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<html>
<head>
<title>
NINTLIB - Multi-dimensional quadrature
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
NINTLIB <br> Multi-dimensional quadrature
</h1>
<hr>
<p>
<b>NINTLIB</b>
is a MATLAB library which
estimates integrals over multi-dimensional
regions.
</p>
<p>
Please note that these routines are simple and academic. A good
program for computing an integral in multiple dimensions must
include error estimation and adaptivity. Simple straightforward
approaches to reducing the error will cause a ruinous explosion
in the number of function evaluations required.
</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>NINTLIB</b> is available in
<a href = "../../c_src/nintlib/nintlib.html">a C version</a> and
<a href = "../../cpp_src/nintlib/nintlib.html">a C++ version</a> and
<a href = "../../f77_src/nintlib/nintlib.html">a FORTRAN77 version</a> and
<a href = "../../f_src/nintlib/nintlib.html">a FORTRAN90 version</a> and
<a href = "../../m_src/nintlib/nintlib.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 multi-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/nint_exactness/nint_exactness.html">
NINT_EXACTNESS</a>,
a MATLAB program which
demonstrates how to measure the
polynomial exactness of a multidimensional quadrature rule.
</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/quadrature_test/quadrature_test.html">
QUADRATURE_TEST</a>,
a MATLAB program which
reads the definition of a
multidimensional quadrature rule from three files, applies
the rule to a number of test integrals, and prints the
results.
</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 = "../../m_src/quadrule_fast/quadrule_fast.html">
QUADRULE_FAST</a>,
a MATLAB library which
defines efficient versions
of a few 1D quadrature rules.
</p>
<p>
<a href = "../../m_src/stroud/stroud.html">
STROUD</a>,
a MATLAB library which
defines
quadrature rules over various "interesting" geometric shapes.
</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
tests multi-dimensional quadrature 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">
Reference:
</h3>
<p>
<ol>
<li>
Philip Davis, Philip Rabinowitz,<br>
Methods of Numerical Integration,<br>
Second Edition,<br>
Dover, 2007,<br>
ISBN: 0486453391,<br>
LC: QA299.3.D28.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "box_nd.m">box_nd.m</a>,
computes the integral of F(X) over a product box.
</li>
<li>
<a href = "i4_huge.m">i4_huge.m</a>,
returns a huge I4.
</li>
<li>
<a href = "monte_carlo_nd.m">monte_carlo_nd.m</a>,
computes a Monte Carlo estimate of an integral in a box.
</li>
<li>
<a href = "p5_nd.m">p5_nd.m</a>,
approximates the integral of F(X) over a product region.
</li>
<li>
<a href = "r8vec_uniform_01.m">r8vec_uniform_01.m</a>,
returns a unit pseudorandom R8VEC.
</li>
<li>
<a href = "romberg_nd.m">romberg_nd.m</a>,
approximates the integral of a F(X) over a product region.
</li>
<li>
<a href = "sample_nd.m">sample_nd.m</a>,
estimates the integral of F(X) over the multi-dimensional unit box.
</li>
<li>
<a href = "sum2_nd.m">sum2_nd.m</a>,
computes the integral of F(X) over a multi-dimensional product region.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a time stamp.
</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 = "nintlib_test.m">nintlib_test.m</a>, calls all the tests;
</li>
<li>
<a href = "nintlib_test_output.txt">nintlib_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "nintlib_testnd.m">nintlib_testnd.m</a>,
calls all the integrators for one test integrand.
</li>
<li>
<a href = "nintlib_test01.m">nintlib_test01.m</a>,
tests BOX_ND.
</li>
<li>
<a href = "nintlib_test02.m">nintlib_test02.m</a>,
tests P5_ND.
</li>
<li>
<a href = "nintlib_test03.m">nintlib_test03.m</a>,
tests ROMBERG_ND.
</li>
<li>
<a href = "nintlib_test04.m">nintlib_test04.m</a>,
tests SAMPLE_ND;
</li>
<li>
<a href = "nintlib_test05.m">nintlib_test05.m</a>,
demonstrates how to refine multi-dimensional integration results.
</li>
<li>
<a href = "nintlib_test06.m">nintlib_test06.m</a>,
tests MONTE_CARLO_ND.
</li>
<li>
<a href = "f1dn.m">f1dn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = 1;
</li>
<li>
<a href = "fbdn.m">fbdn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = 1/(1+(X(1:DIM_NUM)**2));
</li>
<li>
<a href = "fedn.m">fedn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = exp (sum(X(1:DIM_NUM));
</li>
<li>
<a href = "fxdn.m">fxdn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) );
</li>
<li>
<a href = "fx2dn.m">fx2dn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^2 );
</li>
<li>
<a href = "fx3dn.m">fx3dn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 );
</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 01 March 2007.
</i>
<!-- John Burkardt -->
</body>
</html>