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<html>
<head>
<title>
LATIN_EDGE_DATASET - Generate Latin Edge Square Datasets
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LATIN_EDGE_DATASET <br> Generate Latin Edge Square Datasets
</h1>
<hr>
<p>
<b>LATIN_EDGE_DATASET</b>
is a FORTRAN90 program which
creates a Latin Edge Square dataset.
</p>
<p>
A Latin square, in <b>M</b> dimensional space, with <b>N</b> points,
can be thought of as being constructed by dividing each of the
<b>M</b> coordinate dimensions into <b>N</b> equal intervals.
The I-th coordinates of the <b>N</b> subsquares are defined
by assigning each possible value exactly once to one subsquare.
Such a set is called a Latin Square.
</p>
<p>
Now suppose that, in each spatial coordinate, we label successive
squares by the values 0, 1/N-1, 2/N-1, ..., (N-2)/(N-1), 1.
Then each element of our Latin Edge dataset is a vector of N such
values, and our dataset contains N such vectors.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>latin_edge_dataset</b> <i>m</i> <i>n</i> <i>seed</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>
</ul>
The data is written to the file <b>latin_edge_<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>LATIN_EDGE_DATASET</b> is available in
<a href = "../../cpp_src/latin_edge_dataset/latin_edge_dataset.html">a C++ version</a> and
<a href = "../../f_src/latin_edge_dataset/latin_edge_dataset.html">a FORTRAN90 version</a> and
<a href = "../../m_src/latin_edge_dataset/latin_edge_dataset.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/faure_dataset/faure_dataset.html">
FAURE_DATASET</a>,
a FORTRAN90 program which
creates a Faure quasirandom dataset;
</p>
<p>
<a href = "../../f_src/grid_dataset/grid_dataset.html">
GRID_DATASET</a>,
a FORTRAN90 program which
creates a grid sequence and writes it to a file.
</p>
<p>
<a href = "../../f_src/latin_center_dataset/latin_center_dataset.html">
LATIN_CENTER_DATASET</a>,
a FORTRAN90 program which
creates a Latin Center Hypercube dataset;
</p>
<p>
<a href = "../../f_src/latin_edge/latin_edge.html">
LATIN_EDGE</a>,
a FORTRAN90 library which
computes the
Latin Edge squares requested by <b>LATIN_EDGE_DATASET.</b>
</p>
<p>
<a href = "../../datasets/latin_edge/latin_edge.html">
LATIN_EDGE</a>,
a dataset directory which
contains sample datasets created
by <b>LATIN_EDGE_DATASET</b>.
</p>
<p>
<a href = "../../f_src/latin_random_dataset/latin_random_dataset.html">
LATIN_RANDOM_DATASET</a>,
a FORTRAN90 program which
creates a Latin Random Hypercube dataset;
</p>
<p>
<a href = "../../f_src/niederreiter2_dataset/niederreiter2_dataset.html">
NIEDERREITER2_DATASET</a>,
a FORTRAN90 program which
creates a Niederreiter quasirandom dataset with base 2;
</p>
<p>
<a href = "../../f_src/normal_dataset/normal_dataset.html">
NORMAL_DATASET</a>,
a FORTRAN90 program which
generates a dataset of multivariate normal pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../f_src/sobol_dataset/sobol_dataset.html">
SOBOL_DATASET</a>,
a FORTRAN90 program which
computes a Sobol quasirandom sequence and writes it to a file.
</p>
<p>
<a href = "../../f_src/uniform_dataset/uniform_dataset.html">
UNIFORM_DATASET</a>,
a FORTRAN90 program which
generates a dataset of multivariate uniform pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../f_src/van_der_corput_dataset/van_der_corput_dataset.html">
VAN_DER_CORPUT_DATASET</a>,
a FORTRAN90 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>
CJ Colbourn, JH Dinitz,<br>
CRC Handbook of Combinatorial Design,<br>
CRC, 1996.
</li>
<li>
Bennett Fox,<br>
Algorithm 647:<br>
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>
Michael McKay, William Conover, Richard Beckman,<br>
A Comparison of Three Methods for Selecting Values of Input
Variables in the Analysis of Output From a Computer Code,<br>
Technometrics,<br>
Volume 21, pages 239-245, 1979.
</li>
<li>
Albert Nijenhuis, Herbert Wilf,<br>
Combinatorial Algorithms,<br>
Academic Press, 1978, second edition,<br>
ISBN 0-12-519260-6.
</li>
<li>
Herbert Ryser,<br>
Combinatorial Mathematics,<br>
Mathematical Association of America, 1963.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "latin_edge_dataset.f90">latin_edge_dataset.f90</a>,
the source code.
</li>
<li>
<a href = "latin_edge_dataset.sh">latin_edge_dataset.sh</a>,
commands to compile and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Data:
</h3>
<p>
<ul>
<li>
<a href = "latin_edge_02_00100.txt">latin_edge_02_00100.txt</a>,
is the file created by the command <b>latin_edge_dataset 2 100 12346789</b>.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for LATIN_EDGE_DATASET.
</li>
<li>
<b>GET_SEED</b> returns a seed for the random number generator.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</li>
<li>
<b>LATIN_EDGE</b> returns edge points in a Latin square.
</li>
<li>
<b>PERM_UNIFORM</b> selects a random permutation of N objects.
</li>
<li>
<b>R4_UNIFORM_01</b> returns a unit pseudorandom R4.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>S_TO_I4</b> reads an integer value from a string.
</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 = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 14 December 2009.
</i>
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