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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 C++ 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> - 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>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>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 = "../../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 = "../../cpp_src/cg/cg.html">
CG</a>,
a C++ 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 = "../../c_src/csparse/csparse.html">
CSPARSE</a>,
a C library which
carries out the direct solution of sparse linear systems.
</p>
<p>
<a href = "../../cpp_src/gsl/gsl.html">
GSL</a>,
a C++ library which
includes many linear algebra routines.
</p>
<p>
<a href = "../../datasets/hbsmc/hbsmc.html">
HBSMC</a>,
a dataset directory which
contains the Harwell-Boeing Sparse Matrix Collection
of large sparse matrices.
</p>
<p>
<a href = "../../cpp_src/linpack_d/linpack_d.html">
LINPACK_D</a>,
a C++ library which
solves linear systems using double precision real arithmetic;
</p>
<p>
<a href = "../../cpp_src/linpack_bench/linpack_bench.html">
LINPACK_BENCH</a>,
a C++ program which
measures the time taken by <b>LINPACK</b> to solve a
particular linear system.
</p>
<p>
<a href = "../../cpp_src/mgmres/mgmres.html">
MGMRES</a>,
a C++ library which
applies the restarted GMRES algorithm
to solve a sparse linear system.
</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 = "../../cpp_src/test_mat/test_mat.html">
TEST_MAT</a>,
a C++ library which
defines test matrices, some of
which have known determinants, eigenvalues and eigenvectors,
inverses and so on.
</p>
<p>
<a href = "../../cpp_src/toeplitz_cholesky/toeplitz_cholesky.html">
TOEPLITZ_CHOLESKY</a>,
a C++ library which
computes the Cholesky factorization of a nonnegative definite symmetric
Toeplitz matrix.
</p>
<p>
<a href = "../../cpp_src/wathen/wathen.html">
WATHEN</a>,
a C++ library which
compares storage schemes (full, banded, sparse triplet) and
solution strategies (Linpack full, Linpack banded,
conjugate gradient (CG)) for linear systems involving the Wathen matrix,
which can arise when solving a problem using the
finite element method (FEM).
</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 = "linplus.cpp">linplus.cpp</a>, the source code;
</li>
<li>
<a href = "linplus.hpp">linplus.hpp</a>, the include file;
</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.cpp">linplus_prb.cpp</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>C8VEC_PRINT</b> prints a double complex vector.
</li>
<li>
<b>C8VEC_SORT_A2</b> ascending sorts a double complex array by L2 norm.
</li>
<li>
<b>C8VEC_UNITY</b> returns the N roots of unity as a double complex vector.
</li>
<li>
<b>DAXPY</b> adds a constant times one vector to another.
</li>
<li>
<b>R83_CR_FA</b> decomposes a real tridiagonal matrix using cyclic reduction.
</li>
<li>
<b>R83_CR_SL</b> solves a real linear system factored by R83_CR_FA.
</li>
<li>
<b>R83_GS_SL</b> solves a R83 system using Gauss-Seidel iteration.
</li>
<li>
<b>R83_INDICATOR</b> sets up a R83 indicator matrix.
</li>
<li>
<b>R83_JAC_SL</b> solves a R83 system using Jacobi iteration.
</li>
<li>
<b>R83_MXV</b> multiplies a R83 matrix times a vector.
</li>
<li>
<b>R83_NP_DET:</b> determinant of a tridiagonal system factored by R83_NP_FA.
</li>
<li>
<b>R83_NP_FA</b> factors a R83 system without pivoting.
</li>
<li>
<b>R83_NP_FS</b> factors and solves a R83 system.
</li>
<li>
<b>R83_NP_ML</b> computes Ax or xA, where A has been factored by R83_NP_FA.
</li>
<li>
<b>R83_NP_SL</b> solves a R83 system factored by R83_NP_FA.
</li>
<li>
<b>R83_PRINT</b> prints a R83 matrix.
</li>
<li>
<b>R83_PRINT_SOME</b> prints some of a R83 matrix.
</li>
<li>
<b>R83_RANDOM</b> randomizes a R83 matrix.
</li>
<li>
<b>R83_TO_R8GE</b> copies a R83 matrix to a R8GE matrix.
</li>
<li>
<b>R83_VXM</b> multiplies a vector times a R83 matrix.
</li>
<li>
<b>R83_ZERO</b> zeros a 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 a R83P matrix.
</li>
<li>
<b>R83P_INDICATOR</b> sets up a 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 a R83P matrix times a vector.
</li>
<li>
<b>R83P_PRINT</b> prints a R83P matrix.
</li>
<li>
<b>R83P_PRINT_SOME</b> prints some of a R83P matrix.
</li>
<li>
<b>R83P_RANDOM</b> randomizes a R83P matrix.
</li>
<li>
<b>R83P_SL</b> solves a R83P system factored by R83P_FA.
</li>
<li>
<b>R83P_TO_R8GE</b> copies a R83P matrix to a R8GE matrix.
</li>
<li>
<b>R83P_VXM</b> multiplies a vector times a R83P matrix.
</li>
<li>
<b>R83P_ZERO</b> zeros a R83P matrix.
</li>
<li>
<b>R85_INDICATOR</b> sets up a R85 indicator matrix.
</li>
<li>
<b>R85_NP_FS</b> factors and solves a R85 system.
</li>
<li>
<b>R85_MXV</b> multiplies a R85 matrix times a vector.
</li>
<li>
<b>R85_PRINT</b> prints a R85 matrix.
</li>
<li>
<b>R85_PRINT_SOME</b> prints some of a R85 matrix.
</li>
<li>
<b>R85_RANDOM</b> randomizes a R85 matrix.
</li>
<li>
<b>R85_TO_R8GE</b> copies a R85 matrix to a R8GE matrix.
</li>
<li>
<b>R85_VXM</b> multiplies a vector times a R85 matrix.
</li>
<li>
<b>R85_ZERO</b> zeros a R85 matrix.
</li>
<li>
<b>R8BB_ADD</b> adds a value to an entry in a R8BB matrix.
</li>
<li>
<b>R8BB_FA</b> factors a R8BB matrix.
</li>
<li>
<b>R8BB_GET</b> gets a value of a R8BB matrix.
</li>
<li>
<b>R8BB_INDICATOR</b> sets up a R8BB indicator matrix.
</li>
<li>
<b>R8BB_MXV</b> multiplies a R8BB matrix times a vector.
</li>
<li>
<b>R8BB_PRINT</b> prints a R8BB matrix.
</li>
<li>
<b>R8BB_PRINT_SOME</b> prints some of a R8BB matrix.
</li>
<li>
<b>R8BB_RANDOM</b> randomizes a R8BB matrix.
</li>
<li>
<b>R8BB_SET</b> sets a value of a R8BB matrix.
</li>
<li>
<b>R8BB_TO_R8GE</b> copies a R8BB matrix to a R8GE matrix.
</li>
<li>
<b>R8BB_VXM</b> multiplies a vector by a R8BB matrix.
</li>
<li>
<b>R8BB_ZERO</b> zeros a R8BB matrix.
</li>
<li>
<b>R8BLT_DET</b> computes the determinant of a R8BLT matrix.
</li>
<li>
<b>R8BLT_INDICATOR</b> sets up a R8BLT indicator matrix.
</li>
<li>
<b>R8BLT_MXV</b> multiplies a R8BLT matrix times a vector.
</li>
<li>
<b>R8BLT_PRINT</b> prints a R8BLT matrix.
</li>
<li>
<b>R8BLT_PRINT_SOME</b> prints some of a R8BLT matrix.
</li>
<li>
<b>R8BLT_RANDOM</b> randomizes a R8BLT matrix.
</li>
<li>
<b>R8BLT_SL</b> solves a R8BLT system.
</li>
<li>
<b>R8BLT_TO_R8GE</b> copies a R8BLT matrix to a R8GE matrix.
</li>
<li>
<b>R8BLT_VXM</b> multiplies a vector by a R8BLT matrix.
</li>
<li>
<b>R8BLT_ZERO</b> zeros a R8BLT matrix.
</li>
<li>
<b>R8BTO_INDICATOR</b> sets up a R8BTO indicator matrix.
</li>
<li>
<b>R8BTO_MXV</b> multiplies a R8BTO matrix times a vector.
</li>
<li>
<b>R8BTO_PRINT</b> prints a R8BTO matrix.
</li>
<li>
<b>R8BTO_PRINT_SOME</b> prints some of a R8BTO matrix.
</li>
<li>
<b>R8BTO_RANDOM</b> randomizes a R8BTO matrix.
</li>
<li>
<b>R8BTO_TO_R8GE</b> copies a R8BTO matrix to a R8GE matrix.
</li>
<li>
<b>R8BTO_VXM</b> multiplies a vector times a R8BTO matrix.
</li>
<li>
<b>R8BTO_ZERO</b> zeros a R8BTO matrix.
</li>
<li>
<b>R8BUT_DET</b> computes the determinant of a R8BUT matrix.
</li>
<li>
<b>R8BUT_INDICATOR</b> sets up a R8BUT indicator matrix.
</li>
<li>
<b>R8BUT_MXV</b> multiplies a R8BUT matrix times a vector.
</li>
<li>
<b>R8BUT_PRINT</b> prints a R8BUT matrix.
</li>
<li>
<b>R8BUT_PRINT_SOME</b> prints some of a R8BUT matrix.
</li>
<li>
<b>R8BUT_RANDOM</b> randomizes a R8BUT matrix.
</li>
<li>
<b>R8BUT_SL</b> solves a R8BUT system.
</li>
<li>
<b>R8BUT_TO_R8GE</b> copies a R8BUT matrix to a R8GE matrix.
</li>
<li>
<b>R8BUT_VXM</b> multiplies a vector by a R8BUT matrix.
</li>
<li>
<b>R8CB_DET</b> computes the determinant of a R8CB matrix factored by R8CB_NP_FA.
</li>
<li>
<b>R8CB_INDICATOR</b> sets up a 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 a R8CB matrix times a vector.
</li>
<li>
<b>R8CB_NP_FA</b> factors a R8CB matrix by Gaussian elimination.
</li>
<li>
<b>R8CB_NP_SL</b> solves a R8CB system factored by R8CB_NP_FA.
</li>
<li>
<b>R8CB_PRINT</b> prints a R8CB matrix.
</li>
<li>
<b>R8CB_PRINT_SOME</b> prints some of a R8CB matrix.
</li>
<li>
<b>R8CB_RANDOM</b> randomizes a R8CB matrix.
</li>
<li>
<b>R8CB_TO_R8VEC</b> copies a R8CB matrix to a real vector.
</li>
<li>
<b>R8CB_TO_R8GE</b> copies a R8CB matrix to a R8GE matrix.
</li>
<li>
<b>R8CB_VXM</b> multiplies a vector by a R8CB matrix.
</li>
<li>
<b>R8CB_ZERO</b> zeros a R8CB matrix.
</li>
<li>
<b>R8CBB_ADD</b> adds a value to an entry of a R8CBB matrix.
</li>
<li>
<b>R8CBB_ERROR</b> checks the dimensions of a R8CBB matrix.
</li>
<li>
<b>R8CBB_FA</b> factors a R8CBB matrix.
</li>
<li>
<b>R8CBB_GET</b> gets the value of an entry of a R8CBB matrix.
</li>
<li>
<b>R8CBB_INDICATOR</b> sets up a R8CBB indicator matrix.
</li>
<li>
<b>R8CBB_MXV</b> multiplies a R8CBB matrix times a vector.
</li>
<li>
<b>R8CBB_PRINT</b> prints a R8CBB matrix.
</li>
<li>
<b>R8CBB_PRINT_SOME</b> prints some of a R8CBB matrix.
</li>
<li>
<b>R8CBB_RANDOM</b> randomizes a R8CBB matrix.
</li>
<li>
<b>R8CBB_SET</b> sets an entry of a R8CBB matrix.
</li>
<li>
<b>R8CBB_SL</b> solves a R8CBB system factored by R8CBB_FA.
</li>
<li>
<b>R8CBB_TO_R8GE</b> copies a R8CBB matrix to a R8GE matrix.
</li>
<li>
<b>R8CBB_VXM</b> multiplies a vector by a R8CBB matrix.
</li>
<li>
<b>R8CBB_ZERO</b> zeros a R8CBB matrix.
</li>
<li>
<b>R8CC_GET</b> gets a value of a R8CC matrix.
</li>
<li>
<b>R8CC_IJK</b> seeks K, the sparse index of (I,J), the full index of a R8CC matrix.
</li>
<li>
<b>R8CC_INC</b> increments a value of a R8CC matrix.
</li>
<li>
<b>R8CC_INDICATOR</b> sets up a R8CC indicator matrix.
</li>
<li>
<b>R8CC_KIJ</b> seeks (I,J), the full index of K, the sparse index of a R8CC matrix.
</li>
<li>
<b>R8CC_MXV</b> multiplies a R8CC matrix times a vector.
</li>
<li>
<b>R8CC_PRINT</b> prints a R8CC matrix.
</li>
<li>
<b>R8CC_PRINT_SOME</b> prints some of a R8CC matrix.
</li>
<li>
<b>R8CC_RANDOM</b> randomizes a R8CC matrix.
</li>
<li>
<b>R8CC_READ</b> reads a R8CC matrix from three files.
</li>
<li>
<b>R8CC_READ_SIZE</b> reads the sizes of a R8CC sparse matrix from a file.
</li>
<li>
<b>R8CC_SET</b> sets a value of a R8CC matrix.
</li>
<li>
<b>R8CC_TO_R8GE</b> converts a R8CC matrix to a R8GE matrix.
</li>
<li>
<b>R8CC_VXM</b> multiplies a vector times a R8CC matrix.
</li>
<li>
<b>R8CC_WRITE</b> writes a R8CC matrix to three files.
</li>
<li>
<b>R8CC_ZERO</b> zeros a R8CC matrix.
</li>
<li>
<b>R8CI_EVAL</b> returns the eigenvalues of a R8CI matrix.
</li>
<li>
<b>R8CI_INDICATOR</b> sets up a R8CI indicator matrix.
</li>
<li>
<b>R8CI_MXV</b> multiplies a R8CI matrix times a vector.
</li>
<li>
<b>R8CI_PRINT</b> prints a R8CI matrix.
</li>
<li>
<b>R8CI_PRINT_SOME</b> prints some of a R8CI matrix.
</li>
<li>
<b>R8CI_RANDOM</b> randomizes a R8CI matrix.
</li>
<li>
<b>R8CI_SL</b> solves a R8CI system.
</li>
<li>
<b>R8CI_TO_R8GE</b> copies a R8CI matrix to a R8GE matrix.
</li>
<li>
<b>R8CI_VXM</b> multiplies a vector times a R8CI matrix.
</li>
<li>
<b>R8CI_ZERO</b> zeros a R8CI matrix.
</li>
<li>
<b>R8GB_DET</b> computes the determinant of a matrix factored by R8GB_FA or R8GB_TRF.
</li>
<li>
<b>R8GB_FA</b> performs a LINPACK-style PLU factorization of a R8GB matrix.
</li>
<li>
<b>R8GB_INDICATOR</b> sets up a R8GB indicator matrix.
</li>
<li>
<b>R8GB_ML</b> computes A * x or A' * X, using R8GB_FA factors.
</li>
<li>
<b>R8GB_MU</b> computes A * x or A' * X, using R8GB_TRF factors.
</li>
<li>
<b>R8GB_MXV</b> multiplies a R8GB matrix times a vector.
</li>
<li>
<b>R8GB_NZ_NUM</b> counts the nonzeroes in a R8GB matrix.
</li>
<li>
<b>R8GB_PRINT</b> prints a R8GB matrix.
</li>
<li>
<b>R8GB_PRINT_SOME</b> prints some of a R8GB matrix.
</li>
<li>
<b>R8GB_RANDOM</b> randomizes a R8GB matrix.
</li>
<li>
<b>R8GB_SL</b> solves a system factored by R8GB_FA.
</li>
<li>
<b>R8GB_TO_R8S3</b> copies a R8GB matrix to a R8S3 matrix.
</li>
<li>
<b>R8GB_TO_R8SP</b> copies a R8GB matrix to a R8SP matrix.
</li>
<li>
<b>R8GB_TO_R8VEC</b> copies a R8GB matrix to a real vector.
</li>
<li>
<b>R8GB_TO_R8GE</b> copies a R8GB matrix to a R8GE matrix.
</li>
<li>
<b>R8GB_TRF</b> performs a LAPACK-style PLU factorization of a R8GB matrix.
</li>
<li>
<b>R8GB_TRS</b> solves a linear system factored by R8GB_TRF.
</li>
<li>
<b>R8GB_VXM</b> multilies a vector times a R8GB matrix.
</li>
<li>
<b>R8GB_ZERO</b> zeros a R8GB matrix.
</li>
<li>
<b>R8GD_ERROR</b> checks the dimensions of a R8GD matrix.
</li>
<li>
<b>R8GD_INDICATOR</b> sets up a R8GD indicator matrix.
</li>
<li>
<b>R8GD_MXV</b> multiplies a R8GD matrix by a vector.
</li>
<li>
<b>R8GD_PRINT</b> prints a R8GD matrix.
</li>
<li>
<b>R8GD_PRINT_SOME</b> prints some of a R8GD matrix.
</li>
<li>
<b>R8GD_RANDOM</b> randomizes a R8GD matrix.
</li>
<li>
<b>R8GD_TO_R8GE</b> copies a R8GD matrix to a R8GE matrix.
</li>
<li>
<b>R8GD_VXM</b> multiplies a vector by a R8GD matrix.
</li>
<li>
<b>R8GD_ZERO</b> zeros a R8GD matrix.
</li>
<li>
<b>R8GE_CO</b> factors a R8GE matrix and estimates its condition number.
</li>
<li>
<b>R8GE_DET</b> computes the determinant of a matrix factored by R8GE_FA or R8GE_TRF.
</li>
<li>
<b>R8GE_DILU</b> produces the diagonal incomplete LU factor of a R8GE matrix.
</li>
<li>
<b>R8GE_FA</b> performs a LINPACK-style PLU factorization of a R8GE matrix.
</li>
<li>
<b>R8GE_FS</b> factors and solves a R8GE system.
</li>
<li>
<b>R8GE_FS_NEW</b> factors and solves a R8GE system.
</li>
<li>
<b>R8GE_FSS</b> factors and solves multiple R8GE systems.
</li>
<li>
<b>R8GE_FSS_NEW</b> factors and solves multiple R8GE systems.
</li>
<li>
<b>R8GE_IDENTITY</b> sets a R8GE matrix to the identity.
</li>
<li>
<b>R8GE_ILU</b> produces the incomplete LU factors of a R8GE matrix.
</li>
<li>
<b>R8GE_INDICATOR</b> sets up a R8GE indicator matrix.
</li>
<li>
<b>R8GE_INVERSE</b> computes the inverse of a R8GE matrix factored by R8GE_FA.
</li>
<li>
<b>R8GE_ML</b> computes A * x or A' * x, using R8GE_FA factors.
</li>
<li>
<b>R8GE_MU</b> computes A * x or A' * x, using R8GE_TRF factors.
</li>
<li>
<b>R8GE_MXM</b> multiplies two R8GE matrices.
</li>
<li>
<b>R8GE_MXV</b> multiplies a R8GE matrix times a vector.
</li>
<li>
<b>R8GE_NP_DET</b> computes the determinant of a matrix factored by R8GE_NP_FA.
</li>
<li>
<b>R8GE_NP_FA</b> factors a R8GE matrix by nonpivoting Gaussian elimination.
</li>
<li>
<b>R8GE_NP_INVERSE</b> computes the inverse of a matrix factored by R8GE_NP_FA.
</li>