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<html>
<head>
<title>
ASA007 - Inverse of a Symmetric Positive Definite Matrix
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ASA007 <br> Inverse of a Symmetric Positive Definite Matrix
</h1>
<hr>
<p>
<b>ASA007</b>
is a C++ library which
computes the inverse of a symmetric positive definite matrix,
by Michael Healy.
</p>
<p>
<b>ASA007</b> is Applied Statistics Algorithm 7. Source code for many
Applied Statistics Algorithms is available through
<a href = "http://lib.stat.cmu.edu/apstat">STATLIB</a>.
</p>
<p>
The algorithm implemented here uses a compressed storage for both the
matrix <b>A</b> and the factor <b>U</b>. This saves some storage, but
can make computations a little awkward.
</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>ASA007</b> is available in
<a href = "../../c_src/asa007/asa007.html">a C version</a> and
<a href = "../../cpp_src/asa007/asa007.html">a C++ version</a> and
<a href = "../../f77_src/asa007/asa007.html">a FORTRAN77 version</a> and
<a href = "../../f_src/asa007/asa007.html">a FORTRAN90 version</a> and
<a href = "../../m_src/asa007/asa007.html">a MATLAB version</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/asa006/asa006.html">
ASA006</a>,
a C++ library which
computes the Cholesky factorization of a symmetric positive definite
matrix. A version of this routine is used by ASA007.
</p>
<p>
<a href = "../../cpp_src/asa047/asa047.html">
ASA047</a>,
a C++ library which
implements the Nelder-Mead minimization algorithm,
and uses a version of ASA007 for the computation.
</p>
<p>
<a href = "../../f77_src/lapack_examples/lapack_examples.html">
LAPACK_EXAMPLES</a>,
a FORTRAN77 program which
demonstrates the use of the LAPACK linear algebra library.
</p>
<p>
<a href = "../../cpp_src/linpack_d/linpack_d.html">
LINPACK_D</a>,
a C++ library which
includes routines to compute the inverse of symmetric positive matrix
using double precision real arithmetic.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Michael Healy
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Michael Healy,<br>
Algorithm AS 7:
Inversion of a Positive Semi-Definite Symmetric Matrix,<br>
Applied Statistics,<br>
Volume 17, Number 2, 1968, pages 198-199.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "asa007.cpp">asa007.cpp</a>, the source code.
</li>
<li>
<a href = "asa007.hpp">asa007.hpp</a>, the include file.
</li>
<li>
<a href = "asa007.sh">asa007.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "asa007_prb.cpp">asa007_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "asa007_prb.sh">asa007_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "asa007_prb_output.txt">asa007_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CHOLESKY</b> computes the Cholesky factorization of a PDS matrix.
</li>
<li>
<b>SYMINV</b> computes the inverse of a symmetric matrix.
</li>
<li>
<b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 14 December 2011.
</i>
<!-- John Burkardt -->
</body>
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</html>