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<html>
<head>
<title>
LINPACK_S - Linear Algebra Library - Single Precision Real
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LINPACK_S <br> Linear Algebra Library <br> Single Precision Real
</h1>
<hr>
<p>
<b>LINPACK_S</b>
is a FORTRAN90 library which
solves systems of linear
equations for a variety of matrix types and storage modes.
</p>
<p>
<b>LINPACK</b> has officially been superseded by the
LAPACK library. The LAPACK
library uses more modern algorithms and code structure. However,
the LAPACK library can be extraordinarily complex; what is done
in a single <b>LINPACK</b> routine may correspond to 10 or 20 utility
routines in LAPACK. This is fine if you treat LAPACK as a black
box. But if you wish to learn how the algorithm works, or
to adapt it, or to convert the code to another language, this
is a real drawback. This is one reason I still keep a copy
of <b>LINPACK</b> around.
</p>
<p>
Versions of <b>LINPACK</b> in various arithmetic precisions are available
through <a href = "http://www.netlib.org/">the NETLIB web site</a>.
</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">
Language:
</h3>
<p>
<b>LINPACK_S</b> is available in
<a href = "../../c_src/linpack_s/linpack_s.html">a C version</a> and
<a href = "../../cpp_src/linpack_s/linpack_s.html">a C++ version</a> and
<a href = "../../f77_src/linpack_s/linpack_s.html">a FORTRAN77 version</a> and
<a href = "../../f_src/linpack_s/linpack_s.html">a FORTRAN90 version</a> and
<a href = "../../m_src/linpack_s/linpack_s.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/blas1_s/blas1_s.html">
BLAS1_S</a>,
a FORTRAN90 library which
contains basic linear algebra routines for vector-vector operations,
using single precision real arithmetic.
</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_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/linpack_c/linpack_c.html">
LINPACK_C</a>,
a FORTRAN90 library which
solves linear systems using single precision complex arithmetic;
</p>
<p>
<a href = "../../f_src/linpack_d/linpack_d.html">
LINPACK_D</a>,
a FORTRAN90 library which
solves linear systems using double precision real arithmetic;
</p>
<p>
<a href = "../../f_src/linpack_z/linpack_z.html">
LINPACK_Z</a>,
a FORTRAN90 library which
solves linear systems using double precision complex arithmetic;
</p>
<p>
<a href = "../../f_src/linplus/linplus.html">
LINPLUS</a>,
a FORTRAN90 library which
carries out simple manipulations of matrices in a variety of formats.
</p>
<p>
<a href = "../../f_src/nms/nms.html">
NMS</a>,
a FORTRAN90 library which
includes <b>LINPACK</b>.
</p>
<p>
<a href = "../../f_src/slatec/slatec.html">
SLATEC</a>,
a FORTRAN90 library which
collects together a number of standard numerical libraries.
</p>
<p>
<a href = "../../f_src/svd_demo/svd_demo.html">
SVD_DEMO</a>,
a FORTRAN90 program which
demonstrates the singular value decomposition for a simple example.
</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>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<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>
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>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "linpack_s.f90">linpack_s.f90</a>,
the source code;
</li>
<li>
<a href = "linpack_s.sh">
linpack_s.sh</a>, commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "linpack_s_prb.f90">
linpack_s_prb.f90</a>, the calling program;
</li>
<li>
<a href = "linpack_s_prb.sh">
linpack_s_prb.sh</a>, commands to run the calling program;
</li>
<li>
<a href = "linpack_s_prb_output.txt">linpack_s_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>SCHDC</b> computes the Cholesky decomposition of a positive definite matrix.
</li>
<li>
<b>SCHDD</b> downdates an augmented Cholesky decomposition.
</li>
<li>
<b>SCHEX</b> updates the Cholesky factorization of a positive definite matrix.
</li>
<li>
<b>SCHUD</b> updates an augmented Cholesky decomposition.
</li>
<li>
<b>SGBCO</b> factors a real band matrix and estimates its condition.
</li>
<li>
<b>SGBDI</b> computes the determinant of a band matrix factored by SGBCO or SGBFA.
</li>
<li>
<b>SGBFA</b> factors a real band matrix by elimination.
</li>
<li>
<b>SGBSL</b> solves a real banded system factored by SGBCO or SGBFA.
</li>
<li>
<b>SGECO</b> factors a real matrix and estimates its condition number.
</li>
<li>
<b>SGEDI</b> computes the determinant and inverse of a matrix factored by SGECO or SGEFA.
</li>
<li>
<b>SGEFA</b> factors a real general matrix.
</li>
<li>
<b>SGESL</b> solves a real general linear system A * X = B.
</li>
<li>
<b>SGTSL</b> solves a general tridiagonal linear system.
</li>
<li>
<b>SPBCO</b> factors a real symmetric positive definite banded matrix.
</li>
<li>
<b>SPBDI</b> computes the determinant of a matrix factored by SPBCO or SPBFA.
</li>
<li>
<b>SPBFA</b> factors a real symmetric positive definite matrix stored in band form.
</li>
<li>
<b>SPBSL</b> solves a real SPD band system factored by SPBCO or SPBFA.
</li>
<li>
<b>SPOCO</b> factors a real symmetric positive definite matrix and estimates its condition.
</li>
<li>
<b>SPODI</b> computes the determinant and inverse of a certain matrix.
</li>
<li>
<b>SPOFA</b> factors a real symmetric positive definite matrix.
</li>
<li>
<b>SPOSL</b> solves a linear system factored by SPOCO or SPOFA.
</li>
<li>
<b>SPPCO</b> factors a real symmetric positive definite matrix in packed form.
</li>
<li>
<b>SPPDI</b> computes the determinant and inverse of a matrix factored by SPPCO or SPPFA.
</li>
<li>
<b>SPPFA</b> factors a real symmetric positive definite matrix in packed form.
</li>
<li>
<b>SPPSL</b> solves a real symmetric positive definite system factored by SPPCO or SPPFA.
</li>
<li>
<b>SPTSL</b> solves a positive definite tridiagonal linear system.
</li>
<li>
<b>SQRDC</b> computes the QR factorization of a real rectangular matrix.
</li>
<li>
<b>SQRSL</b> computes transformations, projections, and least squares solutions.
</li>
<li>
<b>SSICO</b> factors a real symmetric matrix and estimates its condition.
</li>
<li>
<b>SSIDI</b> computes the determinant, inertia and inverse of a real symmetric matrix.
</li>
<li>
<b>SSIFA</b> factors a real symmetric matrix.
</li>
<li>
<b>SSISL</b> solves a real symmetric system factored by SSIFA.
</li>
<li>
<b>SSPCO</b> factors a real symmetric matrix stored in packed form.
</li>
<li>
<b>SSPDI</b> computes the determinant, inertia and inverse of a real symmetric matrix.
</li>
<li>
<b>SSPFA</b> factors a real symmetric matrix stored in packed form.
</li>
<li>
<b>SSPSL</b> solves the real symmetric system factored by SSPFA.
</li>
<li>
<b>SSVDC</b> computes the singular value decomposition of a real rectangular matrix.
</li>
<li>
<b>STRCO</b> estimates the condition of a real triangular matrix.
</li>
<li>
<b>STRDI</b> computes the determinant and inverse of a real triangular matrix.
</li>
<li>
<b>STRSL</b> solves triangular linear systems.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 24 June 2009.
</i>
<!-- John Burkardt -->
</body>
</html>