate gradient method on a DSD linear system;
• dsd_indicator.m, returns a DSD indicator matrix;
• dsd_mxv.m, multiplies a DSD matrix times a vector;
• dsd_print.m, prints a DSD matrix;
• dsd_print_some.m, prints some of a DSD matrix;
• dsd_random.m, randomizes a DSD matrix;
• dsd_to_dge.m, copies a DSD matrix to a DGE matrix;
• dsm_ml.m, multiplies a DSM matrix that has been factored by DGE_FA times a vector;
• dsm_mxv.m, multiplies a DSM matrix times a vector;
• dsm_print.m, prints a DSM matrix;
• dsm_print_some.m, prints some of a DSM matrix;
• dsm_random.m, randomizes a DSM matrix;
• dsm_sl.m, solves a DSM linear system;
• dsm_to_dge.m, copies a DSM matrix to a DGE matrix;
• dsm_vxm.m, multiplies a vector times a DSM matrix;
• dsp_check.m, checks that a DSP matrix data structure is properly sorted.
• dsp_ij_to_k.m, seeks the compressed index of the (I,J) entry of A.
• dsp_indicator.m, sets up a DSP indicator matrix;
• dsp_mxv.m, multiplies a DSP matrix times a vector;
• dsp_print.m, prints a DSP matrix;
• dsp_print_some.m, prints some of a DSP matrix;
• dsp_random.m, randomizes a DSP matrix;
• dsp_read.m, reads a DSP matrix from a file;
• dsp_read_size.m, reads the size of a DSP matrix from a file;
• dsp_to_dge.m, copies a DSP matrix to a DGE matrix;
• dsp_to_dncf.m, copies a DSP matrix to a DNCF matrix;
• dsp_vxm.m, multiplies a vector times a DSP matrix;
• dsp_write.m, writes a DSP matrix to a file;
• dsr_indicator.m, returns a DSR indicator matrix;
• dsr_mxv.m, multiplies a DSR matrix times a vector;
• dsr_print.m, prints a DSR matrix;
• dsr_print_some.m, prints some of a DSR matrix;
• dsr_random.m, randomizes a DSR matrix;
• dsr_to_dge.m, copies a DSR matrix to a DGE matrix;
• dsr_vxm.m, multiplies a vector times a DSR matrix;
• dss_indicator.m, sets up a DSS indicator matrix;
• dss_mxv.m, multiplies a DSS matrix times a vector;
• dss_print.m, prints a DSS matrix;
• dss_print_some.m, prints some of a DSS matrix;
• dss_random.m, randomizes a DSS matrix;
• dss_to_dge.m, copies a DSS matrix to a DGE matrix;
• dsto_indicator.m, returns a DSTO indicator matrix;
• dsto_inverse.m, returns the inverse of a DSTO indicator matrix;
• dsto_mxv.m, multiplies a DSTO matrix times a vector;
• dsto_print.m, prints a DSTO matrix;
• dsto_print_some.m, prints some of a DSTO matrix;
• dsto_random.m, randomizes a DSTO matrix;
• dsto_sl.m, solves a DSTO linear system;
• dsto_to_dge.m, copies a DSTO matrix to a DGE matrix;
• dsto_yw_sl.m, solves the Yule-Walker equations for a DUT matrix;
• dto_indicator.m, returns a DTO indicator matrix;
• dto_mxv.m, multiplies a DTO matrix times a vector;
• dto_print.m, prints a DTO matrix;
• dto_print_some.m, prints some of a DTO matrix;
• dto_random.m, randomizes a DTO matrix;
• dto_sl.m, solves a DTO linear system;
• dto_to_dge.m, copies a DTO matrix to a DGE matrix;
• dto_vxm.m, multiplies a vector times a DTO matrix;
• dut_det.m, computes the determinant of a DUT matrix;
• dut_indicator.m, returns a DUT indicator matrix;
• dut_inverse.m, returns the inverse of a DUT indicator matrix;
• dut_mxm.m, multiplies two DUT matrices;
• dut_mxv.m, multiplies a DUT matrix times a vector;
• dut_print.m, prints a DUT matrix;
• dut_print_some.m, prints some of a DUT matrix;
• dut_random.m, randomizes a DUT matrix;
• dut_sl.m, solves a DUT linear system;
• dut_vxm.m, multiplies a vector times a DUT matrix;
• dvm_det.m, computes the determinant of a DVM matrix;
• dvm_mxv.m, multiplies a DVM matrix times a vector;
• dvm_print.m, prints a DVM matrix;
• dvm_print_some.m, prints some of a DVM matrix;
• dvm_random.m, randomizes a DVM matrix;
• dvm_sl.m, solves a DVM linear system;
• dvm_to_dge.m, copies a DVM matrix to a DGE matrix;
• dvm_vxm.m, multiplies a vector times a DVM matrix;
• file_delete.m, deletes a file;
• file_exist.m, is TRUE if a given file exists;
• hilbert_inverse.m, returns the inverse of the Hilbert matrix;
• i4_log_10.m, returns the integer part of the logarithm base 10 of abs(X);
• i4_uniform.m, returns a random integer in a given range;
• i4vec_print.m, prints an I4VEC;
• i4vec_search_binary_a.m, uses binary search on an ascending sorted I4VEC to find the occurrence of a given value;
• r4_uniform_01.m, returns a random real number in [0,1];
• r8_sign.m, returns the sign of a double precision number;
• r8_uniform_01.m, is a uniform random number generator;
• r8vec_indicator.m, sets a R8VEC to the indicator vector;
• r8vec_print.m, prints a R8VEC;
• r8vec_print_some.m, prints some of a R8VEC;
• r8vec_read.m, reads a R8VEC from a file;
• r8vec_read_size.m, reads the size of a R8VEC in a file;
• r8vec_to_dcb.m, converts a R8VEC to a DCB matrix;
• r8vec_to_dgb.m, converts a R8VEC to a DGB matrix;
• r8vec_to_dge.m, converts a R8VEC to a DGE matrix;
• r8vec_uniform_01.m, returns a random R8VEC;
• r8vec_write.m, writes a R8VEC to a file;
• r8vec2_print_some.m, prints some of a pair R8VEC's;
• s_len_trim.m, returns the length of a character string to the last nonblank;
• saxpy.m, adds a multiple of one real vector to another;
• sort_heap_external.m, external sorts a list of items into ascending order;
• timestamp.m, prints the current YMDHMS date as a timestamp;

Examples and Tests:

• linplus_test.m, runs all the tests;
• linplus_test.out, the output from all the tests;
• linplus_test0192.m, tests DCC_WRITE;
• linplus_test0193.m, tests DCC_READ_SIZE and DCC_READ;
• linplus_test0194.m, tests R8VEC_TO_DCB and DCB_TO_R8VEC;
• linplus_test0195.m, tests R8VEC_TO_DGB and DGB_TO_R8VEC;
• linplus_test0196.m, tests R8VEC_TO_DGE and DGE_TO_R8VEC;
• linplus_test02.m, tests D3_CR_FA and D3_CR_SL;
• linplus_test03.m, tests D3_CR_FA and D3_CR_SL;
• linplus_test035.m, tests D3_GS_SL;
• linplus_test037.m, tests D3_INDICATOR;
• linplus_test04.m, tests D3_JAC_SL;
• linplus_test05.m, tests D3_NP_DET and D3_NP_FA;
• linplus_test06.m, tests D3_NP_FA and D3_NP_SL;
• linplus_test07.m, tests D3_NP_FS;
• linplus_test08.m, tests D3_NP_ML;
• linplus_test09.m, tests D3P_DET;
• linplus_test10.m, tests D3P_FA and D3P_SL;
• linplus_test105.m, tests D3P_INDICATOR;
• linplus_test11.m, tests D3P_ML;
• linplus_test115.m, tests D5_INDICATOR;
• linplus_test12.m, tests D5_NP_FS;
• linplus_test13.m, tests DBB_FA, DBB_PRINT, DBB_RANDOM, DBB_SL;
• linplus_test14.m, tests DBB_FA and DBB_SL;
• linplus_test15.m, tests DBB_FA and DBB_SL;
• linplus_test151.m, tests DBB_INDICATOR;
• linplus_test152.m, tests DBLT_INDICATOR;
• linplus_test153.m, tests DBLT_MAX, DBLT_RANDOM, DBLT_SL, DBLT_VXM;
• linplus_test154.m, tests DBTO_INDICATOR;
• linplus_test155.m, tests DBTO_MXV and DBTO_VXM;
• linplus_test156.m, tests DBTO_SL;
• linplus_test1565.m, tests DBUT_INDICATOR;
• linplus_test1566.m, tests DBUT_DET, DBUT_MXV, DBUT_RANDOM, DBUT_SL, and DBUT_VXM;
• linplus_test157.m, tests DCB_INDICATOR;
• linplus_test16.m, tests DCB_NP_FA and DCB_DET;
• linplus_test17.m, tests DCB_NP_FA and DCB_NP_SL;
• linplus_test18.m, tests DCB_ML;
• linplus_test19.m, tests DCBB_FA, DCBB_RANDOM, DCBB_SL;
• linplus_test193.m, tests DCBB_INDICATOR;
• linplus_test195.m, tests DCI_EVAL;
• linplus_test197.m, tests DCI_IND;
• linplus_test20.m, tests DCI_SL;
• linplus_test21.m, tests DGB_DET;
• linplus_test22.m, tests DGB_FA and DGB_SL;
• linplus_test23.m, tests DGB_FA and DGB_TRF;
• linplus_test235.m, tests DGB_INDICATOR;
• linplus_test24.m, tests DGB_ML;
• linplus_test25.m, tests DGB_PRINT;
• linplus_test26.m, tests DGB_NZ_NUM;
• linplus_test265.m, tests DGB_TO_DGE and DGE_TO_DGB;
• linplus_test2655.m, tests DGB_TO_DS3;
• linplus_test27.m, tests DGB_TRF and DGB_TRS;
• linplus_test275.m, tests DGB_INDICATOR;
• linplus_test28.m, tests DGB_MXV, DGB_RANDOM, DGB_VXM;
• linplus_test285.m, tests DGE_CO;
• linplus_test29.m, tests DGE_DET;
• linplus_test295.m, tests DGE_DILU;
• linplus_test30.m, tests DGE_FA and DGE_SL;
• linplus_test31.m, tests DGE_FA and DGE_SL;
• linplus_test315.m, tests DGE_ILU;
• linplus_test317.m, tests DGE_INDICATOR;
• linplus_test32.m, tests DGE_NP_FA and DGE_NP_SL;
• linplus_test33.m, tests DGE_NP_FA and DGE_NP_INVERSE;
• linplus_test34.m, tests DGE_FS;
• linplus_test35.m, tests DGE_INVERSE;
• linplus_test36.m, tests DGE_ML;
• linplus_test37.m, tests DGE_NP_ML;
• linplus_test38.m, tests DGE_MU;
• linplus_test385.m, tests DGE_PLU;
• linplus_test39.m, tests DGE_POLY;
• linplus_test40.m, tests DGE_SL_IT;
• linplus_test41.m, tests DGE_TRF and DGE_TRS;
• linplus_test42.m, tests DGE_NP_TRF, DGE_NP_TRM, and DGE_NP_TRS;
• linplus_test422.m, tests DCC_GET, DCC_IJK, DCC_INC, DCC_KIJ, DCC_SET;
• linplus_test423.m, tests DCC_INDICATOR;
• linplus_test425.m, tests DCC_MXV and DCC_VXM;
• linplus_test426.m, tests DCC_PRINT;
• linplus_test428.m, tests DLT_INDICATOR;
• linplus_test43.m, tests DLT_MXV, DLT_SL, DLT_VXM;
• linplus_test44.m, tests DLT_DET, DLT_INV, DLT_MXM, DLT_RANDOM;
• linplus_test443.m, tests DNCF_INDICATOR;
• linplus_test445.m, tests DPBL_INDICATOR;
• linplus_test45.m, tests DPBU_CG;
• linplus_test46.m, tests DPBU_DET;
• linplus_test47.m, tests DPBU_FA, DPBU_RANDOM and DPBU_SL;
• linplus_test48.m, tests DPBU_ML;
• linplus_test485.m, tests DPBU_INDICATOR;
• linplus_test49.m, tests DPBU_SOR;
• linplus_test50.m, tests DPO_FA and DPO_SL;
• linplus_test505.m, tests DPO_FA;
• linplus_test51.m, tests DPO_DET and DPO_INVERSE;
• linplus_test515.m, tests DPO_FA, DPO_SL, DPO_ML, and DPO_MXV;
• linplus_test517.m, tests DPO_INDICATOR;
• linplus_test52.m, tests DPO_RANDOM and DPO_TO_DGE;
• linplus_test525.m, tests DPP_FA and DPP_SL;
• linplus_test527.m, tests DPP_INDICATOR;
• linplus_test53.m, tests DPP_RANDOM;
• linplus_test534.m, tests DS3_WRITE;
• linplus_test535.m, tests DS3_READ_SIZE and DS3_READ;
• linplus_test54.m, tests DSD_CG;
• linplus_test55.m, tests DSD_CG;
• linplus_test555.m, tests DSD_INDICATOR;
• linplus_test56.m, tests DSM_ML;
• linplus_test57.m, tests DSM_ML;
• linplus_test5705.m, tests DSP_IJ_TO_K;
• linplus_test571.m, tests DSM_INDICATOR;
• linplus_test572.m, tests DSP_MXV and DSP_VXM;
• linplus_test5722.m, tests DSP_PRINT;
• linplus_test5724.m, tests DSP_WRITE;
• linplus_test5725.m, tests DSP_READ_SIZE and DSP_READ;
• linplus_test573.m, tests DSR_INDICATOR;
• linplus_test574.m, tests DSR_MXV and DSR_VXM;
• linplus_test5745.m, tests DSR_PRINT;
• linplus_test575.m, tests DSR_RANDOM;
• linplus_test577.m, tests DSS_INDICATOR;
• linplus_test58.m, tests DSS_MXV and DSS_PRINT;
• linplus_test581.m, tests DSTO_INDICATOR;
• linplus_test583.m, tests DSTO_INVERSE;
• linplus_test585.m, tests DSTO_MXV and DSTO_YW_SL;
• linplus_test587.m, tests DSTO_SL;
• linplus_test589.m, tests DSTO_INDICATOR;
• linplus_test59.m, tests DSTO_SL;
• linplus_test60.m, tests DUT_DET, DUT_INVERSE, DUT_MXM and DUT_RANDOM;
• linplus_test605.m, tests DUT_INDICATOR;
• linplus_test61.m, tests DUT_MXV, DUT_SL and DUT_VXM;
• linplus_test62.m, tests DVM_DET;
• linplus_test63.m, tests DVM_SL;

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