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<html>
<head>
<title>
NORMAL_DATASET - Generate Multivariate Normal Random Datasets
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
NORMAL_DATASET <br> Generate Multivariate Normal Random Datasets
</h1>
<hr>
<p>
<b>NORMAL_DATASET</b>
is a C++ program which
creates a multivariate normal random dataset and writes it to a file.
</p>
<p>
The multivariate normal distribution for the M dimensional vector X
has the form:
<pre>
pdf(X) = (2*pi*det(A))**(-M/2) * exp(-0.5*(X-MU)'*inverse(A)*(X-MU))
</pre>
where MU is the mean vector, and A is a positive definite symmetric
matrix called the variance-covariance matrix.
</p>
<p>
To create X, an MxN matrix containing N samples from this distribution,
it is only necessary to
<ol>
<li>
create an MxN vector Y, each of whose elements is a sample of the
1-dimensional normal distribution with mean 0 and variance 1;
</li>
<li>
determine the upper triangular Cholesky factor R of the matrix A, so that
A = R' * R;
</li>
<li>
compute X = MU + R' * Y.
</li>
</ol>
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>normal_dataset</b> <i>m</i> <i>n</i> <i>seed</i> <i>mu</i> <i>a</i>
</blockquote>
where
<ul>
<li>
<i>m</i> is the spatial dimension;
</li>
<li>
<i>n</i> is the number of points to generate;
</li>
<li>
<i>seed</i> is the initial seed value;
</li>
<li>
<i>mu</i> is the mean vector, of length <i>m</i>;
</li>
<li>
<i>a</i> is the positive definite symmetric variance-covariance matrix
of dimension <i>m</i> by <i>m</i>.
</li>
</ul>
The data is written to the file <b>normal_<i>m</i>_<i>n</i>.txt</b>.
</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>NORMAL_DATASET</b> is available in
<a href = "../../cpp_src/normal_dataset/normal_dataset.html">a C++ version</a> and
<a href = "../../f_src/normal_dataset/normal_dataset.html">a FORTRAN90 version</a> and
<a href = "../../m_src/normal_dataset/normal_dataset.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/cvt_dataset/cvt_dataset.html">
CVT_DATASET</a>,
a C++ program which
computes a Centroidal Voronoi Tessellation and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/faure_dataset/faure_dataset.html">
FAURE_DATASET</a>,
a C++ program which
creates a Faure quasirandom dataset;
</p>
<p>
<a href = "../../cpp_src/grid_dataset/grid_dataset.html">
GRID_DATASET</a>,
a C++ program which
creates a grid sequence and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/halton_dataset/halton_dataset.html">
HALTON_DATASET</a>,
a C++ program which
creates a Halton sequence and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/hammersley_dataset/hammersley_dataset.html">
HAMMERSLEY_DATASET</a>,
a C++ program which
creates a Hammersley sequence and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/hex_grid_dataset/hex_grid_dataset.html">
HEX_GRID_DATASET</a>,
a C++ program which
creates a hexagonal grid dataset and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/ihs_dataset/ihs_dataset.html">
IHS_DATASET</a>,
a C++ program which
creates an improved distributed Latin hypercube dataset and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/latin_center_dataset/latin_center_dataset.html">
LATIN_CENTER_DATASET</a>,
a C++ program which
creates a Latin Center Hypercube dataset;
</p>
<p>
<a href = "../../cpp_src/latin_edge_dataset/latin_edge_dataset.html">
LATIN_EDGE_DATASET</a>,
a C++ program which
creates a Latin Edge Hypercube dataset;
</p>
<p>
<a href = "../../cpp_src/latin_random_dataset/latin_random_dataset.html">
LATIN_RANDOM_DATASET</a>,
a C++ program which
creates a Latin Random Hypercube dataset;
</p>
<p>
<a href = "../../cpp_src/lcvt_dataset/lcvt_dataset.html">
LCVT_DATASET</a>,
a C++ program which
computes a latinized Centroidal Voronoi Tessellation and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/niederreiter2_dataset/niederreiter2_dataset.html">
NIEDERREITER2_DATASET</a>,
a C++ program which
creates a Niederreiter quasirandom dataset with base 2;
</p>
<p>
<a href = "../../cpp_src/normal/normal.html">
NORMAL</a>,
a C++ library which
computes normally distributed pseudorandom values.
</p>
<p>
<a href = "../../cpp_src/sobol_dataset/sobol_dataset.html">
SOBOL_DATASET</a>,
a C++ program which
computes a Sobol quasirandom sequence and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/uniform_dataset/uniform_dataset.html">
UNIFORM_DATASET</a>,
a C++ program which
generates a dataset of uniform pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../cpp_src/van_der_corput_dataset/van_der_corput_dataset.html">
VAN_DER_CORPUT_DATASET</a>,
a C++ program which
creates a van der Corput quasirandom sequence and writes it to a file.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Paul Bratley, Bennett Fox, Linus Schrage,<br>
A Guide to Simulation,<br>
Springer Verlag, pages 201-202, 1983.
</li>
<li>
Donald Knuth, <br>
The Art of Computer Programming,<br>
Volume 2: Seminumerical Algorithms,<br>
Addison Wesley, 1969.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "normal_dataset.cpp">normal_dataset.cpp</a>,
the source code.
</li>
<li>
<a href = "normal_dataset.sh">normal_dataset.sh</a>,
commands to compile and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples:
</h3>
<p>
<ul>
<li>
<a href = "normal_2_1000.txt">normal_2_1000.txt</a>,
is the file created in response to the command <pre>
<b>"normal_dataset 2 1000 123456789 1 2 1 0 0 3"</b>.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for NORMAL_DATASET.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>MULTINORMAL_SAMPLE</b> samples a multivariate normal distribution.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file with no header.
</li>
<li>
<b>R8PO_FA</b> factors a R8PO matrix.
</li>
<li>
<b>R8VEC_NORMAL_01_NEW</b> returns a unit pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01_NEW</b> returns a new unit pseudorandom R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 09 December 2009.
</i>
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