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<html>
<head>
<title>
INTEGRAL_TEST - Tests for Equal-Weight Quadrature Rules
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
INTEGRAL_TEST <br> Tests for Equal-Weight Quadrature Rules
</h1>
<hr>
<p>
<b>INTEGRAL_TEST</b>
is a FORTRAN90 program which
tests the suitability of a set of N points for quadrature
in an M-dimensional hypercube.
</p>
<p>
<b>INTEGRAL_TEST</b> can handle both unweighted and weighted
integration schemes.
</p>
<p>
The point sets we are interested in have been generated by a
variety of algorithms, and are stored as datasets, of
spatial dimension M = 2, 7 and 16, and point set sizes N = 10, 100,
1,000 and 10,000. The point set types include:
<ul>
<li>
<a href = "../../datasets/cvt/cvt.html">
Centroidal Voronoi Tessellation values,</a>
</li>
<li>
<a href = "../../datasets/faure/faure.html">
Faure quasirandom values,</a>
</li>
<li>
<a href = "../../datasets/halton/halton.html">
Halton quasirandom values,</a>
</li>
<li>
<a href = "../../datasets/hammersley/hammersley.html">
Hammersley quasirandom values,</a>
</li>
<li>
<a href = "../../datasets/ihs/ihs.html">
Improved Distributed Hypercube Sampling (IHS) values,</a>
</li>
<li>
<a href = "../../datasets/latin_center/latin_center.html">
Latin Center Square values,</a>
</li>
<li>
<a href = "../../datasets/latin_edge/latin_edge.html">
Latin Edge Square values,</a>
</li>
<li>
<a href = "../../datasets/latin_random/latin_random.html">
Latin Random Square values,</a>
</li>
<li>
<a href = "../../datasets/niederreiter2/niederreiter2.html">
Niederreiter quasirandom values (base 2),</a>
</li>
<li>
<a href = "../../datasets/sobol/sobol.html">
Sobol quasirandom values,</a>
</li>
<li>
<a href = "../../datasets/uniform/uniform.html">
uniform random values.</a>
</li>
</ul>
</p>
<p>
The test integrals are selected from the set in
<a href = "../test_nint/test_nint.html">TEST_NINT</a>.
Each integral is to be approximated simply by averaging
the integrand values at each point in the dataset, and
multiplying by the volume of the integration region.
(In a few cases, where the integral is not over the
unit hypercube, the dataset points are suitably adjusted).
</p>
<p>
The relative error in the computed integral is determined for
each of the selected problems. (Certain integrals with a
base point that can be varied are computed 100 times, with
randomly varying basepoint). The results for
each problem, expressed as a percentage, are averaged, to produce
a single "score" for the given set of points.
</p>
<p>
Here is a table of the datasets, spatial dimensions, and number of
points used versus the averaged integration scores:
<table "border = 1">
<tr><th align = left>Set</th><th align = right>Dimension</th><th align = right>Points</th>
<th align = right>Unweighted</th><th align = right>Weight A</th><th align = right>Weight D</th></tr>
<tr><td>CVT </td><td> 2</td><td> 10</td><td> 6.527</td><td> 7.327</td><td> 7.217</td></tr>
<tr><td>CVT </td><td> 2</td><td> 100</td><td> 1.512</td><td> 1.082</td><td> 0.879</td></tr>
<tr><td>CVT </td><td> 2</td><td> 1000</td><td> 0.797</td><td> 0.471</td><td> 0.079</td></tr>
<tr><td>CVT </td><td> 7</td><td> 10</td><td>156.461</td><td>156.700</td><td>156.565</td></tr>
<tr><td>CVT </td><td> 7</td><td> 100</td><td> 24.674</td><td> 24.679</td><td> 24.541</td></tr>
<tr><td>CVT </td><td> 7</td><td> 1000</td><td> 20.996</td><td> 21.432</td><td> 21.309</td></tr>
<tr><td>CVT </td><td> 16</td><td> 10</td><td>1160750</td><td>1160760</td><td>1160750</td></tr>
<tr><td>CVT </td><td> 16</td><td> 100</td><td> 76.241</td><td> 76.214</td><td> 76.229</td></tr>
<tr><td>CVT </td><td> 16</td><td> 1000</td><td> 48.725</td><td> 48.772</td><td> 48.721</td></tr>
<tr><td>Halton </td><td> 2</td><td> 10</td><td> 19.023</td><td> 6.526</td><td> 6.284</td></tr>
<tr><td>Halton </td><td> 2</td><td> 100</td><td> 1.599</td><td> 1.063</td><td> 0.888</td></tr>
<tr><td>Halton </td><td> 2</td><td> 1000</td><td> 0.169</td><td> 0.508</td><td> 0.043</td></tr>
<tr><td>Uniform</td><td> 2</td><td> 10</td><td> 19.849</td><td> 8.085</td><td> 8.325</td></tr>
<tr><td>Uniform</td><td> 2</td><td> 100</td><td> 2.869</td><td> 1.487</td><td> 1.314</td></tr>
<tr><td>Uniform</td><td> 2</td><td> 1000</td><td> 1.140</td><td> 0.455</td><td> 0.087</td></tr>
<tr><td>Uniform</td><td> 7</td><td> 10</td><td> 32.924</td><td> 21.208</td><td> 21.044</td></tr>
<tr><td>Uniform</td><td> 7</td><td> 100</td><td> 12.117</td><td> 22.773</td><td> 22.216</td></tr>
<tr><td>Uniform</td><td> 7</td><td> 1000</td><td> 3.101</td><td> 8.172</td><td> 8.672</td></tr>
<tr><td>Uniform</td><td> 16</td><td> 10</td><td> 31.020</td><td> 26.886</td><td> 26.862</td></tr>
<tr><td>Uniform</td><td> 16</td><td> 100</td><td> 14.839</td><td> 33.115</td><td> 32.332</td></tr>
<tr><td>Uniform</td><td> 16</td><td> 1000</td><td> 7.973</td><td> 24.000</td><td> 26.003</td></tr>
</table>
</p>
<h3 align = "center">
An Important Quote:
</h3>
<p>
<blockquote><i>
"When good results are obtained in integrating a high-dimensional
function, we should conclude first of all that an especially tractable
integrand was tried and not that a generally successful method has
been found. A secondary conclusion is that we might have made a
very good choice in selecting an integration method to exploit whatever
features of f made it tractable."
</i></blockquote>
Art Owen,<br>
Latin Supercube Sampling for Very High Dimensional Simulation,<br>
ACM Transactions on Modeling and Computer Simulations,<br>
Volume 8, Number 1, January 1998, pages 71-102.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<dl>
<dt>
<b>integral_test</b> <i>input_file</i>
</dt>
<dd>
for unweighted integration.
</dd>
<dt>
<b>integral_test</b> <i>input_file</i> <i>weight_file</i>
</dt>
<dd>
for integration with a weight file.
</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">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/nint_exactness/nint_exactness.html">
NINT_EXACTNESS</a>,
a FORTRAN90 program which
demonstrates how to measure the
polynomial exactness of a multidimensional quadrature rule.
</p>
<p>
<a href = "../../f_src/product_rule/product_rule.html">
PRODUCT_RULE</a>,
a FORTRAN90 program which
constructs a product rule
from identical 1D factor rules.
</p>
<p>
<a href = "../../datasets/quadrature_rules/quadrature_rules.html">
QUADRATURE_RULES</a>,
a dataset directory which
contains sets of files that define quadrature
rules over various 1D intervals or multidimensional hypercubes.
</p>
<p>
<a href = "../../f_src/testpack/testpack.html">
TESTPACK</a>,
a FORTRAN90 library which
defines a set of integrands used to test multidimensional quadrature.
</p>
<p>
<a href = "../../f_src/voronoi_weight/voronoi_weight.html">
VORONOI_WEIGHT</a>,
a FORTRAN90 program which
is given an arbitrary set of points and
determines a suitable set of quadrature weights to associate with
them, using Voronoi techniques.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Paul Bratley, Bennett Fox, Harald Niederreiter,<br>
Implementation and Tests of Low-Discrepancy Sequences,<br>
ACM Transactions on Modeling and Computer Simulation,<br>
Volume 2, Number 3, pages 195-213, 1992.
</li>
<li>
Paul Bratley, Bennett Fox, Harald Niederreiter,<br>
Algorithm 738:
Programs to Generate Niederreiter's Low-Discrepancy Sequences,<br>
ACM Transactions on Mathematical Software,<br>
Volume 20, Number 4, pages 494-495, 1994.
</li>
<li>
Bennett Fox,<br>
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,<br>
ACM Transactions on Mathematical Software,<br>
Volume 12, Number 4, pages 362-376, 1986.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "integral_test.f90">integral_test.f90</A>,
the source code.
</li>
<li>
<a href = "integral_test.sh">integral_test.sh</a>,
commands to compile, link and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
Results for <a href = "../../datasets/cvt/cvt_02_00010.txt">
cvt_02_00010.txt</a>, with various weights:
<ul>
<li>
<a href = "cvt_02_00010.sh">cvt_02_00010.sh</a>,
commands to run the tests.
</li>
<li>
<a href = "cvt_02_00010.out">cvt_02_00010.out</a>,
no weighting
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00010_weight_a.txt">
cvt_02_00010_weight_a.txt</a>,
weight set A.
</li>
<li>
<a href = "cvt_02_00010_a.out">cvt_02_00010_a.out</a>,
results for weight set A.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00010_weight_b.txt">
cvt_02_00010_weight_b.txt</a>,
weight set B.
</li>
<li>
<a href = "cvt_02_00010_b.out">cvt_02_00010_b.out</a>,
results for weight set B.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00010_weight_c.txt">
cvt_02_00010_weight_c.txt</a>,
weight set C.
</li>
<li>
<a href = "cvt_02_00010_c.out">cvt_02_00010_c.out</a>,
results for weight set C.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00010_weight_d.txt">
cvt_02_00010_weight_d.txt</a>,
weight set D.
</li>
<li>
<a href = "cvt_02_00010_d.out">cvt_02_00010_d.out</a>,
results for weight set D.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00010_weight_e.txt">
cvt_02_00010_weight_e.txt</a>,
weight set E.
</li>
<li>
<a href = "cvt_02_00010_e.out">cvt_02_00010_e.out</a>,
results for weight set E.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00010_weight_f.txt">
cvt_02_00010_weight_f.txt</a>,
weight set F.
</li>
<li>
<a href = "cvt_02_00010_f.out">cvt_02_00010_f.out</a>,
results for weight set F.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00010_weight_g.txt">
cvt_02_00010_weight_g.txt</a>,
weight set G.
</li>
<li>
<a href = "cvt_02_00010_g.out">cvt_02_00010_g.out</a>,
results for weight set G.
</li>
</ul>
</p>
<p>
Results for <a href = "../../datasets/cvt/cvt_02_00100.txt">
cvt_02_00100.txt</a>, with various weights:
<ul>
<li>
<a href = "cvt_02_00100.sh">cvt_02_00100.sh</a>,
commands to run the tests.
</li>
<li>
<a href = "cvt_02_00100.out">cvt_02_00100.out</a>,
no weighting
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00100_weight_a.txt">
cvt_02_00100_weight_a.txt</a>,
weight set A.
</li>
<li>
<a href = "cvt_02_00100_a.out">cvt_02_00100_a.out</a>,
results for weight set A.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00100_weight_b.txt">
cvt_02_00100_weight_b.txt</a>,
weight set B.
</li>
<li>
<a href = "cvt_02_00100_b.out">cvt_02_00100_b.out</a>,
results for weight set B.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00100_weight_c.txt">
cvt_02_00100_weight_c.txt</a>,
weight set C.
</li>
<li>
<a href = "cvt_02_00100_c.out">cvt_02_00100_c.out</a>,
results for weight set C.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00100_weight_d.txt">
cvt_02_00100_weight_d.txt</a>,
weight set D.
</li>
<li>
<a href = "cvt_02_00100_d.out">cvt_02_00100_d.out</a>,
results for weight set D.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00100_weight_e.txt">
cvt_02_00100_weight_e.txt</a>,
weight set E.
</li>
<li>
<a href = "cvt_02_00100_e.out">cvt_02_00100_e.out</a>,
results for weight set E.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00100_weight_f.txt">
cvt_02_00100_weight_f.txt</a>,
weight set F.
</li>
<li>
<a href = "cvt_02_00100_f.out">cvt_02_00100_f.out</a>,
results for weight set F.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_00100_weight_g.txt">
cvt_02_00100_weight_g.txt</a>,
weight set G.
</li>
<li>
<a href = "cvt_02_00100_g.out">cvt_02_00100_g.out</a>,
results for weight set G.
</li>
</ul>
</p>
<p>
Results for <a href = "../../datasets/cvt/cvt_02_01000.txt">
cvt_02_01000.txt</a>, with various weights:
<ul>
<li>
<a href = "cvt_02_01000.sh">cvt_02_01000.sh</a>,
commands to run the tests.
</li>
<li>
<a href = "cvt_02_01000.out">cvt_02_01000.out</a>,
no weighting
</li>
<li>
<a href = "../voronoi_weight/cvt_02_01000_weight_a.txt">
cvt_02_01000_weight_a.txt</a>,
weight set A.
</li>
<li>
<a href = "cvt_02_01000_a.out">cvt_02_01000_a.out</a>,
results for weight set A.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_01000_weight_b.txt">
cvt_02_01000_weight_b.txt</a>,
weight set B.
</li>
<li>
<a href = "cvt_02_01000_b.out">cvt_02_01000_b.out</a>,
results for weight set B.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_01000_weight_c.txt">
cvt_02_01000_weight_c.txt</a>,
weight set C.
</li>
<li>
<a href = "cvt_02_01000_c.out">cvt_02_01000_c.out</a>,
results for weight set C.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_01000_weight_d.txt">
cvt_02_01000_weight_d.txt</a>,
weight set D.
</li>
<li>
<a href = "cvt_02_01000_d.out">cvt_02_01000_d.out</a>,
results for weight set D.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_01000_weight_e.txt">
cvt_02_01000_weight_e.txt</a>,
weight set E.
</li>
<li>
<a href = "cvt_02_01000_e.out">cvt_02_01000_e.out</a>,
results for weight set E.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_01000_weight_f.txt">
cvt_02_01000_weight_f.txt</a>,
weight set F.
</li>
<li>
<a href = "cvt_02_01000_f.out">cvt_02_01000_f.out</a>,
results for weight set F.
</li>
<li>
<a href = "../voronoi_weight/cvt_02_01000_weight_g.txt">
cvt_02_01000_weight_g.txt</a>,
weight set G.
</li>
<li>
<a href = "cvt_02_01000_g.out">cvt_02_01000_g.out</a>,
results for weight set G.
</li>
</ul>
</p>
<p>
Results for <a href = "../../datasets/halton/halton_02_00010.txt">
halton_02_00010.txt</a>, with various weights:
<ul>
<li>
<a href = "halton_02_00010.sh">halton_02_00010.sh</a>,
commands to run the tests.
</li>
<li>
<a href = "halton_02_00010.out">halton_02_00010.out</a>,
no weighting
</li>
<li>
<a href = "../voronoi_weight/halton_02_00010_weight_a.txt">
halton_02_00010_weight_a.txt</a>,
weight set A.
</li>
<li>
<a href = "halton_02_00010_a.out">halton_02_00010_a.out</a>,
results for weight set A.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00010_weight_b.txt">
halton_02_00010_weight_b.txt</a>,
weight set B.
</li>
<li>
<a href = "halton_02_00010_b.out">halton_02_00010_b.out</a>,
results for weight set B.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00010_weight_c.txt">
halton_02_00010_weight_c.txt</a>,
weight set C.
</li>
<li>
<a href = "halton_02_00010_c.out">halton_02_00010_c.out</a>,
results for weight set C.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00010_weight_d.txt">
halton_02_00010_weight_d.txt</a>,
weight set D.
</li>
<li>
<a href = "halton_02_00010_d.out">halton_02_00010_d.out</a>,
results for weight set D.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00010_weight_e.txt">
halton_02_00010_weight_e.txt</a>,
weight set E.
</li>
<li>
<a href = "halton_02_00010_e.out">halton_02_00010_e.out</a>,
results for weight set E.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00010_weight_f.txt">
halton_02_00010_weight_f.txt</a>,
weight set F.
</li>
<li>
<a href = "halton_02_00010_f.out">halton_02_00010_f.out</a>,
results for weight set F.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00010_weight_g.txt">
halton_02_00010_weight_g.txt</a>,
weight set G.
</li>
<li>
<a href = "halton_02_00010_g.out">halton_02_00010_g.out</a>,
results for weight set G.
</li>
</ul>
</p>
<p>
Results for <a href = "../../datasets/halton/halton_02_00100.txt">
halton_02_00100.txt</a>, with various weights:
<ul>
<li>
<a href = "halton_02_00100.sh">halton_02_00100.sh</a>,
commands to run the tests.
</li>
<li>
<a href = "halton_02_00100.out">halton_02_00100.out</a>,
no weighting
</li>
<li>
<a href = "../voronoi_weight/halton_02_00100_weight_a.txt">
halton_02_00100_weight_a.txt</a>,
weight set A.
</li>
<li>
<a href = "halton_02_00100_a.out">halton_02_00100_a.out</a>,
results for weight set A.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00100_weight_b.txt">
halton_02_00100_weight_b.txt</a>,
weight set B.
</li>
<li>
<a href = "halton_02_00100_b.out">halton_02_00100_b.out</a>,
results for weight set B.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00100_weight_c.txt">
halton_02_00100_weight_c.txt</a>,
weight set C.
</li>
<li>
<a href = "halton_02_00100_c.out">halton_02_00100_c.out</a>,
results for weight set C.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00100_weight_d.txt">
halton_02_00100_weight_d.txt</a>,
weight set D.
</li>
<li>
<a href = "halton_02_00100_d.out">halton_02_00100_d.out</a>,
results for weight set D.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00100_weight_e.txt">
halton_02_00100_weight_e.txt</a>,
weight set E.
</li>
<li>
<a href = "halton_02_00100_e.out">halton_02_00100_e.out</a>,
results for weight set E.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00100_weight_f.txt">
halton_02_00100_weight_f.txt</a>,
weight set F.
</li>
<li>
<a href = "halton_02_00100_f.out">halton_02_00100_f.out</a>,
results for weight set F.
</li>
<li>
<a href = "../voronoi_weight/halton_02_00100_weight_g.txt">
halton_02_00100_weight_g.txt</a>,
weight set G.
</li>
<li>
<a href = "halton_02_00100_g.out">halton_02_00100_g.out</a>,
results for weight set G.
</li>
</ul>
</p>
<p>
Results for <a href = "../../datasets/halton/halton_02_01000.txt">
halton_02_01000.txt</a>, with various weights:
<ul>
<li>
<a href = "halton_02_01000.sh">halton_02_01000.sh</a>,
commands to run the tests.
</li>
<li>
<a href = "halton_02_01000.out">halton_02_01000.out</a>,
no weighting
</li>
<li>
<a href = "../voronoi_weight/halton_02_01000_weight_a.txt">
halton_02_01000_weight_a.txt</a>,
weight set A.
</li>
<li>
<a href = "halton_02_01000_a.out">halton_02_01000_a.out</a>,
results for weight set A.
</li>
<li>
<a href = "../voronoi_weight/halton_02_01000_weight_b.txt">
halton_02_01000_weight_b.txt</a>,
weight set B.
</li>
<li>
<a href = "halton_02_01000_b.out">halton_02_01000_b.out</a>,
results for weight set B.
</li>
<li>
<a href = "../voronoi_weight/halton_02_01000_weight_c.txt">
halton_02_01000_weight_c.txt</a>,
weight set C.
</li>
<li>
<a href = "halton_02_01000_c.out">halton_02_01000_c.out</a>,
results for weight set C.
</li>
<li>
<a href = "../voronoi_weight/halton_02_01000_weight_d.txt">
halton_02_01000_weight_d.txt</a>,
weight set D.
</li>
<li>
<a href = "halton_02_01000_d.out">halton_02_01000_d.out</a>,
results for weight set D.
</li>
<li>
<a href = "../voronoi_weight/halton_02_01000_weight_e.txt">
halton_02_01000_weight_e.txt</a>,
weight set E.
</li>
<li>
<a href = "halton_02_01000_e.out">halton_02_01000_e.out</a>,
results for weight set E.
</li>
<li>
<a href = "../voronoi_weight/halton_02_01000_weight_f.txt">
halton_02_01000_weight_f.txt</a>,
weight set F.
</li>
<li>
<a href = "halton_02_01000_f.out">halton_02_01000_f.out</a>,
results for weight set F.
</li>
<li>
<a href = "../voronoi_weight/halton_02_01000_weight_g.txt">
halton_02_01000_weight_g.txt</a>,
weight set G.
</li>
<li>
<a href = "halton_02_01000_g.out">halton_02_01000_g.out</a>,
results for weight set G.
</li>
</ul>
</p>
<p>
Results for <a href = "../../datasets/uniform/uniform_02_00010.txt">
uniform_02_00010.txt</a>, with various weights:
<ul>
<li>
<a href = "uniform_02_00010.sh">uniform_02_00010.sh</a>,
commands to run the tests.
</li>
<li>
<a href = "uniform_02_00010.out">uniform_02_00010.out</a>,
no weighting
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00010_weight_a.txt">
uniform_02_00010_weight_a.txt</a>,
weight set A.
</li>
<li>
<a href = "uniform_02_00010_a.out">uniform_02_00010_a.out</a>,
results for weight set A.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00010_weight_b.txt">
uniform_02_00010_weight_b.txt</a>,
weight set B.
</li>
<li>
<a href = "uniform_02_00010_b.out">uniform_02_00010_b.out</a>,
results for weight set B.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00010_weight_c.txt">
uniform_02_00010_weight_c.txt</a>,
weight set C.
</li>
<li>
<a href = "uniform_02_00010_c.out">uniform_02_00010_c.out</a>,
results for weight set C.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00010_weight_d.txt">
uniform_02_00010_weight_d.txt</a>,
weight set D.
</li>
<li>
<a href = "uniform_02_00010_d.out">uniform_02_00010_d.out</a>,
results for weight set D.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00010_weight_e.txt">
uniform_02_00010_weight_e.txt</a>,
weight set E.
</li>
<li>
<a href = "uniform_02_00010_e.out">uniform_02_00010_e.out</a>,
results for weight set E.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00010_weight_f.txt">
uniform_02_00010_weight_f.txt</a>,
weight set F.
</li>
<li>
<a href = "uniform_02_00010_f.out">uniform_02_00010_f.out</a>,
results for weight set F.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00010_weight_g.txt">
uniform_02_00010_weight_g.txt</a>,
weight set G.
</li>
<li>
<a href = "uniform_02_00010_g.out">uniform_02_00010_g.out</a>,
results for weight set G.
</li>
</ul>
</p>
<p>
Results for <a href = "../../datasets/uniform/uniform_02_00100.txt">
uniform_02_00100.txt</a>, with various weights:
<ul>
<li>
<a href = "uniform_02_00100.sh">uniform_02_00100.sh</a>,
commands to run the tests.
</li>
<li>
<a href = "uniform_02_00100.out">uniform_02_00100.out</a>,
no weighting
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00100_weight_a.txt">
uniform_02_00100_weight_a.txt</a>,
weight set A.
</li>
<li>
<a href = "uniform_02_00100_a.out">uniform_02_00100_a.out</a>,
results for weight set A.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00100_weight_b.txt">
uniform_02_00100_weight_b.txt</a>,
weight set B.
</li>
<li>
<a href = "uniform_02_00100_b.out">uniform_02_00100_b.out</a>,
results for weight set B.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00100_weight_c.txt">
uniform_02_00100_weight_c.txt</a>,
weight set C.
</li>
<li>
<a href = "uniform_02_00100_c.out">uniform_02_00100_c.out</a>,
results for weight set C.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00100_weight_d.txt">
uniform_02_00100_weight_d.txt</a>,
weight set D.
</li>
<li>
<a href = "uniform_02_00100_d.out">uniform_02_00100_d.out</a>,
results for weight set D.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00100_weight_e.txt">
uniform_02_00100_weight_e.txt</a>,
weight set E.
</li>
<li>
<a href = "uniform_02_00100_e.out">uniform_02_00100_e.out</a>,
results for weight set E.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00100_weight_f.txt">
uniform_02_00100_weight_f.txt</a>,
weight set F.
</li>
<li>
<a href = "uniform_02_00100_f.out">uniform_02_00100_f.out</a>,
results for weight set F.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_00100_weight_g.txt">
uniform_02_00100_weight_g.txt</a>,
weight set G.
</li>
<li>
<a href = "uniform_02_00100_g.out">uniform_02_00100_g.out</a>,
results for weight set G.
</li>
</ul>
</p>
<p>
Results for <a href = "../../datasets/uniform/uniform_02_01000.txt">
uniform_02_01000.txt</a>, with various weights:
<ul>
<li>
<a href = "uniform_02_01000.sh">uniform_02_01000.sh</a>,
commands to run the tests.
</li>
<li>
<a href = "uniform_02_01000.out">uniform_02_01000.out</a>,
no weighting
</li>
<li>
<a href = "../voronoi_weight/uniform_02_01000_weight_a.txt">
uniform_02_01000_weight_a.txt</a>,
weight set A.
</li>
<li>
<a href = "uniform_02_01000_a.out">uniform_02_01000_a.out</a>,
results for weight set A.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_01000_weight_b.txt">
uniform_02_01000_weight_b.txt</a>,
weight set B.
</li>
<li>
<a href = "uniform_02_01000_b.out">uniform_02_01000_b.out</a>,
results for weight set B.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_01000_weight_c.txt">
uniform_02_01000_weight_c.txt</a>,
weight set C.
</li>
<li>
<a href = "uniform_02_01000_c.out">uniform_02_01000_c.out</a>,
results for weight set C.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_01000_weight_d.txt">
uniform_02_01000_weight_d.txt</a>,
weight set D.
</li>
<li>
<a href = "uniform_02_01000_d.out">uniform_02_01000_d.out</a>,
results for weight set D.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_01000_weight_e.txt">
uniform_02_01000_weight_e.txt</a>,
weight set E.
</li>
<li>
<a href = "uniform_02_01000_e.out">uniform_02_01000_e.out</a>,
results for weight set E.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_01000_weight_f.txt">
uniform_02_01000_weight_f.txt</a>,
weight set F.
</li>
<li>
<a href = "uniform_02_01000_f.out">uniform_02_01000_f.out</a>,
results for weight set F.
</li>
<li>
<a href = "../voronoi_weight/uniform_02_01000_weight_g.txt">
uniform_02_01000_weight_g.txt</a>,
weight set G.
</li>
<li>
<a href = "uniform_02_01000_g.out">uniform_02_01000_g.out</a>,
results for weight set G.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for INTEGRAL_TEST.
</li>
<li>
<b>CH_IS_DIGIT</b> returns .TRUE. if a character is a decimal digit.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>DIGIT_INC</b> increments a decimal digit.
</li>
<li>
<b>DIGIT_TO_CH</b> returns the character representation of a decimal digit.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.