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<html>
<head>
<title>
LINPLUS - Linear Algebra Utilities
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LINPLUS <br> Linear Algebra Utilities
</h1>
<hr>
<p>
<b>LINPLUS</b>
is a MATLAB library which
carries out operations such as matrix-vector products,
matrix factorization, linear solvers including Gauss-elimination,
Jacobi iteration, Gauss-Seidel iteration, Conjugate Gradient (CG),
for matrices in a
variety of formats, including banded, border-banded, circulant, lower
triangular, pentadiagonal, sparse, symmetric, toeplitz, tridiagonal,
upper triangular and vandermonde formats.
</p>
<p>
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:
<ul>
<li>
<b>C83</b> - Double complex tridiagonal;
</li>
<li>
<b>C8CI</b> - Double complex circulant;
</li>
<li>
<b>C8GE</b> - Double complex general;
</li>
<li>
<b>C8TO</b> - Double complex Toeplitz;
</li>
<li>
<b>R83</b> - Real double precision tridiagonal;
</li>
<li>
<b>R83P</b> - Real double precision tridiagonal periodic;
</li>
<li>
<b>R83S</b> - Real double precision tridiagonal scalar;
</li>
<li>
<b>R85</b> - Real double precision pentadiagonal;
</li>
<li>
<b>R8BB</b> - Real double precision border-banded;
</li>
<li>
<b>R8BLT</b> - Real double precision banded lower triangular matrix;
</li>
<li>
<b>R8BTO</b> - Real double precision block Toeplitz;
</li>
<li>
<b>R8BUT</b> - Real double precision banded upper triangular matrix;
</li>
<li>
<b>R8CB</b> - Real double precision compact band;
</li>
<li>
<b>R8CBB</b> - Real double precision compact border-banded;
</li>
<li>
<b>R8CC</b> - Real double precision compressed column sparse
= Harwell Boeing Real Unsymmetric Assembled (RUA) format
= MATLAB sparse format;
</li>
<li>
<b>R8CI</b> - Real double precision circulant;
</li>
<li>
<b>R8GB</b> - Real double precision general band,
used by LINPACK and LAPACK;
</li>
<li>
<b>R8GD</b> - Real double precision general diagonal;
</li>
<li>
<b>R8GE</b> - Real double precision general, used by LINPACK and LAPACK;
</li>
<li>
<b>R8LT</b> - Real double precision lower triangular;
</li>
<li>
<b>R8NCF</b> - Real double precision Nonsymmetric Coordinate Format
(one of the formats used by NSPCG);
</li>
<li>
<b>R8PBL</b> - Real double precision positive-definite symmetric band
matrix, store diagonal and lower triangle;
</li>
<li>
<b>R8PBU</b> - Real double precision positive-definite symmetric band
matrix, store diagonal and upper triangle;
</li>
<li>
<b>R8PO</b> - Real double precision positive-definite symmetric,
used by LINPACK and LAPACK;
</li>
<li>
<b>R8PP</b> - Real double precision positive-definite symmetric Packed,
used by LINPACK and LAPACK;
</li>
<li>
<b>R8RI</b> - Real double precision Row-Indexed matrix,
used by Numerical Recipes;
</li>
<li>
<b>R8S3</b> - Real double precision sparse matrix stored by row,
column, value (used by SLAP/DLAP, symmetric or nonsymmetric);
</li>
<li>
<b>R8SD</b> - Real double precision symmetric diagonal;
</li>
<li>
<b>R8SM</b> - Real double precision Sherman Morrison system A - u * v';
</li>
<li>
<b>R8SP</b> - Real 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));
</li>
<li>
<b>R8SR</b> - Real double precision sparse matrix stored by rows;
</li>
<li>
<b>R8SS</b> - Real double precision symmetric skyline;
</li>
<li>
<b>R8STO</b> - Real double precision symmetric Toeplitz;
</li>
<li>
<b>R8TO</b> - Real double precision Toeplitz;
</li>
<li>
<b>R8UT</b> - Real double precision upper triangular;
</li>
<li>
<b>R8UTP</b> - Real double precision upper triangular, packed
(only nonzeros are stored);
</li>
<li>
<b>R8VM</b> - Real double precision Vandermonde;
</li>
<li>
<b>R8VEC</b> - Real double precision vector, which in some cases
is used to store a matrix;
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>LINPLUS</b> is available in
<a href = "../../c_src/linplus/linplus.html">a C version </a> and
<a href = "../../cpp_src/linplus/linplus.html">a C++ version </a> and
<a href = "../../f77_src/linplus/linplus.html">a FORTRAN77 version </a> and
<a href = "../../f_src/linplus/linplus.html">a FORTRAN90 version </a> and
<a href = "../../m_src/linplus/linplus.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../data/cc/cc.html">
CC</a>,
a data directory which
contains examples of the Compressed Column (CC)
sparse matrix file format;
</p>
<p>
<a href = "../../m_src/cg/cg.html">
CG</a>,
a MATLAB library which
implements a simple version of the conjugate gradient (CG) method
for solving a system of linear equations of the form A*x=b,
suitable for situations in which the matrix A is positive definite
(only real, positive eigenvalues) and symmetric.
</p>
<p>
<a href = "../../m_src/cg_rc/cg_rc.html">
CG_RC</a>,
a MATLAB library which
implements the conjugate gradient method for solving
a positive definite sparse linear system A*x=b, using reverse communication.
</p>
<p>
<a href = "../../data/cr/cr.html">
CR</a>,
a data directory which
contains examples of the Compressed Row (CR)
sparse matrix file format;
</p>
<p>
<a href = "../../m_src/linpack_d/linpack_d.html">
LINPACK_D</a>,
a MATLAB library which
is a linear algebra package to solve linear systems for a variety of
matrix storage formats.
</p>
<p>
<a href = "../../m_src/mgmres/mgmres.html">
MGMRES</a>,
a MATLAB library which
applies the restarted GMRES algorithm
to solve a sparse linear system.
</p>
<p>
<a href = "../../f_src/sparsekit/sparsekit.html">
SPARSEKIT</a>,
a FORTRAN90 library which
carries out operations on sparse matrices, including conversion between
various formats.
</p>
<p>
<a href = "../../c_src/superlu/superlu.html">
SUPERLU</a>,
a C library which
implements some very fast solvers
for systems of sparse linear equations.
</p>
<p>
<a href = "../../m_src/templates/templates.html">
TEMPLATES</a>,
a MATLAB library which
implements various iterative methods for solving a linear system.
</p>
<p>
<a href = "../../m_src/test_mat/test_mat.html">
TEST_MAT</a>,
a MATLAB library which
defines test matrices, some of
which have known determinants, eigenvalues and eigenvectors,
inverses and so on.
</p>
<p>
<a href = "../../m_src/toeplitz_cholesky/toeplitz_cholesky.html">
TOEPLITZ_CHOLESKY</a>,
a MATLAB library which
computes the Cholesky factorization of a nonnegative definite symmetric
Toeplitz matrix.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford,
James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum,
Sven Hammarling, Alan McKenney, Danny Sorensen,<br>
LAPACK User's Guide,<br>
Third Edition,<br>
SIAM, 1999,<br>
ISBN: 0898714478,<br>
LC: QA76.73.F25L36.
</li>
<li>
Frank Beckman,<br>
The Solution of Linear Equations by the Conjugate Gradient Method,<br>
in Mathematical Methods for Digital Computers,<br>
edited by John Ralston, Herbert Wilf,<br>
Wiley, 1967,<br>
ISBN: 0471706892.
</li>
<li>
Paul Bratley, Bennett Fox, Linus Schrage,<br>
A Guide to Simulation,<br>
Second Edition,<br>
Springer, 1987,<br>
ISBN: 0387964673.
</li>
<li>
Ward Cheney, David Kincaid,<br>
Numerical Mathematics and Computing,<br>
Brooks-Cole Publishing, 2004,<br>
ISBN: 0534201121.
</li>
<li>
Philip Davis,<br>
Circulant Matrices,<br>
Second Edition,<br>
Chelsea, 1994,<br>
ISBN: 0828403384,<br>
LC: QA188.D37.
</li>
<li>
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
LINPACK User's Guide,<br>
SIAM, 1979,<br>
ISBN13: 978-0-898711-72-1,<br>
LC: QA214.L56.
</li>
<li>
Iain Duff, Roger Grimes, John Lewis,<br>
User's Guide for the Harwell-Boeing Sparse Matrix Collection,<br>
October 1992.
</li>
<li>
Bennett Fox,<br>
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,<br>
ACM Transactions on Mathematical Software,<br>
Volume 12, Number 4, December 1986, pages 362-376.
</li>
<li>
Gene Golub, Charles VanLoan,<br>
Matrix Computations,
Third Edition,<br>
Johns Hopkins, 1996,<br>
ISBN: 0-8018-4513-X,<br>
LC: QA188.G65.
</li>
<li>
Roger Hockney,<br>
A fast direct solution of Poisson's equation using Fourier Analysis,<br>
Journal of the ACM,<br>
Volume 12, Number 1, pages 95-113, January 1965.
</li>
<li>
David Kahaner, Cleve Moler, Steven Nash,<br>
Numerical Methods and Software,<br>
Prentice Hall, 1989,<br>
ISBN: 0-13-627258-4,<br>
LC: TA345.K34.
</li>
<li>
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,<br>
Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage,<br>
ACM Transactions on Mathematical Software,<br>
Volume 5, Number 3, September 1979, pages 308-323.
</li>
<li>
Albert Nijenhuis, Herbert Wilf,<br>
Combinatorial Algorithms for Computers and Calculators,<br>
Second Edition,<br>
Academic Press, 1978,<br>
ISBN: 0-12-519260-6,<br>
LC: QA164.N54.
</li>
<li>
William Press, Brian Flannery, Saul Teukolsky, William Vetterling,<br>
Numerical Recipes in FORTRAN: The Art of Scientific Computing,<br>
Third Edition,<br>
Cambridge University Press, 2007,<br>
ISBN13: 978-0-521-88068-8,<br>
LC: QA297.N866.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "c8_le_l2.m">c8_le_l2.m</a>,
( X <= Y ) for C8 values and the L2 norm;
</li>
<li>
<a href = "c8_swap.m">c8_swap.m</a>,
swaps two C8 values;
</li>
<li>
<a href = "c83_cr_fa.m">c83_cr_fa.m</a>,
factors a C83 system using cyclic reduction;
</li>
<li>
<a href = "c83_cr_sl.m">c83_cr_sl.m</a>,
solves a C83 system factored by c83_cr_fa;
</li>
<li>
<a href = "c83_cr_sls.m">c83_cr_sls.m</a>,
solves multiple C83 systems factored by c83_cr_fa;
</li>
<li>
<a href = "c83_indicator.m">c83_indicator.m</a>,
sets up a C83 indicator matrix.
</li>
<li>
<a href = "c83_mxv.m">c83_mxv.m</a>,
multiplies a C83 matrix times a vector;
</li>
<li>
<a href = "c8mat_print.m">c8mat_print.m</a>,
prints a C8MAT.
</li>
<li>
<a href = "c8mat_print_some.m">c8mat_print_some.m</a>,
prints some of a C8MAT.
</li>
<li>
<a href = "c8vec_indicator.m">c8vec_indicator.m</a>,
sets a C8VEC to the indicator vector.
</li>
<li>
<a href = "c8vec_print.m">c8vec_print.m</a>,
prints a C8 vector.
</li>
<li>
<a href = "c8vec_print_some.m">c8vec_print_some.m</a>,
prints some of a C8VEC.
</li>
<li>
<a href = "c8vec_sort_a2.m">c8vec_sort_a2.m</a>,
sorts a C8 vector by L2 norm;
</li>
<li>
<a href = "c8vec_unity.m">c8vec_unity.m</a>,
returns the N roots of unity;
</li>
<li>
<a href = "r83_cr_fa.m">r83_cr_fa.m</a>,
factors an R83 system using cyclic reduction;
</li>
<li>
<a href = "r83_cr_sl.m">r83_cr_sl.m</a>,
solves an R83 system factored by r83_cr_fa;
</li>
<li>
<a href = "r83_cr_sls.m">r83_cr_sls.m</a>,
solves several R83 systems factored by r83_cr_fa;
</li>
<li>
<a href = "r83_gs_sl.m">r83_jac_sl.m</a>,
solves an R83 system using Gauss-Seidel iteration;
</li>
<li>
<a href = "r83_indicator.m">r83_indicator.m</a>,
sets up an R83 indicator matrix;
</li>
<li>
<a href = "r83_jac_sl.m">r83_jac_sl.m</a>,
solves an R83 system using Jacobi iteration;
</li>
<li>
<a href = "r83_mxv.m">r83_mxv.m</a>,
multiplies an R83 matrix times a vector;
</li>
<li>
<a href = "r83_np_det.m">r83_np_det.m</a>,
returns the determinant of a system factored by R83_NP_FA;
</li>
<li>
<a href = "r83_np_fa.m">r83_np_fa.m</a>,
factors an R83 linear system with no pivoting;
</li>
<li>
<a href = "r83_np_fs.m">r83_np_fs.m</a>,
factors and solves an R83 linear system with no pivoting;
</li>
<li>
<a href = "r83_np_ml.m">r83_np_ml.m</a>,
computes A * x or x * A, where A has been factored by R83_NP_FA;
</li>
<li>
<a href = "r83_np_sl.m">r83_np_sl.m</a>,
solves an R83 linear system factored by R83_NP_FA;
</li>
<li>
<a href = "r83_print.m">r83_print.m</a>,
prints an R83 matrix;
</li>
<li>
<a href = "r83_print_some.m">r83_print_some.m</a>,
prints some of an R83 matrix;
</li>
<li>
<a href = "r83_random.m">r83_random.m</a>,
randomizes an R83 matrix;
</li>
<li>
<a href = "r83_to_r8ge.m">r83_to_r8ge.m</a>,
copies an R83 matrix to an R8GE matrix;
</li>
<li>
<a href = "r83_vxm.m">r83_vxm.m</a>,
multiplies a vector times an R83 matrix;
</li>
<li>
<a href = "r83np_fs.m">r83np_fs.m</a>,
factors and solves an R83NP linear system with no pivoting;
</li>
<li>
<a href = "r83p_det.m">r83p_det.m</a>,
computes the determinant of an R83P matrix factored by
R83P_FA;
</li>
<li>
<a href = "r83p_fa.m">r83p_fa.m</a>,
factors an R83P matrix;
</li>
<li>
<a href = "r83p_indicator.m">r83p_indicator.m</a>,
returns an R83P indicator matrix;
</li>
<li>
<a href = "r83p_ml.m">r83p_ml.m</a>,
computes A*x or A'*x after A has been factored by R83P_FA;
</li>
<li>
<a href = "r83p_mxv.m">r83p_mxv.m</a>,
multiplies an R83P matrix times a vector;
</li>
<li>
<a href = "r83p_print.m">r83p_print.m</a>,
prints an R83P matrix;
</li>
<li>
<a href = "r83p_print_some.m">r83p_print_some.m</a>,
prints some of an R83P matrix;
</li>
<li>
<a href = "r83p_random.m">r83p_random.m</a>,
randomizes an R83P matrix;
</li>
<li>
<a href = "r83p_sl.m">r83p_sl.m</a>,
solves an R83P linear system factored by R83P_FA;
</li>
<li>
<a href = "r83p_to_r8ge.m">r83p_to_r8ge.m</a>,
copies an R83P matrix to an R8GE matrix;
</li>
<li>
<a href = "r83p_vxm.m">r83p_vxm.m</a>,
multiplies a vector times an R83P matrix;
</li>
<li>
<a href = "r83s_mxv.m">r83s_mxv.m</a>,
multiplies an R83S matrix times a vector;
</li>
<li>
<a href = "r83s_print.m">r83s_print.m</a>,
prints an R83S matrix;
</li>
<li>
<a href = "r83s_print_some.m">r83s_print_some.m</a>,
prints some of an R83S matrix;
</li>
<li>
<a href = "r83s_random.m">r83s_random.m</a>,
randomizes an R83S matrix;
</li>
<li>
<a href = "r85_indicator.m">r85_indicator.m</a>,
returns an R85 indicator matrix;
</li>
<li>
<a href = "r85_mxv.m">r85_mxv.m</a>,
multiplies an R85 matrix times a vector;
</li>
<li>
<a href = "r85_np_fs.m">r85_np_fs.m</a>,
factors and solves an R85 linear system with no pivoting;
</li>
<li>
<a href = "r85_print.m">r85_print.m</a>,
prints an R85 matrix;
</li>
<li>
<a href = "r85_print_some.m">r85_print_some.m</a>,
prints some of an R85 matrix;
</li>
<li>
<a href = "r85_random.m">r85_random.m</a>,
randomizes an R85 matrix;
</li>
<li>
<a href = "r85_to_r8ge.m">r85_to_r8ge.m</a>,
copies an R85 matrix to an R8GE matrix;
</li>
<li>
<a href = "r85_vxm.m">r85_vxm.m</a>,
multiplies a vector times an R85 matrix;
</li>
<li>
<a href = "daxpy.m">daxpy.m</a>,
adds a multiple of one real vector to another;
</li>
<li>
<a href = "r8bb_add.m">r8bb_add.m</a>,
adds a value to an entry in an R8BB matrix;
</li>
<li>
<a href = "r8bb_fa.m">r8bb_fa.m</a>,
factors an R8BB matrix;
</li>
<li>
<a href = "r8bb_get.m">r8bb_get.m</a>,
gets the value of an entry in an R8BB matrix;
</li>
<li>
<a href = "r8bb_indicator.m">r8bb_indicator.m</a>,
returns an R8BB indicator matrix;
</li>
<li>
<a href = "r8bb_mxv.m">r8bb_mxv.m</a>,
multiplies an R8BB matrix times a vector;
</li>
<li>
<a href = "r8bb_print.m">r8bb_print.m</a>,
prints an R8BB matrix;
</li>
<li>
<a href = "r8bb_print_some.m">r8bb_print_some.m</a>,
prints some of an R8BB matrix;
</li>
<li>
<a href = "r8bb_random.m">r8bb_random.m</a>,
returns a random R8BB matrix;
</li>
<li>
<a href = "r8bb_set.m">r8bb_set.m</a>,
sets one entry of an R8BB matrix;
</li>
<li>
<a href = "r8bb_sl.m">r8bb_sl.m</a>,
solves a linear system that was factored by R8BB_FA;
</li>
<li>
<a href = "r8bb_to_r8ge.m">r8bb_to_r8ge.m</a>,
copies an R8BB matrix to an R8GE matrix;
</li>
<li>
<a href = "r8bb_vxm.m">r8bb_vxm.m</a>,
multiplies a vector times an R8BB matrix;
</li>
<li>
<a href = "r8blt_det.m">r8blt_det.m</a>,
returns the determinant of an R8BLT matrix;
</li>
<li>
<a href = "r8blt_indicator.m">r8blt_indicator.m</a>,
returns an R8BLT indicator matrix;
</li>
<li>
<a href = "r8blt_mxv.m">r8blt_mxv.m</a>,
multiplies an R8BLT matrix times a vector;
</li>
<li>
<a href = "r8blt_print.m">r8blt_print.m</a>,
prints an R8BLT matrix;
</li>
<li>
<a href = "r8blt_print_some.m">r8blt_print_some.m</a>,
prints some of an R8BLT matrix;
</li>
<li>
<a href = "r8blt_random.m">r8blt_random.m</a>,
randomizes an R8BLT matrix;
</li>
<li>
<a href = "r8blt_sl.m">r8blt_sl.m</a>,
solves an R8BLT linear system;
</li>
<li>
<a href = "r8blt_to_r8ge.m">r8blt_to_r8ge.m</a>,
copies an R8BLT matrix to an R8GE matrix;
</li>
<li>
<a href = "r8blt_vxm.m">r8blt_vxm.m</a>,
multiplies a vector times an R8BLT matrix;
</li>
<li>
<a href = "r8bto_indicator.m">r8bto_indicator.m</a>,
returns an R8BTO indicator matrix;
</li>
<li>
<a href = "r8bto_mxv.m">r8bto_mxv.m</a>,
multiplies an R8BTO matrix times a vector;
</li>
<li>
<a href = "r8bto_print.m">r8bto_print.m</a>,
prints an R8BTO matrix;
</li>
<li>
<a href = "r8bto_print_some.m">r8bto_print_some.m</a>,
prints some of an R8BTO matrix;
</li>
<li>
<a href = "r8bto_random.m">r8bto_random.m</a>,
randomizes an R8BTO matrix;
</li>
<li>
<b>(r8bto_sl.m)</b>,
solves an R8BTO linear system (this routine is NOT available
in a MATLAB version);
</li>
<li>
<a href = "r8bto_vxm.m">r8bto_vxm.m</a>,
multiplies a vector times an R8BTO matrix;
</li>
<li>
<a href = "r8but_det.m">r8but_det.m</a>,
returns the determinant of an R8BUT matrix;
</li>
<li>
<a href = "r8but_indicator.m">r8but_indicator.m</a>,
returns an R8BUT indicator matrix;
</li>
<li>
<a href = "r8but_mxv.m">r8but_mxv.m</a>,
multiplies an R8BUT matrix times a vector;
</li>
<li>
<a href = "r8but_print.m">r8but_print.m</a>,
prints an R8BUT matrix;
</li>
<li>
<a href = "r8but_print_some.m">r8but_print_some.m</a>,
prints some of an R8BUT matrix;
</li>
<li>
<a href = "r8but_random.m">r8but_random.m</a>,
randomizes an R8BUT matrix;
</li>
<li>
<a href = "r8but_sl.m">r8but_sl.m</a>,
solves an R8BUT linear system;
</li>
<li>
<a href = "r8but_to_r8ge.m">r8but_to_r8ge.m</a>,
copies an R8BUT matrix to an R8GE matrix;
</li>
<li>
<a href = "r8but_vxm.m">r8but_vxm.m</a>,
multiplies a vector times an R8BUT matrix;
</li>
<li>
<a href = "r8cb_det.m">r8cb_det.m</a>,
returns the determinant of an R8CB matrix;
</li>
<li>
<a href = "r8cb_indicator.m">r8cb_indicator.m</a>,
returns an R8CB indicator matrix;
</li>
<li>
<a href = "r8cb_ml.m">r8cb_ml.m</a>,
computes A*x or A'*x after A has been factored by R8CB_NP_FA;
</li>
<li>
<a href = "r8cb_mxv.m">r8cb_mxv.m</a>,
multiplies an R8CB matrix times a vector;
</li>
<li>
<a href = "r8cb_np_fa.m">r8cb_np_fa.m</a>,
factors an R8CB linear system with no pivoting;
</li>
<li>
<a href = "r8cb_np_sl.m">r8cb_np_sl.m</a>,
solves an R8CB linear system;
</li>
<li>
<a href = "r8cb_print.m">r8cb_print.m</a>,
prints an R8CB matrix;
</li>
<li>
<a href = "r8cb_print_some.m">r8cb_print_some.m</a>,
prints some of an R8CB matrix;
</li>
<li>
<a href = "r8cb_random.m">r8cb_random.m</a>,
randomizes an R8CB matrix;
</li>
<li>
<a href = "r8cb_to_r8ge.m">r8cb_to_r8ge.m</a>,
copies an R8CB matrix to an R8GE matrix;
</li>
<li>
<a href = "r8cb_vxm.m">r8cb_vxm.m</a>,
multiplies a vector times an R8CB matrix;
</li>
<li>
<a href = "r8cbb_to_r8ge.m">r8cbb_to_r8ge.m</a>,
copies an R8CBB matrix to an R8GE matrix;
</li>
<li>
<a href = "r8cbb_add.m">r8cbb_add.m</a>,
adds a value to an entry of an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_fa.m">r8cbb_fa.m</a>,
factors an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_get.m">r8cbb_get.m</a>,
gets one entry of an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_indicator.m">r8cbb_indicator.m</a>,
returns an R8CBB indicator matrix;
</li>
<li>
<a href = "r8cbb_mxv.m">r8cbb_mxv.m</a>,
multiplies a vector times an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_print.m">r8cbb_print.m</a>,
print an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_print_some.m">r8cbb_print_some.m</a>,
prints some of an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_random.m">r8cbb_random.m</a>,
returns a random R8CBB matrix;
</li>
<li>
<a href = "r8cbb_set.m">r8cbb_set.m</a>,
sets one entry of an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_sl.m">r8cbb_sl.m</a>,
solves a linear system factored by R8CBB_FA;
</li>
<li>
<a href = "r8cbb_vxm.m">r8cbb_vxm.m</a>,
multiplies a vector times an R8CBB matrix;
</li>
<li>
<a href = "r8cc_get.m">r8cc_get.m</a>,
gets an entry from an R8CC matrix.
</li>
<li>
<a href = "r8cc_ijk.m">r8cc_ijk.m</a>,
gets the sparse index from the full indices in an R8CC matrix.
</li>
<li>
<a href = "r8cc_inc.m">r8cc_inc.m</a>,
increments an entry from an R8CC matrix.
</li>
<li>
<a href = "r8cc_indicator.m">r8cc_indicator.m</a>,
returns an R8CC indicator matrix;
</li>
<li>
<a href = "r8cc_kij.m">r8cc_kij.m</a>,
gets the full indices from the sparse index in an R8CC matrix.
</li>
<li>
<a href = "r8cc_mxv.m">r8cc_mxv.m</a>,
multiplies an R8CC matrix times a vector;
</li>
<li>
<a href = "r8cc_print.m">r8cc_print.m</a>,
prints an R8CC matrix;
</li>
<li>
<a href = "r8cc_print_some.m">r8cc_print_some.m</a>,
prints some of an R8CC matrix;
</li>
<li>
<a href = "r8cc_random.m">r8cc_random.m</a>,
randomizes an R8CC matrix;
</li>
<li>
<a href = "r8cc_read.m">r8cc_read.m</a>,
reads an R8CC matrix from three files;
</li>
<li>
<a href = "r8cc_read_size.m">r8cc_read_size.m</a>,
reads the sizes associated with an R8CC matrix stored in three files;
</li>
<li>
<a href = "r8cc_set.m">r8cc_set.m</a>,
sets an entry in an R8CC matrix.
</li>
<li>
<a href = "r8cc_to_r8ge.m">r8cc_to_r8ge.m</a>,
solves an R8CC linear system;
</li>
<li>
<a href = "r8cc_vxm.m">r8cc_vxm.m</a>,
multiplies a vector times an R8CC matrix;
</li>
<li>
<a href = "r8cc_write.m">r8cc_write.m</a>,
writes an R8CC matrix to three files;
</li>
<li>
<a href = "r8ci_eval.m">r8ci_eval.m</a>,
returns the eigenvalues of an R8CI matrix;
</li>
<li>
<a href = "r8ci_indicator.m">r8ci_indicator.m</a>,
returns an R8CI indicator matrix;
</li>
<li>
<a href = "r8ci_mxv.m">r8ci_mxv.m</a>,
multiplies an R8CI matrix times a vector;
</li>
<li>
<a href = "r8ci_print.m">r8ci_print.m</a>,
prints an R8CI matrix;
</li>
<li>
<a href = "r8ci_print_some.m">r8ci_print_some.m</a>,
prints some of an R8CI matrix;
</li>
<li>
<a href = "r8ci_random.m">r8ci_random.m</a>,
randomizes an R8CI matrix;
</li>
<li>
<a href = "r8ci_sl.m">r8ci_sl.m</a>,
solves an R8CI linear system;
</li>
<li>
<a href = "r8ci_to_r8ge.m">r8ci_to_r8ge.m</a>,
copies an R8CI matrix to an R8GE matrix;
</li>
<li>
<a href = "r8ci_vxm.m">r8ci_vxm.m</a>,
multiplies a vector times an R8CI matrix;
</li>
<li>
<a href = "r8gb_det.m">r8gb_det.m</a>,
computes the determinant of an R8GB matrix factored by
R8GB_FA or R8GB_TRF;
</li>
<li>
<a href = "r8gb_fa.m">r8gb_fa.m</a>,
performs a LINPACK style PLU factorization of an R8GB matrix;
</li>
<li>
<a href = "r8gb_indicator.m">r8gb_indicator.m</a>,
returns an R8GB indicator matrix;
</li>
<li>
<a href = "r8gb_ml.m">r8gb_ml.m</a>,
computes A*x or A'*x after A has been factored by R8GB_FA;
</li>
<li>
<a href = "r8gb_mu.m">r8gb_mu.m</a>,
computes A*x or A'*x after A has been factored by R8GB_TRF;
</li>
<li>
<a href = "r8gb_mxv.m">r8gb_mxv.m</a>,
multiplies an R8GB matrix times a vector;
</li>
<li>
<a href = "r8gb_nz_num.m">r8gb_nz_num.m</a>,
counts the nonzeroes in an R8GB matrix;
</li>
<li>
<a href = "r8gb_print.m">r8gb_print.m</a>,
prints an R8GB matrix.;
</li>
<li>
<a href = "r8gb_print_some.m">r8gb_print_some.m</a>,
prints some of an R8GB matrix;
</li>
<li>