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testpack.html
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<html>
<head>
<title>
TESTPACK - Testing Multidimensional Integration Routines
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TESTPACK <br> Testing Multidimensional Integration Routines
</h1>
<hr>
<p>
<b>TESTPACK</b>
is a MATLAB program which
demonstrates the testing of a routine for multidimensional
integration.
</p>
<p>
In this case, the code being tested is a subroutine known as
ADAPT, written by Genz. The code is tested on six test integrand
functions, also defined by Genz. The test is done with a variety
of spatial dimensions, parameter values, and difficulty factors.
</p>
<p>
With <b>M</b> denoting the spatial dimension, <b>R</b> a parameter,
<b>C</b> a scaling vector, and <b>X0</b> a displacement vector,
the test functions can be summarized as:
<ol>
<li>
f(x) = cos ( 2 * pi * r + sum ( c(1:m) * x(1:m) ) ), <br>
Genz "Oscillatory";
</li>
<li>
f(x) = 1 / product ( c(1:m)^2 + (x(1:m) - x0(1:m))^2),<br>
Genz "Product Peak";
</li>
<li>
f(x) = 1 / ( 1 + sum ( c(1:m) * x(1:m) ) )^(m+r),<br>
Genz "Corner Peak";
</li>
<li>
f(x) = exp(-sum(c(1:m)^2 * ( x(1:m) - x0(1:m))^2 ) ),<br>
Genz "Gaussian";
</li>
<li>
f(x) = exp ( - sum ( c(1:m) * abs ( x(1:m) - x0(1:m) ) ) ),<br>
Genz "Continuous";
</li>
<li>
f(x) = exp(sum(c(1:m)*x(1:m)) for x(1:m) <= x0(1:m), 0 otherwise,<br>
Genz "Discontinuous";
</li>
</ol>
</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>TESTPACK</b> is available in
<a href = "../../cpp_src/testpack/testpack.html">a C++ version</a> and
<a href = "../../f77_src/testpack/testpack.html">a FORTRAN77 version</a> and
<a href = "../../f_src/testpack/testpack.html">a FORTRAN90 version</a> and
<a href = "../../m_src/testpack/testpack.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/integral_test/integral_test.html">
INTEGRAL_TEST</a>,
a FORTRAN90 program which
tests the suitability of
a set of N points for use in an equal-weight quadrature rule over
the M-dimensional unit hypercube.
</p>
<p>
<a href = "../../f_src/intlib/intlib.html">
INTLIB</a>,
a FORTRAN90 library which
estimates the integral of a function over a one-dimensional interval.
</p>
<p>
<a href = "../../m_src/nintlib/nintlib.html">
NINTLIB</a>,
a MATLAB library which
estimates
the integral of a function over a one-dimensional interval.
</p>
<p>
<a href = "../../m_src/product_rule/product_rule.html">
PRODUCT_RULE</a>,
a MATLAB program which
can create a multidimensional quadrature rule as a product of
one dimensional rules.
</p>
<p>
<a href = "../../m_src/quadrule/quadrule.html">
QUADRULE</a>,
a MATLAB library which
defines a variety of
(mostly 1-dimensional) quadrature rules.
</p>
<p>
<a href = "../../c_src/smolpack/smolpack.html">
SMOLPACK</a>,
a C library which
uses the Genz test functions
to demonstrate quadrature in multiple dimensions using a sparse grid.
</p>
<p>
<a href = "../../m_src/spinterp/spinterp.html">
SPINTERP</a>,
a MATLAB library which
uses the Genz test functions
to demonstrate multilinear interpolation on a sparse grid.
</p>
<p>
<a href = "../../m_src/stroud/stroud.html">
STROUD</a>
a MATLAB library which
defines a variety of
quadrature rules over various "interesting" geometric shapes.
</p>
<p>
<a href = "../../m_src/test_nint/test_nint.html">
TEST_NINT</a>
a MATLAB library which
can be used to test N-dimensional
quadrature routines.
</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>
<li>
John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
Charles Mesztenyi, John Rice, Henry Thatcher,
Christoph Witzgall,<br>
Computer Approximations,<br>
Wiley, 1968,<br>
LC: QA297.C64.
</li>
<li>
Linus Schrage,<br>
A More Portable Fortran Random Number Generator,<br>
ACM Transactions on Mathematical Software,<br>
Volume 5, Number 2, June 1979, pages 132-138.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "testpack.m">testpack.m</a>
is the main program for testing TESTPACK.
</li>
<li>
<a href = "adapt.m">adapt.m</a>
carries out adaptive multidimensional quadrature.
</li>
<li>
<a href = "genz_function.m">genz_function.m</a>
evaluates one of the test integrand functions.
</li>
<li>
<a href = "genz_integral.m">genz_integral.m</a>
computes the exact integrals of the test functions.
</li>
<li>
<a href = "genz_name.m">genz_name.m</a>
returns the "name" of one of the test functions.
</li>
<li>
<a href = "genz_phi.m">genz_phi.m</a>
estimates the normal cumulative density function.
</li>
<li>
<a href = "genz_random.m">genz_random.m</a>
is a portable random number generator
</li>
<li>
<a href = "multst.m">multst.m</a>
tests a multidimensional integration routine.
</li>
<li>
<a href = "r8vec_median.m">r8vec_median.m</a>
computes the median of an R8VEC.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints out the current YMDHMS date as a timestamp.
</li>
<li>
<a href = "tuple_next.m">tuple_next.m</a>
computes the next element of a tuple space.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "testpack_output.txt">testpack_output.txt</a>,
the output file.
</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 26 May 2007.
</i>
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