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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 FORTRAN90 program which
reads a data file containing
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>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>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>
<blockquote>
<b>table_quality</b> <i>filename</i>
</blockquote>
where
<ul>
<li>
<i>filename</i> is the name of the file containing the point coordinates.
</li>
</ul>
</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 = "../../f_src/diaphony/diaphony.html">
DIAPHONY</a>,
a FORTRAN90 program which
reads a file of N points in M dimensions and computes its diaphony, a measure
of point dispersion.
</p>
<p>
<a href = "../../f_src/quality/quality.html">
QUALITY</a>,
a FORTRAN90 library which
supplies the routines that compute the
quality measures needed by <b>TABLE_QUALITY</b>.
</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 = "../../data/table/table.html">
TABLE</a>,
the data format which
is used for the input to this program.
</p>
<p>
<a href = "../../f_src/table_latinize/table_latinize.html">
TABLE_LATINIZE</a>,
a FORTRAN90 program which
reads a file of
points and creates a "latinized" version by adjusting the data.
</p>
<p>
<a href = "../../f_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a FORTRAN90 program which
can evaluate a triangulation of a given set of nodes.
</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>
Douglas 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.f90">table_quality.f90</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>
<li>
<b>SAMPLE_ROUTINE</b> returns sample points in the user's region.
</li>
<li>
<b>ALPHA_MEASURE</b> determines the triangulated pointset quality measure ALPHA.
</li>
<li>
<b>ARC_COSINE</b> computes the arc cosine function, with argument truncation.
</li>
<li>
<b>AREA_MEASURE</b> determines the area ratio quality measure.
</li>
<li>
<b>BANDWIDTH_MESH:</b> bandwidth of finite element mesh.
</li>
<li>
<b>BETA_MEASURE</b> determines the pointset quality measure BETA.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>CHI_MEASURE</b> determines the pointset quality measure CHI.
</li>
<li>
<b>D_MEASURE</b> determines the pointset quality measure D.
</li>
<li>
<b>DGE_DET</b> computes the determinant of a square matrix in DGE storage.
</li>
<li>
<b>DIAEDG</b> chooses a diagonal edge.
</li>
<li>
<b>DTRIS2</b> constructs a Delaunay triangulation of 2D vertices.
</li>
<li>
<b>E_MEASURE</b> determines the pointset quality measure E.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>FIND_CLOSEST</b> finds the nearest R point to each S point.
</li>
<li>
<b>GAMMA_MEASURE</b> determines the pointset quality measure GAMMA.
</li>
<li>
<b>GET_INPUT_FILE_NAME</b> gets the input file name.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>H_MEASURE</b> determines the pointset quality measure H.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of integer division.
</li>
<li>
<b>I4_WRAP</b> forces an integer to lie between given limits by wrapping.
</li>
<li>
<b>I4VEC_INDICATOR</b> sets an I4VEC to the indicator vector.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>LAMBDA_MEASURE</b> determines the pointset quality measure LAMBDA.
</li>
<li>
<b>LRLINE</b> determines if a point is left of, right or, or on a directed line.
</li>
<li>
<b>MU_MEASURE</b> determines the pointset quality measure MU.
</li>
<li>
<b>NU_MEASURE</b> determines the pointset quality measure NU.
</li>
<li>
<b>PERM_INV</b> inverts a permutation "in place".
</li>
<li>
<b>POINTSET_SPACING</b> determines the minimum spacing between points in the set.
</li>
<li>
<b>Q_MEASURE</b> determines the triangulated pointset quality measure Q.
</li>
<li>
<b>R0_MEASURE</b> determines the pointset quality measure R0.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R82VEC_PERMUTE</b> permutes an R82 vector in place.
</li>
<li>
<b>R82VEC_SORT_HEAP_INDEX_A</b> does an indexed heap ascending sort of an R82VEC.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_IN_01</b> is TRUE if the entries of an R8MAT are in the range [0,1].
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_UNIFORM_01</b> returns a unit pseudorandom R8MAT.
</li>
<li>
<b>R8VEC_NORMAL_01</b> returns a unit pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>RADIUS_MAXIMUS</b> finds the biggest possible nonintersecting sphere.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>SAMPLE_HYPERCUBE_UNIFORM</b> returns sample points in the unit hypercube.
</li>
<li>
<b>SAMPLE_SPHERE_UNIFORM</b> samples points inside the unit sphere.
</li>
<li>
<b>SPHERE_MEASURE</b> determines the pointset quality measure S.
</li>
<li>
<b>SPHERE_VOLUME_ND</b> computes the volume of a sphere in ND.
</li>
<li>
<b>SWAPEC</b> swaps diagonal edges until all triangles are Delaunay.
</li>
<li>
<b>TAU_MEASURE</b> determines the pointset quality measure TAU.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>VBEDG</b> determines which boundary edges are visible to a point.
</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 01 May 2010.
</i>
<!-- John Burkardt -->
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