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<html>
<head>
<title>
QUADRATURE_TEST_GENZ - Quadrature Rule Applied to Genz Integrals
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
QUADRATURE_TEST_GENZ <br> Quadrature Rule Applied to Genz Integrals
</h1>
<hr>
<p>
<b>QUADRATURE_TEST_GENZ</b>
is a FORTRAN90 program which
reads three files that define
a quadrature rule, applies the quadrature rule to the set of
Genz test integrals, and reports the results.
</p>
<p>
The quadrature rule is defined by three text files:
<ol>
<li>
<i>the "X" file</i> lists the abscissas (N rows, M columns);
</li>
<li>
<i>the "W" file</i> lists the weights (N rows);
</li>
<li>
<i>the "R" file</i> lists the integration region corners
(2 rows, M columns);
</li>
</ol>
For more on quadrature rules, see the <b>QUADRATURE_RULES</b>
listing below.
</p>
<p>
The Genz integrand functions include:
<ol>
<li>
"Oscillatory": f(x) = cos ( 2 * pi * r + sum ( c(1:m) * x(1:m) ) );
</li>
<li>
"Product Peak": f(x) = 1 / product ( c(1:m)**2 + (x(1:m) - x0(1:m))**2);
</li>
<li>
"Corner Peak": f(x) = 1 / ( 1 + sum ( c(1:m) * x(1:m) ) )**(m+r);
</li>
<li>
"Gaussian": f(x) = exp(-sum(c(1:m)**2 * ( x(1:m) - x0(1:m))**2 ) );
</li>
<li>
"Continuous": f(x) = exp ( - sum ( c(1:m) * abs ( x(1:m) - x0(1:m) ) ) );
</li>
<li>
"Discontinuous": f(x) = exp(sum(c(1:m)*x(1:m)) for x(1:m) <= x0(1:m), 0 otherwise;
</li>
</ol>
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<b>quadrature_test_genz</b> <i>prefix</i>
<dl>
<dt>
<i>prefix</i>
</dt>
<dd>
the common prefix for the files containing the abscissa (X),
weight (W) and region (R) information of the quadrature rule;
</dd>
</dl>
</p>
<p>
If the arguments are not supplied on the command line, the
program will prompt for them.
</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 = "../../cpp_src/gsl/gsl.html">
GSL</a>,
a C++ library which
includes routines for estimating multidimensional integrals.
</p>
<p>
<a href = "../../f_src/integral_test/integral_test.html">
INTEGRAL_TEST</a>,
a FORTRAN90 program which
uses test integrals to evaluate sets of quadrature points.
</p>
<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/nintlib/nintlib.html">
NINTLIB</a>,
a FORTRAN90 library which
numerically estimates integrals
in multiple dimensions.
</p>
<p>
<a href = "../../datasets/quadrature_rules/quadrature_rules.html">
QUADRATURE_RULES</a>,
a dataset directory which
contains a description and examples of quadrature rules defined
by a set of "X", "W" and "R" files.
</p>
<p>
<a href = "../../f_src/quadrature_test/quadrature_test.html">
QUADRATURE_TEST</a>,
a FORTRAN90 program which
reads files defining a quadrature rule, and
applies them to all the test integrals defined by <b>TEST_NINT</b>.
</p>
<p>
<a href = "../../f_src/stroud/stroud.html">
STROUD</a>,
a FORTRAN90 library which
contains quadrature
rules for a variety of unusual areas, surfaces and volumes in 2D,
3D and N-dimensions.
</p>
<p>
<a href = "../../f_src/test_nint/test_nint.html">
TEST_NINT</a>,
a FORTRAN90 library which
defines a set of integrand functions to be used for testing
multidimensional quadrature rules and routines.
</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>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Alan Genz,<br>
Testing Multidimensional Integration Routines,<br>
in Tools, Methods, and Languages for Scientific and
Engineering Computation,<br>
edited by B Ford, JC Rault, F Thomasset,<br>
North-Holland, 1984, pages 81-94,<br>
ISBN: 0444875700,<br>
LC: Q183.9.I53.
</li>
<li>
Alan Genz,<br>
A Package for Testing Multiple Integration Subroutines,<br>
in Numerical Integration:
Recent Developments, Software and Applications,<br>
edited by Patrick Keast, Graeme Fairweather,<br>
Reidel, 1987, pages 337-340,<br>
ISBN: 9027725144,<br>
LC: QA299.3.N38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "quadrature_test_genz.f90">quadrature_test_genz.f90</a>,
the source code.
</li>
<li>
<a href = "quadrature_test_genz.sh">quadrature_test_genz.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>CC_D2_LEVEL4</b> is a Clenshaw-Curtis sparse grid quadrature
rule in dimension 2 of level 4, 65 points.
<ul>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d2_level4_x.txt">
cc_d2_level4_x.txt</a>,
the "X" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d2_level4_w.txt">
cc_d2_level4_w.txt</a>,
the "W" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d2_level4_r.txt">
cc_d2_level4_r.txt</a>,
the "R" file.
</li>
<li>
<a href = "cc_d2_level4_test.txt">cc_d2_level4_test.txt</a>,
the test results.
</li>
</ul>
</p>
<p>
<b>CC_D2_LEVEL5</b> is a Clenshaw-Curtis sparse grid quadrature
rule in dimension 2 of level 5, 145 points.
<ul>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d2_level5_x.txt">
cc_d2_level5_x.txt</a>,
the "X" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d2_level5_w.txt">
cc_d2_level5_w.txt</a>,
the "W" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d2_level5_r.txt">
cc_d2_level5_r.txt</a>,
the "R" file.
</li>
<li>
<a href = "cc_d2_level5_test.txt">cc_d2_level5_test.txt</a>,
the test results.
</li>
</ul>
</p>
<p>
<b>CC_D6_LEVEL0</b> is a Clenshaw-Curtis sparse grid quadrature
rule in dimension 6 of level 0, 1 point.
<ul>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level0_x.txt">
cc_d6_level0_x.txt</a>,
the "X" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level0_w.txt">
cc_d6_level0_w.txt</a>,
the "W" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level0_r.txt">
cc_d6_level0_r.txt</a>,
the "R" file.
</li>
<li>
<a href = "cc_d6_level0_test.txt">cc_d6_level0_test.txt</a>,
the test results.
</li>
</ul>
</p>
<p>
<b>CC_D6_LEVEL1</b> is a Clenshaw-Curtis sparse grid quadrature
rule in dimension 6 of level 1, 13 points.
<ul>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level1_x.txt">
cc_d6_level1_x.txt</a>,
the "X" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level1_w.txt">
cc_d6_level1_w.txt</a>,
the "W" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level1_r.txt">
cc_d6_level1_r.txt</a>,
the "R" file.
</li>
<li>
<a href = "cc_d6_level1_test.txt">cc_d6_level1_test.txt</a>,
the test results.
</li>
</ul>
</p>
<p>
<b>CC_D6_LEVEL2</b> is a Clenshaw-Curtis sparse grid quadrature
rule in dimension 6 of level 2, 85 points.
<ul>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level2_x.txt">
cc_d6_level2_x.txt</a>,
the "X" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level2_w.txt">
cc_d6_level2_w.txt</a>,
the "W" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level2_r.txt">
cc_d6_level2_r.txt</a>,
the "R" file.
</li>
<li>
<a href = "cc_d6_level2_test.txt">cc_d6_level2_test.txt</a>,
the test results.
</li>
</ul>
</p>
<p>
<b>CC_D6_LEVEL3</b> is a Clenshaw-Curtis sparse grid quadrature
rule in dimension 6 of level 3, 389 points.
<ul>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level3_x.txt">
cc_d6_level3_x.txt</a>,
the "X" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level3_w.txt">
cc_d6_level3_w.txt</a>,
the "W" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level3_r.txt">
cc_d6_level3_r.txt</a>,
the "R" file.
</li>
<li>
<a href = "cc_d6_level3_test.txt">cc_d6_level3_test.txt</a>,
the test results.
</li>
</ul>
</p>
<p>
<b>CC_D6_LEVEL4</b> is a Clenshaw-Curtis sparse grid quadrature
rule in dimension 6 of level 4, 1457 points.
<ul>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level4_x.txt">
cc_d6_level4_x.txt</a>,
the "X" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level4_w.txt">
cc_d6_level4_w.txt</a>,
the "W" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level4_r.txt">
cc_d6_level4_r.txt</a>,
the "R" file.
</li>
<li>
<a href = "cc_d6_level4_test.txt">cc_d6_level4_test.txt</a>,
the test results.
</li>
</ul>
</p>
<p>
<b>CC_D6_LEVEL5</b> is a Clenshaw-Curtis sparse grid quadrature
rule in dimension 6 of level 5, 4865 points.
<ul>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level5_x.txt">
cc_d6_level5_x.txt</a>,
the "X" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level5_w.txt">
cc_d6_level5_w.txt</a>,
the "W" file.
</li>
<li>
<a href = "../../datasets/sparse_grid_cc/cc_d6_level5_r.txt">
cc_d6_level5_r.txt</a>,
the "R" file.
</li>
<li>
<a href = "cc_d6_level5_test.txt">cc_d6_level5_test.txt</a>,
the test results.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for QUADRATURE_TEST_GENZ.
</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>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>GET_UNIT</b> returns a free FORTRAN unit number.
</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>S_TO_I4</b> reads an I4 from a string.
</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>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 17 October 2007.
</i>
<!-- John Burkardt -->
</body>
</html>