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<html>
<head>
<title>
TOMS659 - The Sobol Quasirandom Sequence
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS659 <br> The Sobol Quasirandom Sequence
</h1>
<hr>
<p>
<b>TOMS659</b> is a FORTRAN90 library which
computes elements of the Sobol quasirandom sequence.
</p>
<p>
A quasirandom or low discrepancy sequence, such as the Faure,
Halton, Hammersley, Niederreiter or Sobol sequences, is
"less random" than a pseudorandom number sequence, but
more useful for such tasks as approximation of integrals in
higher dimensions, and in global optimization.
This is because low discrepancy sequences tend to sample
space "more uniformly" than random numbers. Algorithms
that use such sequences may have superior convergence.
</p>
<p>
The original, true, correct version of ACM TOMS Algorithm 659
is available through ACM:
<a href = "http://www.acm.org/pubs/calgo/">
http://www.acm.org/pubs/calgo</a>
or NETLIB:
<a href = "http://www.netlib.org/toms/index.html">
http://www.netlib.org/toms/index.html</a>.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TOMS659</b> is available in
<a href = "../../f77_src/toms659/toms659.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms659/toms659.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cvt/cvt.html">
CVT</a>,
a FORTRAN90 library which
computes elements of a Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../f_src/faure/faure.html">
FAURE</a>,
a FORTRAN90 library which
computes elements of a Faure quasirandom sequence.
</p>
<p>
<a href = "../../f_src/grid/grid.html">
GRID</a>,
a FORTRAN90 library which
computes elements of a grid dataset.
</p>
<p>
<a href = "../../cpp_src/gsl/gsl.html">
GSL</a>,
a C++ library which
includes routines to compute
elements of the Sobol sequence.
</p>
<p>
<a href = "../../f_src/halton/halton.html">
HALTON</a>,
a FORTRAN90 library which
computes elements of a Halton
quasirandom sequence.
</p>
<p>
<a href = "../../f_src/hammersley/hammersley.html">
HAMMERSLEY</a>,
a FORTRAN90 library which
computes elements of a Hammersley
quasirandom sequence.
</p>
<p>
<a href = "../../f_src/hex_grid/hex_grid.html">
HEX_GRID</a>,
a FORTRAN90 library which
computes elements of a hexagonal
grid dataset.
</p>
<p>
<a href = "../../f_src/hex_grid_angle/hex_grid_angle.html">
HEX_GRID_ANGLE</a>,
a FORTRAN90 library which
computes elements of an angled
hexagonal grid dataset.
</p>
<p>
<a href = "../../f_src/ihs/ihs.html">
IHS</a>,
a FORTRAN90 library which
computes elements of an
improved distributed Latin hypercube dataset.
</p>
<p>
<a href = "../../f_src/latin_center/latin_center.html">
LATIN_CENTER</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube
dataset, choosing center points.
</p>
<p>
<a href = "../../f_src/latin_edge/latin_edge.html">
LATIN_EDGE</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube
dataset, choosing edge points.
</p>
<p>
<a href = "../../f_src/latin_random/latin_random.html">
LATIN_RANDOM</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube
dataset, choosing points at random.
</p>
<p>
<a href = "../../f_src/lcvt/lcvt.html">
LCVT</a>,
a FORTRAN90 library which
computes a latinized Centroidal Voronoi
Tessellation.
</p>
<p>
<a href = "../../f_src/niederreiter2/niederreiter2.html">
NIEDERREITER2</a>,
a FORTRAN90 library which
computes elements of a Niederreiter
quasirandom sequence with base 2.
</p>
<p>
<a href = "../../f_src/sobol/sobol.html">
SOBOL</a>,
a FORTRAN90 library which
computes elements of the Sobol sequence.
</p>
<p>
<a href = "../../f_src/sobol_dataset/sobol_dataset.html">
SOBOL_DATASET</a>,
a FORTRAN90 program which
specifies a Sobol
dataset and writing it to a file.
</p>
<p>
<a href = "../../f_src/toms647/toms647.html">
TOMS647</a>,
a FORTRAN90 library which
is a version of ACM TOMS algorithm 647,
for evaluating Faure, Halton and Sobol sequences.
</p>
<p>
<a href = "../../f_src/uniform/uniform.html">
UNIFORM</a>,
a FORTRAN90 library which
computes elements of a uniform
pseudorandom sequence.
</p>
<p>
<a href = "../../f_src/van_der_corput/van_der_corput.html">
VAN_DER_CORPUT</a>,
a FORTRAN90 library which
computes elements of a van der Corput
quasirandom sequence.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
IA Antonov, VM Saleev,<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>
Stephen Joe, Frances Kuo<br>
Remark on Algorithm 659:
Implementing Sobol's Quasirandom Sequence Generator,<br>
ACM Transactions on Mathematical Software,<br>
Volume 29, Number 1, pages 49-57, March 2003.
</li>
<li>
Harald Niederreiter,<br>
Random Number Generation and quasi-Monte Carlo Methods,<br>
SIAM, 1992,<br>
ISBN13: 978-0-898712-95-7.
</li>
<li>
William Press, Brian Flannery, Saul Teukolsky, William Vetterling,<br>
Numerical Recipes in FORTRAN: The Art of Scientific Computing,<br>
Second Edition,<br>
Cambridge University Press, 1992,<br>
LC: QA297.N866,<br>
ISBN: 0-521-43064-X.
</li>
<li>
Ilya Sobol,<br>
USSR Computational Mathematics and Mathematical Physics,<br>
Volume 16, pages 236-242, 1977.
</li>
<li>
Ilya Sobol, YL 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 = "toms659.f90">toms659.f90</a>,
the source code;
</li>
<li>
<a href = "toms659.sh">toms659.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms659_prb.f90">toms659_prb.f90</a>,
a sample calling program;
</li>
<li>
<a href = "toms659_prb_input.txt">toms659_prb_input.txt</a>,
an input file;
</li>
<li>
<a href = "toms659_prb.sh">toms659_prb.sh</a>,
commands to compile, link and run the test program;
</li>
<li>
<a href = "toms659_prb_output.txt">toms659_prb_output.txt</a>,
output from a run of the test program;
</li>
<li>
<a href = "toms659_prb.output_expected.txt">toms659_prb.output_expected.txt</a>,
the expected output from the run;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BDSOBL</b> initializes labelled common block /SOBDAT/.
</li>
<li>
<b>INSOBL</b> initializes the Sobol sequence computation.
</li>
<li>
<b>GOSOBL</b> generates a new quasirandom vector with each call.
</li>
<li>
<b>EXOR</b> calculates the exclusive OR of its two input parameters.
</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 22 January 2011.
</i>
<!-- John Burkardt -->
</body>
</html>