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table_quality.html
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<html>
<head>
<title>
TABLE_QUALITY - Quality Measures for Pointsets in M dimensions
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TABLE_QUALITY <br> Interactive Program for <br> Point Dispersion Quality
</h1>
<hr>
<p>
<b>TABLE_QUALITY</b>
is a C++ program which
reads a data file contains
the coordinates of N points in an M dimensional region,
and computes some measures of the quality of dispersion
of the points.
</p>
<p>
The program assumes that the pointset lies in the unit hypercube.
However, it is easy to modify the program to handle other regions.
A single routine, named <b>sample_routine</b>, is required to return
sample points in the region. To handle a different region,
simply modify this routine, and rebuild the program. One other
built-in routine is already available, for sampling the unit sphere.
</p>
<p>
The unit hypercube in M dimensional space is simply the set of
all vectors whose entries are between 0 and 1. It is
a natural abstraction of the unit line segment, the unit square,
and the unit cube, and represents a very simple chunk of <b>M</b>
dimensional space.
</p>
<p>
The quality measures computed include:
<ul>
<li>
<b>Alpha</b>, the minimum angle measure
(for triangulated 2D datasets only);
</li>
<li>
<b>Beta</b>, the standard deviation of the minimum spacing
between nodes, normalized by the average spacing;
</li>
<li>
<b>Chi</b>, the regularity measure;
</li>
<li>
<b>D</b>, the second moment determinant measure;
</li>
<li>
<b>E</b>, the Voronoi energy measure;
</li>
<li>
<b>Gamma</b>, the mesh ratio;
</li>
<li>
<b>H</b>, the point distribution norm;
</li>
<li>
<b>Lambda</b>, the COV measure;
</li>
<li>
<b>Mu</b>, the point distribution ratio;
</li>
<li>
<b>Nu</b>, the cell volume deviation;
</li>
<li>
<b>Q</b>, the triangle shape uniformity measure
(for triangulated 2D datasets only);
</li>
<li>
<b>R0</b>, the Riesz S=0 energy;
</li>
<li>
<b>S</b>, the sphere volume measure
(unit hypercube datasets only).
</li>
<li>
<b>Tau</b>, the second moment trace measure;
</li>
</ul>
</p>
<p>
The program also prints:
<ul>
<li>
<b>Gamma_min</b>, the minimum spacing between nodes;
</li>
<li>
<b>Gamma_ave</b>, the average spacing between nodes;
</li>
<li>
<b>Gamma_max</b>, the maximum spacing between nodes;
</li>
<li>
<b>Gamma_std</b>, the standard deviation of the spacing
between nodes;
</li>
</ul>
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<dl>
<dt>
<b>table_quality</b> <i>filename</i>
</dt>
<dd>
reads the data in <i>filename</i>, computes the quality
measures, and prints them out.
</dd>
</dl>
</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>TABLE_QUALITY</b> is available in
<a href = "../../cpp_src/table_quality/table_quality.html">a C++ version</a> and
<a href = "../../f_src/table_quality/table_quality.html">a FORTRAN90 version</a> and
<a href = "../../m_src/table_quality/table_quality.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/diaphony/diaphony.html">
DIAPHONY</a>,
a C++ program which
reads a file of N points in M dimensions and computes its diaphony, a measure
of point dispersion.
</p>
<p>
<a href = "../../cpp_src/quality/quality.html">
QUALITY</a>,
a C++ library which
makes the computations needed
by TABLE_QUALITY. To build a copy of <b>TABLE_QUALITY</b>,
a compiled copy of the <b>QUALITY</b> library must be available.
</p>
<p>
<a href = "../../cpp_src/star_discrepancy/star_discrepancy.html">
STAR_DISCREPANCY</a>,
a C++ program which
reads a TABLE file of M points in N dimensions (presumed to lie in the
unit hypercube) and computes bounds on the star discrepancy,
a measure of dispersion, by Eric Thiemard.
</p>
<p>
<a href = "../../cpp_src/table_latinize/table_latinize.html">
TABLE_LATINIZE</a>,
a C++ program which
can read a TABLE file
and write out a "latinized" version.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
David Field,<br>
Qualitative Measures for Initial Meshes,<br>
International Journal of Numerical Methods in Engineering,<br>
Volume 47, 2000, pages 887-906.
</li>
<li>
D P Hardin, Edward Saff,<br>
Discretizing Manifolds via Minimum Energy Points,<br>
Notices of the AMS,<br>
Volume 51, Number 10, November 2004, pages 1186-1194.
</li>
<li>
Per-Olof Persson, Gilbert Strang,<br>
A Simple Mesh Generator in MATLAB,<br>
SIAM Review,<br>
Volume 46, Number 2, pages 329-345, June 2004.
</li>
<li>
Yuki Saka, Max Gunzburger, John Burkardt,<br>
Latinized, Improved LHS, and CVT Point Sets in Hypercubes, <br>
International Journal of Numerical Analysis and Modeling,<br>
Volume 4, Number 3-4, 2007, pages 729-743,
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "table_quality.cpp">table_quality.cpp</a>,
the source code.
</li>
<li>
<a href = "table_quality.sh">table_quality.sh</a>,
commands to compile, link and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "cvt_02_00100.txt">cvt_02_00100.txt</a>,
a set of 100 CVT points in 2D.
</li>
<li>
<a href = "cvt_02_00100_quality.txt">
cvt_02_00100_quality.txt</a>,
the quality analysis.
</li>
<li>
<a href = "cvt_07_00010.txt">cvt_07_00010.txt</a>,
a set of 10 CVT points in 7D.
</li>
<li>
<a href = "cvt_07_00010_quality.txt">cvt_07_00010_quality.txt</a>,
the quality analysis.
</li>
<li>
<a href = "halton_02_00100.txt">halton_02_00100.txt</a>,
a set of 100 Halton points in 2D.
</li>
<li>
<a href = "halton_02_00100_quality.txt">
halton_02_00100_quality.txt</a>,
the quality analysis.
</li>
<li>
<a href = "degen_02_00130.txt">
degen_02_00130.txt</a>,
a set of 130 points in 2D, which involve a degenerate triangulation.
</li>
<li>
<a href = "degen_02_00130_quality.txt">
degen_02_00130_quality.txt</a>,
the quality analysis.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TABLE_QUALITY.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 31 August 2005.
</i>
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