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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 FORTRAN90 library which
carries out simple manipulations of matrices in a variety of formats,
including matrices stored in banded, border-banded, circulant,
lower triangular, pentadiagonal, sparse, sparse,
toeplitz, tridiagonal, upper triangular and vandermonde formats.
</p>
<p>
The routines are primarily organized by the arithmetic type, and 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> - Complex double precision tridiagonal;
</li>
<li>
<b>C8CI</b> - Complex double precision circulant;
</li>
<li>
<b>C8GE</b> - Complex double precision general;
</li>
<li>
<b>C8TO</b> - Complex double precision Toeplitz;
</li>
<li>
<b>R83</b> - Real double precision tridiagonal;
</li>
<li>
<b>R83P</b> - Real double precision tridiagonal periodic;
</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>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 diagonal
and 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>R8VEC</b> - Real double precision vector, which in some cases
is used to store a matrix;
</li>
<li>
<b>R8VM</b> - Real double precision Vandermonde;
</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 = "../../f_src/blas1/blas1.html">
BLAS1</a>,
a FORTRAN90 library which
contains level 1 basic linear algebra routines.
</p>
<p>
<a href = "../../f_src/condition/condition.html">
CONDITION</a>,
a FORTRAN90 library which
implements methods of computing or estimating the condition number of a matrix.
</p>
<p>
<a href = "../../c_src/csparse/csparse.html">
CSPARSE</a>,
a C library which
carries out the direct solution of sparse linear systems.
</p>
<p>
<a href = "../../f_src/cyclic_reduction/cyclic_reduction.html">
CYCLIC_REDUCTION</a>,
a FORTRAN90 library which
solves a tridiagonal linear system using cyclic reduction.
</p>
<p>
<a href = "../../f_src/dlap/dlap.html">
DLAP</a>,
a FORTRAN90 library which
carries out the iterative solution of sparse linear systems.
</p>
<p>
<a href = "../../data/dsp/dsp.html">
DSP</a>,
a file format which
can be used to store a sparse matrix in a file.
</p>
<p>
<a href = "../../cpp_src/gsl/gsl.html">
GSL</a>,
C++ programs which
illustrate the use of the Gnu Scientific Library;
</p>
<p>
<a href = "../../f_src/hb_to_st/hb_to_st.html">
HB_TO_ST</a>,
a FORTRAN90 program which
converts a sparse matrix from Harwell-Boeing to sparse triplet format.
</p>
<p>
<a href = "../../datasets/hbsmc/hbsmc.html">
HBSMC</a>,
a dataset directory which
contains the Harwell Boeing Sparse Matrix Collection;
</p>
<p>
<a href = "../../f_src/lapack_examples/lapack_examples.html">
LAPACK_EXAMPLES</a>,
a FORTRAN90 program which
demonstrates the use of the LAPACK linear algebra library.
</p>
<p>
<a href = "../../f_src/linpack/linpack.html">
LINPACK</a>,
a FORTRAN90 library which
factors and solves systems of linear equations in a variety of
formats and arithmetic types.
</p>
<p>
<a href = "../../f_src/linpack_bench/linpack_bench.html">
LINPACK_BENCH</a>,
a FORTRAN90 program which
measures the time taken by <b>LINPACK</b> to solve a
particular linear system.
</p>
<p>
<a href = "../../f_src/mgmres/mgmres.html">
MGMRES</a>,
a FORTRAN90 library which
applies the restarted GMRES algorithm to solve a sparse linear system.
</p>
<p>
<a href = "../../f_src/qr_solve/qr_solve.html">
QR_SOLVE</a>,
a FORTRAN90 library which
computes the least squares solution of a linear system A*x=b.
</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/super_lu/super_lu.html">
SUPER_LU</a>,
a C library which
implements some very fast direct
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 = "../../f_src/test_mat/test_mat.html">
TEST_MAT</a>,
a FORTRAN90 library which
defines test matrices, some of
which have known determinants, eigenvalues and eigenvectors,
inverses and so on.
</p>
<p>
<a href = "../../f_src/toeplitz_cholesky/toeplitz_cholesky.html">
TOEPLITZ_CHOLESKY</a>,
a FORTRAN90 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>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "linplus.f90">linplus.f90</a>, the source code;
</li>
<li>
<a href = "linplus.sh">linplus.sh</a>, commands to compile
the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "linplus_prb.f90">linplus_prb.f90</a>, the calling program;
</li>
<li>
<a href = "linplus_prb.sh">linplus_prb.sh</a>, commands to
compile and run the calling program;
</li>
<li>
<a href = "linplus_prb_output.txt">linplus_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>C8_LE_L2</b> := X <= Y for the L2 norm on C8 values.
</li>
<li>
<b>C8_SWAP</b> swaps two C8's.
</li>
<li>
<b>C83_CR_FA</b> decomposes a C83 matrix using cyclic reduction.
</li>
<li>
<b>C83_CR_SLS</b> solves several linear systems factored by C83_CR_FA.
</li>
<li>
<b>C83_INDICATOR</b> sets up a C83 indicator matrix.
</li>
<li>
<b>C83_JAC_SL</b> solves a C83 system using Jacobi iteration.
</li>
<li>
<b>C83_MXV</b> multiplies a C83 matrix times a C8VEC.
</li>
<li>
<b>C83_NP_DET</b> returns the determinant of a C83 system factored by C83_NP_FA.
</li>
<li>
<b>C83_NP_FA</b> factors a C83 matrix without pivoting.
</li>
<li>
<b>C83_NP_FS</b> factors and solves a C83 system.
</li>
<li>
<b>C83_NP_ML</b> computes A * x or x * A, where A has been factored by C83_NP_FA.
</li>
<li>
<b>C83_NP_SL</b> solves a C83 system factored by C83_NP_FA.
</li>
<li>
<b>C83_PRINT</b> prints a C83 matrix.
</li>
<li>
<b>C83_PRINT_SOME</b> prints some of a C83 matrix.
</li>
<li>
<b>C83_RANDOM</b> randomizes a C83 matrix.
</li>
<li>
<b>C83_TO_C8GE</b> copies a C83 matrix into a C8GE matrix.
</li>
<li>
<b>C83_VXM</b> multiplies a C8VEC by a C83 matrix.
</li>
<li>
<b>C8CI_EVAL</b> returns the eigenvalues of a C8CI matrix.
</li>
<li>
<b>C8CI_MXV</b> multiplies a C8CI matrix times a C8VEC.
</li>
<li>
<b>C8CI_PRINT</b> prints a C8CI matrix.
</li>
<li>
<b>C8CI_PRINT_SOME</b> prints some of a C8CI matrix.
</li>
<li>
<b>C8CI_RANDOM</b> randomizes a C8CI matrix.
</li>
<li>
<b>C8CI_SL</b> solves a C8CI system.
</li>
<li>
<b>C8CI_TO_C8GE</b> copies a C8CI matrix to a C8GE matrix.
</li>
<li>
<b>C8CI_VXM</b> multiplies a C8VEC by a C8CI matrix.
</li>
<li>
<b>C8GE_RANDOM</b> randomizes a C8GE matrix.
</li>
<li>
<b>C8MAT_PRINT</b> prints a C8MAT.
</li>
<li>
<b>C8MAT_PRINT_SOME</b> prints some of a C8MAT.
</li>
<li>
<b>C8MAT_UNIFORM_01</b> returns a unit pseudorandom C8MAT.
</li>
<li>
<b>C8TO_MXV</b> multiplies a C8TO matrix times a C8VEC.
</li>
<li>
<b>C8TO_PRINT</b> prints a C8TO matrix.
</li>
<li>
<b>C8TO_PRINT_SOME</b> prints some of a C8TO matrix.
</li>
<li>
<b>C8TO_RANDOM</b> randomizes a C8TO matrix.
</li>
<li>
<b>C8TO_SL</b> solves a C8TO system.
</li>
<li>
<b>C8TO_TO_C8GE</b> copies a C8TO matrix to a C8GE matrix.
</li>
<li>
<b>C8TO_VXM</b> multiplies a C8VEC by a C8TO matrix.
</li>
<li>
<b>C8VEC_INDICATOR</b> sets a C8VEC to an "indicator" vector.
</li>
<li>
<b>C8VEC_PRINT</b> prints a C8VEC, with an optional title.
</li>
<li>
<b>C8VEC_PRINT_SOME</b> prints some of a C8VEC.
</li>
<li>
<b>C8VEC_SORT_A2</b> ascending sorts a C8VEC by L2 norm.
</li>
<li>
<b>C8VEC_UNIFORM_01</b> returns a unit pseudorandom C8VEC.
</li>
<li>
<b>C8VEC_UNITY</b> returns the N roots of unity as a C8VEC.
</li>
<li>
<b>DAXPY</b> adds a constant times one R8VEC to another.
</li>
<li>
<b>FILE_DELETE</b> deletes a named file if it exists.
</li>
<li>
<b>FILE_EXIST</b> reports whether a file exists.
</li>
<li>
<b>FILE_IS_OPEN</b> reports whether a file (specified by filename) is open.
</li>
<li>
<b>GET_SEED</b> returns a seed for the random number generator.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>HILBERT_INVERSE</b> returns the inverse of the Hilbert matrix.
</li>
<li>
<b>I4_LOG_10</b> returns the integer part of the logarithm base 10 of an I4.
</li>
<li>
<b>I4_SWAP</b> swaps two I4's.
</li>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>I4VEC_SEARCH_BINARY_A</b> searches an ascending sorted I4VEC for a value.
</li>
<li>
<b>R8_IS_INT</b> determines if an R8 represents an integer value.
</li>
<li>
<b>R8_SWAP</b> switches two R8's.
</li>
<li>
<b>R8_UNIFORM</b> returns a scaled pseudorandom R8.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R83_CR_FA</b> decomposes an R83 matrix using cyclic reduction.
</li>
<li>
<b>R83_CR_SLS</b> solves several linear systems factored by R83_CR_FA.
</li>
<li>
<b>R83_GS_SL</b> solves an R83 system using Gauss-Seidel iteration.
</li>
<li>
<b>R83_INDICATOR</b> sets up an R83 indicator matrix.
</li>
<li>
<b>R83_JAC_SL</b> solves an R83 system using Jacobi iteration.
</li>
<li>
<b>R83_MXV</b> multiplies an R83 matrix times an R8VEC.
</li>
<li>
<b>R83_NP_DET</b> returns the determinant of an R83 system factored by R83_NP_FA.
</li>
<li>
<b>R83_NP_FA</b> factors an R83 matrix without pivoting.
</li>
<li>
<b>R83_NP_FS</b> factors and solves an R83 system.
</li>
<li>
<b>R83_NP_FSS</b> factors and solves multiple R83 systems.
</li>
<li>
<b>R83_NP_ML</b> computes A * x or x * A, where A has been factored by R83_NP_FA.
</li>
<li>
<b>R83_NP_SL</b> solves an R83 system factored by R83_NP_FA.
</li>
<li>
<b>R83_PRINT</b> prints an R83 matrix.
</li>
<li>
<b>R83_PRINT_SOME</b> prints some of an R83 matrix.
</li>
<li>
<b>R83_RANDOM</b> randomizes an R83 matrix.
</li>
<li>
<b>R83_TO_R8GE</b> copies an R83 matrix to an R8GE matrix.
</li>
<li>
<b>R83_VXM</b> multiplies an R8VEC by an R83 matrix.
</li>
<li>
<b>R83NP_FS</b> factors and solves an R83NP system.
</li>
<li>
<b>R83P_DET</b> computes the determinant of a matrix factored by R83P_FA.
</li>
<li>
<b>R83P_FA</b> factors an R83P matrix.
</li>
<li>
<b>R83P_INDICATOR</b> sets up an R83P indicator matrix.
</li>
<li>
<b>R83P_ML</b> computes A * x or x * A, where A has been factored by R83P_FA.
</li>
<li>
<b>R83P_MXV</b> multiplies an R83P matrix by an R8VEC.
</li>
<li>
<b>R83P_PRINT</b> prints an R83P matrix.
</li>
<li>
<b>R83P_PRINT_SOME</b> prints some of an R83P matrix.
</li>
<li>
<b>R83P_RANDOM</b> randomizes an R83P matrix.
</li>
<li>
<b>R83P_SL</b> solves an R83P system.
</li>
<li>
<b>R83P_TO_R8GE</b> copies an R83P matrix to an R8GE matrix.
</li>
<li>
<b>R83P_VXM</b> multiplies an R8VEC by an R83P matrix.
</li>
<li>
<b>R85_INDICATOR</b> sets up an R85 indicator matrix.
</li>
<li>
<b>R85_NP_FS</b> factors and solves an R85 linear system.
</li>
<li>
<b>R85_MXV</b> multiplies an R85 matrix by an R8VEC.
</li>
<li>
<b>R85_PRINT</b> prints an R85 matrix.
</li>
<li>
<b>R85_PRINT_SOME</b> prints some of an R85 matrix.
</li>
<li>
<b>R85_RANDOM</b> randomizes an R85 matrix.
</li>
<li>
<b>R85_TO_R8GE</b> copies an R85 matrix into an R8GE matrix.
</li>
<li>
<b>R85_VXM</b> multiplies an R8VEC by an R85 matrix.
</li>
<li>
<b>R8BB_ADD</b> adds a value to an entry in an R8BB matrix.
</li>
<li>
<b>R8BB_FA</b> factors an R8BB matrix.
</li>
<li>
<b>R8BB_GET</b> returns an entry of an R8BB matrix.
</li>
<li>
<b>R8BB_INDICATOR</b> sets up an R8BB indicator matrix.
</li>
<li>
<b>R8BB_MXV</b> multiplies an R8BB matrix by an R8VEC.
</li>
<li>
<b>R8BB_PRINT</b> prints an R8BB matrix.
</li>
<li>
<b>R8BB_PRINT_SOME</b> prints some of an R8BB matrix.
</li>
<li>
<b>R8BB_RANDOM</b> randomizes an R8BB matrix.
</li>
<li>
<b>R8BB_SET</b> sets an entry of an R8BB matrix.
</li>
<li>
<b>R8BB_SL</b> solves an R8BB system factored by R8BB_FA.
</li>
<li>
<b>R8BB_TO_R8GE</b> copies an R8BB matrix to an R8GE matrix.
</li>
<li>
<b>R8BB_VXM</b> multiplies an R8VEC by an R8BB matrix.
</li>
<li>
<b>R8BLT_DET</b> computes the determinant of an R8BLT matrix.
</li>
<li>
<b>R8BLT_INDICATOR</b> sets up an R8BLT indicator matrix.
</li>
<li>
<b>R8BLT_MXV</b> multiplies an R8BLT matrix by an R8VEC.
</li>
<li>
<b>R8BLT_PRINT</b> prints an R8BLT matrix.
</li>
<li>
<b>R8BLT_PRINT_SOME</b> prints some of an R8BLT matrix.
</li>
<li>
<b>R8BLT_RANDOM</b> randomizes an R8BLT matrix.
</li>
<li>
<b>R8BLT_SL</b> solves an R8BLT system.
</li>
<li>
<b>R8BLT_TO_R8GE</b> copies an R8BLT matrix to an R8GE matrix.
</li>
<li>
<b>R8BLT_VXM</b> multiplies an R8VEC by an R8BLT matrix.
</li>
<li>
<b>R8BTO_INDICATOR</b> sets up an R8BTO indicator matrix.
</li>
<li>
<b>R8BTO_MXV</b> multiplies an R8BTO matrix by an R8VEC.
</li>
<li>
<b>R8BTO_PRINT</b> prints an R8BTO matrix.
</li>
<li>
<b>R8BTO_PRINT_SOME</b> prints some of an R8BTO matrix.
</li>
<li>
<b>R8BTO_RANDOM</b> randomizes an R8BTO matrix.
</li>
<li>
<b>R8BTO_SL</b> solves an R8BTO system.
</li>
<li>
<b>R8BTO_TO_R8GE</b> copies an R8BTO matrix to an R8GE matrix.
</li>
<li>
<b>R8BTO_VXM</b> multiplies an R8VEC by an R8BTO matrix.
</li>
<li>
<b>R8BUT_DET</b> computes the determinant of an R8BUT matrix.
</li>
<li>
<b>R8BUT_INDICATOR</b> sets up an R8BUT indicator matrix.
</li>
<li>
<b>R8BUT_MXV</b> multiplies an R8BUT matrix by an R8VEC.
</li>
<li>
<b>R8BUT_PRINT</b> prints an R8BUT matrix.
</li>
<li>
<b>R8BUT_PRINT_SOME</b> prints some of an R8BUT matrix.
</li>
<li>
<b>R8BUT_RANDOM</b> randomizes an R8BUT matrix.
</li>
<li>
<b>R8BUT_SL</b> solves an R8BUT system.
</li>
<li>
<b>R8BUT_TO_R8GE</b> copies an R8BUT matrix to an R8GE matrix.
</li>
<li>
<b>R8BUT_VXM</b> multiplies an R8VECr by an R8BUT matrix.
</li>
<li>
<b>R8CB_DET</b> computes the determinant of an R8CB matrix factored by R8CB_NP_FA.
</li>
<li>
<b>R8CB_INDICATOR</b> sets up an R8CB indicator matrix.
</li>
<li>
<b>R8CB_ML</b> computes A * x or A' * X, using R8CB_NP_FA factors.
</li>
<li>
<b>R8CB_MXV</b> multiplies an R8CB matrix by an R8VEC.
</li>
<li>
<b>R8CB_NP_FA</b> factors an R8CB matrix by Gaussian elimination.
</li>
<li>
<b>R8CB_NP_SL</b> solves an R8CB system factored by R8CB_NP_FA.
</li>
<li>
<b>R8CB_PRINT</b> prints an R8CB matrix.
</li>
<li>
<b>R8CB_PRINT_SOME</b> prints some of an R8CB matrix.
</li>
<li>
<b>R8CB_RANDOM</b> randomizes an R8CB matrix.
</li>
<li>
<b>R8CB_TO_R8VEC</b> copies an R8CB matrix to an R8VEC.
</li>
<li>
<b>R8CB_TO_R8GE</b> copies an R8CB matrix to an R8GE matrix.
</li>
<li>
<b>R8CB_VXM</b> multiplies an R8VECr by an R8CB matrix.
</li>
<li>
<b>R8CBB_ADD</b> adds a value to an entry of an R8CBB matrix.
</li>
<li>
<b>R8CBB_ERROR</b> checks the dimensions of an R8CBB matrix.
</li>
<li>
<b>R8CBB_FA</b> factors an R8CBB matrix.
</li>
<li>
<b>R8CBB_GET</b> returns the value of an entry of an R8CBB matrix.
</li>
<li>
<b>R8CBB_INDICATOR</b> sets up an R8CBB indicator matrix.
</li>
<li>
<b>R8CBB_MXV</b> multiplies an R8CBB matrix by an R8VEC.
</li>
<li>
<b>R8CBB_PRINT</b> prints an R8CBB matrix.
</li>
<li>
<b>R8CBB_PRINT_SOME</b> prints some of an R8CBB matrix.
</li>
<li>
<b>R8CBB_RANDOM</b> randomizes an R8CBB matrix.
</li>
<li>
<b>R8CBB_SET</b> sets the value of an entry in an R8CBB matrix.
</li>
<li>
<b>R8CBB_SL</b> solves an R8CBB system factored by R8CBB_FA.
</li>
<li>
<b>R8CBB_TO_R8GE</b> copies an R8CBB matrix to an R8GE matrix.
</li>
<li>
<b>R8CBB_VXM</b> multiplies an R8VEC by an R8CBB matrix.
</li>
<li>
<b>R8CC_GET</b> gets a value of an R8CC matrix.
</li>
<li>
<b>R8CC_IJK</b> seeks K, the sparse index of (I,J), the full index of an R8CC matrix.
</li>
<li>
<b>R8CC_INC</b> increments a value of an R8CC matrix.
</li>
<li>
<b>R8CC_INDICATOR</b> sets up an R8CC indicator matrix.
</li>
<li>
<b>R8CC_KIJ</b> seeks (I,J), the full index of K, the sparse index of an R8CC matrix.
</li>
<li>
<b>R8CC_MXV</b> multiplies an R8CC matrix by an R8VEC.
</li>
<li>
<b>R8CC_PRINT</b> prints an R8CC matrix.
</li>
<li>
<b>R8CC_PRINT_SOME</b> prints some of an R8CC matrix.
</li>
<li>
<b>R8CC_RANDOM</b> randomizes an R8CC matrix.
</li>
<li>
<b>R8CC_READ</b> reads an R8CC matrix from three files.
</li>
<li>
<b>R8CC_READ_SIZE</b> reads the sizes of an R8CC sparse matrix from a file.
</li>
<li>
<b>R8CC_SET</b> sets a value of an R8CC matrix.
</li>
<li>
<b>R8CC_TO_R8GE</b> converts an R8CC matrix to an R8GE matrix.
</li>
<li>
<b>R8CC_VXM</b> multiplies an R8VEC times an R8CC matrix.
</li>
<li>
<b>R8CC_WRITE</b> writes an R8CC matrix to three files.
</li>
<li>
<b>R8CI_EVAL</b> returns the eigenvalues of an R8CI matrix.
</li>
<li>
<b>R8CI_INDICATOR</b> sets up an R8CI indicator matrix.
</li>
<li>
<b>R8CI_MXV</b> multiplies an R8CI matrix by an R8VEC.
</li>
<li>
<b>R8CI_PRINT</b> prints an R8CI matrix.
</li>
<li>
<b>R8CI_PRINT_SOME</b> prints some of an R8CI matrix.
</li>
<li>
<b>R8CI_RANDOM</b> randomizes an R8CI matrix.