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latin_random.html
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latin_random.html
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<html>
<head>
<title>
LATIN_RANDOM - Latin Random Squares in M dimensions
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LATIN_RANDOM <br> Latin Random Squares in M dimensions
</h1>
<hr>
<p>
<b>LATIN_RANDOM</b>
is a FORTRAN90 library which
makes Latin random squares.
</p>
<p>
A Latin square is a selection of one point from each row and
column of a square matrix or table. In <b>M</b> dimensions, the
corresponding item is a set of <b>N</b> points, where, in each dimension,
there is exactly one point whose coordinates are in a given
"column" or range of values. To emphasize the
use of higher dimensions, these objects are sometimes called
Latin hypersquares.
</p>
<p>
A Latin Random Square (I just made up this name) is a set of
<b>N</b> points, where one point is taken at random from each of the
subsquares of a Latin Square. These points may be regarded as
an <b>M</b> dimensional quasirandom pointset.
</p>
<p>
Here is an image of a Latin random grid with spatial
dimension <b>M</b> = 2
and number of points <b>N</b> = 10.
</p>
<img src = "../../datasets/latin_random/latin_random_02_00010.png"
height = "440"
width = "340">
<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_RANDOM</b> is available in
<a href = "../../cpp_src/latin_random/latin_random.html">a C++ version</a> and
<a href = "../../f_src/latin_random/latin_random.html">a FORTRAN90 version</a> and
<a href = "../../m_src/latin_random/latin_random.html">a MATLAB 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 = "../../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_cover/latin_cover.html">
LATIN_COVER</a>,
a FORTRAN90 library which
produces N Latin squares which cover an NxN square.
</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 = "../../datasets/latin_random/latin_random.html">
LATIN_RANDOM</a>,
a dataset directory which
contains a number of examples of datasets created by <b>LATIN_RANDOM</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/lattice_rule/lattice_rule.html">
LATTICE_RULE</a>,
a FORTRAN90 library which
approximates multidimensional integrals using lattice rules.
</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/normal/normal.html">
NORMAL</a>,
a FORTRAN90 library which
computes elements of a
sequence of pseudorandom normally distributed values.
</p>
<p>
<a href = "../../f_src/sobol/sobol.html">
SOBOL</a>,
a FORTRAN90 library which
computes elements of a Sobol quasirandom sequence.
</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>
Paul Bratley, Bennett Fox, Linus Schrage,<br>
A Guide to Simulation,<br>
Springer Verlag, pages 201-202, 1983.
</li>
<li>
C J Colbourn and J H 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_random.f90">latin_random.f90</a>, the source code.
</li>
<li>
<a href = "latin_random.sh">latin_random.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "latin_random_prb.f90">latin_random_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "latin_random_prb.sh">latin_random_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "latin_random_prb_output.txt">latin_random_prb_output.txt</a>,
the output from a run of the sample program.
</li>
<li>
<a href = "../../datasets/lhs/latin_random.txt">latin_random.txt</a>,
the coordinates of a dataset created by the program;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<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_RANDOM</b> returns points in a Latin Random 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>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>RANDOM_INITIALIZE</b> initializes the FORTRAN 90 random number seed.
</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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