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sobol_dataset.html
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<html>
<head>
<title>
SOBOL_DATASET - Generate Sobol Datasets
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SOBOL_DATASET <br> Generate Sobol Datasets
</h1>
<hr>
<p>
<b>SOBOL_DATASET</b>
is a MATLAB program which
creates a Sobol dataset.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<i>r</i> = <b>sobol_dataset</b> ( <i>m</i>, <i>n</i>, <i>skip</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>skip</i> is the initial number of points to skip over.
The value of <i>skip</i> is used to allow the sequence to
"warm up". One common strategy is to set <i>skip</i> to
the smallest power of 2 which is equal to or greater than <i>n</i>.
</li>
<li>
<i>r</i> is the computed <i>m</i> by <i>n</i> sequence.
<li>
</ul>
The data is written to the file <b>sobol_<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>SOBOL_DATASET</b> is available in
<a href = "../../cpp_src/sobol_dataset/sobol_dataset.html">a C++ version</a> and
<a href = "../../f_src/sobol_dataset/sobol_dataset.html">a FORTRAN90 version</a> and
<a href = "../../m_src/sobol_dataset/sobol_dataset.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/faure_dataset/faure_dataset.html">
FAURE_DATASET</a>,
a MATLAB program which
creates a Faure quasirandom dataset;
</p>
<p>
<a href = "../../m_src/grid_dataset/grid_dataset.html">
GRID_DATASET</a>,
a MATLAB program which
creates a grid sequence and writes it to a file.
</p>
<p>
<a href = "../../m_src/latin_center_dataset/latin_center_dataset.html">
LATIN_CENTER_DATASET</a>,
a MATLAB program which
creates a Latin Center Hypercube dataset;
</p>
<p>
<a href = "../../m_src/latin_edge_dataset/latin_edge_dataset.html">
LATIN_EDGE_DATASET</a>,
a MATLAB program which
creates a Latin Edge Hypercube dataset;
</p>
<p>
<a href = "../../m_src/latin_random_dataset/latin_random_dataset.html">
LATIN_RANDOM_DATASET</a>,
a MATLAB program which
creates a Latin Random Hypercube dataset;
</p>
<p>
<a href = "../../m_src/niederreiter2_dataset/niederreiter2_dataset.html">
NIEDERREITER2_DATASET</a>,
a MATLAB program which
creates a Niederreiter quasirandom dataset with base 2;
</p>
<p>
<a href = "../../m_src/normal_dataset/normal_dataset.html">
NORMAL_DATASET</a>,
a MATLAB program which
generates a dataset of multivariate normal pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../datasets/sobol/sobol.html">
SOBOL</a>,
a dataset directory which
contains sample Sobol datasets
created by <b>SOBOL_DATASET</b>.
</p>
<p>
<a href = "../../m_src/sobol/sobol.html">
SOBOL</a>,
a MATLAB library which
computes elements of a Sobol quasirandom sequence.
</p>
<p>
<a href = "../../m_src/uniform_dataset/uniform_dataset.html">
UNIFORM_DATASET</a>,
a MATLAB program which
generates a dataset of multivariate uniform pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../m_src/van_der_corput_dataset/van_der_corput_dataset.html">
VAN_DER_CORPUT_DATASET</a>,
a MATLAB program which
creates a van der Corput quasirandom sequence and writes it to a file.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
IA Antonov, VM Saleev,<br>
An Economic Method of Computing LP Tau-Sequences,<br>
USSR Computational Mathematics and Mathematical Physics,<br>
Volume 19, 1980, pages 252 - 256.
</li>
<li>
Paul Bratley, Bennett Fox,<br>
Algorithm 659:
Implementing Sobol's Quasirandom Sequence Generator,<br>
ACM Transactions on Mathematical Software,<br>
Volume 14, Number 1, pages 88-100, 1988.
</li>
<li>
Paul Bratley, Bennett Fox, Linus Schrage,<br>
A Guide to Simulation,<br>
Springer Verlag, pages 201-202, 1983.
</li>
<li>
Paul Bratley, Bennett Fox, Harald Niederreiter,<br>
Implementation and Tests of Low Discrepancy Sequences,<br>
ACM Transactions on Modeling and Computer Simulation,<br>
Volume 2, Number 3, pages 195-213, 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, pages 362-376, 1986.
</li>
<li>
Harald Niederreiter,<br>
Random Number Generation and quasi-Monte Carlo Methods,<br>
SIAM, 1992.
</li>
<li>
William Press, Brian Flannery, Saul Teukolsky, William Vetterling,<br>
Numerical Recipes: The Art of Scientific Computing,<br>
Cambridge University Press.
</li>
<li>
Ilya Sobol,<br>
USSR Computational Mathematics and Mathematical Physics,<br>
Volume 16, pages 236-242, 1977.
</li>
<li>
Ilya Sobol, Levitan, <br>
The Production of Points Uniformly Distributed in a Multidimensional
Cube (in Russian),<br>
Preprint IPM Akad. Nauk SSSR, <br>
Number 40, Moscow 1976.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sobol_dataset.m">sobol_dataset.m</a>,
the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sobol_02_00100.txt">sobol_02_00100.txt</a>,
the Sobol dataset of dimension 2, computing 100 points, after skipping 128 points.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 12 December 2009.
</i>
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