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<html>
<head>
<title>
CVT_MOD_DATASET - Centroidal Voronoi Tessellation on Logical Torus
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CVT_MOD_DATASET <br> Centroidal Voronoi Tessellation on Logical Torus
</h1>
<hr>
<p>
<b>CVT_MOD_DATASET</b>
is a FORTRAN90 program which
creates Centroidal Voronoi Tessellation (CVT) datasets in which the
geometry is a logical torus.
</p>
<p>
A 2D unit logical torus is the unit square, but with "wraparound".
This is the connectivity frequently seen in video games, in which
a spaceship flies off the top of the screen and immediately reappears
at the bottom of the screen. In the general M-dimensional case,
the extreme minimum and maximum values of each coordinate are
identified, and modular arithmetic may be used to determine
distances.
</p>
<p>
For details on the underlying CVT calculation, refer to
<a href =
"../../f_src/cvt_dataset/cvt_dataset.html">
CVT_DATASET</a>. This program is a modification of that one, in
which distances are computed using modular arithmetic. For the
current code, the region is a unit hypercube, although there's
no real difficulty in allowing the widths in each dimension to
vary.
</p>
<p>
A reasonable set of input commands might be:
<pre>
# cvt_mod_02_00010.inp
#
m = 2
n = 10
seed = 123456789
#
initialize random
sample_function_cvt = random
sample_num_cvt = 500000
iterate 100
write cvt_mod_02_00010.txt
#
quit
</pre>
</p>
<p>
Here, the user first specifies the spatial dimension <b>M</b>, the
number of generators <b>N</b>, and the random number seed
(for later reproducibility).
</p>
<p>
Then, the user specifies that the initial positions of the generators
are to chosen at random; that during the iterations, the volume
estimation will also be done using random sampling, and that the
number of sampling points in an iteration will be 500,000.
The <b>iterate 100</b> command causes 100 iterations to be carried
out, and then the resulting generators are written to a file.
</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">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cvt_mod/cvt_mod.html">
CVT_MOD</a>,
a FORTRAN90 library which
contains routines which compute the datasets.
A compiled copy of this library is necessary to build
<b>CVT_MOD_DATASET</b>.
</p>
<p>
<a href = "../../datasets/cvt_mod/cvt_mod.html">
CVT_MOD</a>,
a dataset directory which
contains sample files created
by <b>CVT_MOD_DATASET</b>.
</p>
<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_dataset/latin_edge_dataset.html">
LATIN_EDGE_DATASET</a>,
a FORTRAN90 program which
creates a Latin Edge Hypercube dataset;
</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>
Franz Aurenhammer,<br>
Voronoi diagrams -
a study of a fundamental geometric data structure,<br>
ACM Computing Surveys,<br>
Volume 23, Number 3, pages 345-405, September 1991.
</li>
<li>
John Burkardt, Max Gunzburger, Janet Peterson, Rebecca Brannon,<br>
User Manual and Supporting Information for Library of Codes
for Centroidal Voronoi Placement and Associated Zeroth,
First, and Second Moment Determination,<br>
Sandia National Laboratories Technical Report SAND2002-0099,<br>
February 2002,<br>
<a href = "../../publications/bgpb_2002.pdf">
../../publications/bgpb_2002.pdf </a>
</li>
<li>
Qiang Du, Vance Faber, Max Gunzburger,<br>
Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
SIAM Review, Volume 41, 1999, pages 637-676.
</li>
<li>
Lili Ju, Qiang Du, Max Gunzburger,<br>
Probabilistic methods for centroidal Voronoi tessellations
and their parallel implementations,<br>
Parallel Computing,<br>
Volume 28, 2002, pages 1477-1500.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "cvt_mod_dataset.f90">cvt_mod_dataset.f90</a>,
the source code;
</li>
<li>
<a href = "cvt_mod_dataset.sh">cvt_mod_dataset.sh</a>,
commands to compile and load the source code;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for CVT_MOD_DATASET.
</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 26 November 2006.
</i>
<!-- John Burkardt -->
</body>
</html>