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<html>
<head>
<title>
ASA053 - Wishart Variate Generator
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ASA053 <br> Wishart Variate Generator
</h1>
<hr>
<p>
<b>ASA053</b>
is a C++ library which
returns samples from the Wishart distribution.
</p>
<p>
As far as I can tell, there are two mistakes in the printed text
of the algorithm; one involves incorrectly determining the number
of degrees of freedom for the ChiSquared distribution; the
other omits an absolute value sign when inverting the Wilson-Hilferty
formula, so that square roots of negative values are occasionally
requested. These mistakes have been corrected here.
</p>
<p>
Source code for many Applied Statistics Algorithms is available through
<a href = "http://lib.stat.cmu.edu/apstat">STATLIB</a>.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files 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>ASA053</b> is available in
<a href = "../../c_src/asa053/asa053.html">a C version</a> and
<a href = "../../cpp_src/asa053/asa053.html">a C++ version</a> and
<a href = "../../f77_src/asa053/asa053.html">a FORTRAN77 version</a> and
<a href = "../../f_src/asa053/asa053.html">a FORTRAN90 version</a> and
<a href = "../../m_src/asa053/asa053.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/wishart/wishart.html">
WISHART</a>,
a C++ library which
produces sample matrices from the Wishart or Bartlett distributions,
useful for sampling random covariance matrices.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Stanley Sawyer,<br>
Wishart Distributions and Inverse-Wishart Sampling,<br>
Washington University,<br>
30 April 2007, 12 pages.
</li>
<li>
William Smith, Ronald Hocking,<br>
Algorithm AS 53, Wishart Variate Generator,<br>
Applied Statistics,<br>
Volume 21, Number 3, pages 341-345, 1972.
</li>
</ol>
</p>
<h3 align = "center">
Original Source Code:
</h3>
<p>
<ul>
<li>
<a href = "asa053_original.f">asa053_original.f</a>,
the original text of the source code. Note that the
line "DF = N - I + 1" is believed (by me) to be incorrect,
and is replaced in the present version by "DF = NP - I + 1".
</li>
</ul>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "asa053.cpp">asa053.cpp</a>, the source code.
</li>
<li>
<a href = "asa053.hpp">asa053.hpp</a>, the include file.
</li>
<li>
<a href = "asa053.sh">asa053.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "asa053_prb.cpp">asa053_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "asa053_prb.sh">asa053_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "asa053_prb_output.txt">asa053_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8PP_PRINT</b> prints an R8PP matrix.
</li>
<li>
<b>R8PP_PRINT_SOME</b> prints some of an R8PP matrix.
</li>
<li>
<b>R8UTP_PRINT</b> prints an R8UTP matrix.
</li>
<li>
<b>R8UTP_PRINT_SOME</b> prints some of an R8UTP matrix.
</li>
<li>
<b>RNORM</b> returns two independent standard random normal deviates.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>WSHRT</b> returns a random Wishart variate.
</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 16 April 2014.
</i>
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