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quadrature_test_2d.html
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<html>
<head>
<title>
QUADRATURE_TEST_2D - Quadrature Rules Applied to 2D Test Integrals
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
QUADRATURE_TEST_2D <br> Quadrature Rules Applied to 2D Test Integrals
</h1>
<hr>
<p>
<b>QUADRATURE_TEST_2D</b>
is a MATLAB program which
reads three files that define
a 2D quadrature rule, applies the quadrature rule to a set of
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 test integrals come from the <b>TEST_INT_2D</b> library.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>quadrature_test_2d</b> ( '<i>prefix</i>' )
</blockquote>
where
<ul>
<li>
<i>prefix</i>, the common prefix for the files containing the abscissa (X),
weight (W) and region (R) information of the quadrature rule;
</li>
</ul>
</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">
Languages:
</h3>
<p>
<b>QUADRATURE_TEST_2D</b> is available in
<a href = "../../cpp_src/quadrature_test_2d/quadrature_test_2d.html">a C++ version</a> and
<a href = "../../f_src/quadrature_test_2d/quadrature_test_2d.html">a FORTRAN90 version</a> and
<a href = "../../m_src/quadrature_test_2d/quadrature_test_2d.html">a MATLAB version</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 = "../../m_src/nint_exactness/nint_exactness.html">
NINT_EXACTNESS</a>,
a MATLAB program which
measures the polynomial exactness of a multidimensional quadrature rule.
</p>
<p>
<a href = "../../m_src/nintlib/nintlib.html">
NINTLIB</a>,
a MATLAB library which
numerically estimates integrals in multiple dimensions.
</p>
<p>
<a href = "../../m_src/product_rule/product_rule.html">
PRODUCT_RULE</a>,
a MATLAB program which
creates a multidimensional quadrature rule as a product of
one dimensional rules.
</p>
<p>
<a href = "../../datasets/product_rule_gl/product_rule_gl.html">
PRODUCT_RULE_GL</a>,
a dataset directory which
contains multidimensional quadrature rules formed as products
of 1D Gauss-Legendre rules.
</p>
<p>
<a href = "../../datasets/product_rule_tanh_sinh/product_rule_tanh_sinh.html">
PRODUCT_RULE_TANH_SINH</a>,
a dataset directory which
contains multidimensional quadrature rules formed as products
of 1D tanh-sinh rules.
</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 = "../../m_src/quadrature_test/quadrature_test.html">
QUADRATURE_TEST</a>,
a MATLAB 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 = "../../datasets/sparse_grid_tanh_sinh/sparse_grid_tanh_sinh.html">
SPARSE_GRID_TANH_SINH</a>,
a dataset directory which
contains multidimensional Smolyak sparse grids based on a 1D tanh-sinh rule;
</p>
<p>
<a href = "../../m_src/stroud/stroud.html">
STROUD</a>,
a MATLAB library which
contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D,
3D and N-dimensions.
</p>
<p>
<a href = "../../m_src/test_int_2d/test_int_2d.html">
TEST_INT_2D</a>,
a MATLAB library which
defines test integrands for 2D quadrature rules.
</p>
<p>
<a href = "../../m_src/test_nint/test_nint.html">
TEST_NINT</a>,
a MATLAB library which
defines integrand functions for testing
multidimensional quadrature rules and routines.
</p>
<p>
<a href = "../../m_src/testpack/testpack.html">
TESTPACK</a>,
a MATLAB library which
defines a set of integrands used to test multidimensional quadrature.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "quadrature_test_2d.m">quadrature_test_2d.m</a>,
the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>PRODUCT_RULE_GL</b> is a family of Gauss_Legendre product rules which
includes 2D rules of orders 1x1, 2x2, 4x4,
8x8, 16x16 and 32x32.
<ul>
<li>
<a href = "../../datasets/product_rule_gl/product_rule_gl.html">
product_rule_gl.html</a>,
describes the Gauss-Legendre product rules.
</li>
<li>
<a href = "product_rule_gl_output.txt">
product_rule_gl_output</a>,
the output from running the test on the 2D rules.
</li>
</ul>
</p>
<p>
<b>PRODUCT_RULE_TANH_SINH</b> is a family of tanh-sinh product rules which
includes 2D rules of orders 1x1, 3x3, 7x7,
15x15, 31x31, 63x63, and 127x127 points.
<ul>
<li>
<a href = "../../datasets/product_rule_tanh_sinh/product_rule_tanh_sinh.html">
product_rule_tanh_sinh.html</a>,
describes the tanh-sinh product rules.
</li>
<li>
<a href = "product_rule_tanh_sinh_output.txt">
product_rule_tanh_sinh_output</a>,
the output from running the test on the 2D rules.
</li>
</ul>
</p>
<p>
<b>SPARSE_GRID_CC</b> is a family of Clenshaw Curtis sparse grid rules which
includes rules of order 1, 5, 13, 29, 65, 145, 321, 705. 1537, 3329 and 7169 points.
<i>These rules have problems with many of the test integrands, which have
endpoint singularities.</i>
<ul>
<li>
<a href = "../../datasets/sparse_grid_cc/sparse_grid_cc.html">
sparse_grid_cc.html</a>,
describes the Clenshaw Curtis sparse grid rules.
</li>
<li>
<a href = "sparse_grid_cc_output.txt">
sparse_grid_cc_output</a>,
the output from running the test on the 2D rules.
</li>
</ul>
</p>
<p>
<b>SPARSE_GRID_F2</b> is a family of Fejer Type 2 sparse grid rules which
includes rules of order 1, 5, 17, 49, 129, 321, 769, and 1793 points.
<ul>
<li>
<a href = "../../datasets/sparse_grid_f2/sparse_grid_f2.html">
sparse_grid_f2.html</a>,
describes the Fejer Type 2 sparse grid rules.
</li>
<li>
<a href = "sparse_grid_f2_output.txt">
sparse_grid_f2_output</a>,
the output from running the test on the 2D rules.
</li>
</ul>
</p>
<p>
<b>SPARSE_GRID_NCO</b> is a family of Newton Cotes Open sparse grid rules which
includes rules of order 1, 5, 17, 49, 129, 321, and 769 points.
<i>These rules do a terrible job, which reflects the instability of the
Newton Cotes rules.</i>
<ul>
<li>
<a href = "../../datasets/sparse_grid_nco/sparse_grid_nco.html">
sparse_grid_nco.html</a>,
describes the Newton Cotes Open sparse grid rules.
</li>
<li>
<a href = "sparse_grid_nco_output.txt">
sparse_grid_nco_output</a>,
the output from running the test on the 2D rules.
</li>
</ul>
</p>
<p>
<b>SPARSE_GRID_TANH_SINH</b> is a family of tanh-sinh sparse grid rules which
includes rules of order 1, 5, 17, 49, 129, 321, 769, 1793 and 4097 points.
<ul>
<li>
<a href = "../../datasets/sparse_grid_tanh_sinh/sparse_grid_tanh_sinh.html">
sparse_grid_tanh_sinh.html</a>,
describes the tanh-sinh sparse grid rules.
</li>
<li>
<a href = "sparse_grid_tanh_sinh_output.txt">
sparse_grid_tanh_sinh_output</a>,
the output from running the test on the 2D rules.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 10 August 2009.
</i>
<!-- John Burkardt -->
</body>
</html>