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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 FORTRAN90 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/cubpack/cubpack.html">
CUBPACK</a>,
a FORTRAN90 library which
estimates the integral of a function over a collection of N-dimensional
hyperrectangles and simplices.
</p>
<p>
<a href = "../../f_src/fekete/fekete.html">
FEKETE</a>,
a FORTRAN90 library which
defines Fekete rules for interpolation or quadrature on a triangle.
</p>
<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 = "../../f_src/nint_exactness/nint_exactness.html">
NINT_EXACTNESS</a>,
a FORTRAN90 program which
measures 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 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/quadrule/quadrule.html">
QUADRULE</a>,
a FORTRAN90 library which
defines a variety of
(mostly 1-dimensional) quadrature rules.
</p>
<p>
<a href = "../../f77_src/simpack/simpack.html">
SIMPACK</a>,
a FORTRAN77 library which
approximates the integral of a function or vector of functions
over a multidimensional simplex, or a region which is the
sum of multidimensional simplexes.
</p>
<p>
<a href = "../../f_src/stroud/stroud.html">
STROUD</a>,
a FORTRAN90 library which
defines a variety of
quadrature rules over various "interesting" geometric shapes.
</p>
<p>
<a href = "../../f_src/test_int_2d/test_int_2d.html">
TEST_INT_2D</a>,
a FORTRAN90 library which
defines test integrands for 2D quadrature rules.
</p>
<p>
<a href = "../../f_src/test_nint/test_nint.html">
TEST_NINT</a>,
a FORTRAN90 library which
defines test functioins for multi-dimensional quadrature 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>
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 = "nintlib.f90">nintlib.f90</a>, the source code.
</li>
<li>
<a href = "nintlib.sh">nintlib.sh</a>, commands to
compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "nintlib_prb.f90">nintlib_prb.f90</a>, a sample problem.
</li>
<li>
<a href = "nintlib_prb.sh">nintlib_prb.sh</a>, commands to
compile, link and run the sample problem.
</li>
<li>
<a href = "nintlib_prb_output.txt">nintlib_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BOX_ND</b> estimates a multidimensional integral using a product rule.
</li>
<li>
<b>MONTE_CARLO_ND</b> estimates a multidimensional integral using Monte Carlo.
</li>
<li>
<b>P5_ND</b> estimates a multidimensional integral using a formula of exactness 5.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>ROMBERG_ND</b> estimates a multidimensional integral using Romberg integration.
</li>
<li>
<b>SAMPLE_ND</b> estimates a multidimensional integral using sampling.
</li>
<li>
<b>SUM2_ND</b> estimates a multidimensional integral using a product rule.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TUPLE_NEXT</b> computes the next element of a tuple space.
</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 30 August 2005.
</i>
<!-- John Burkardt -->
</body>
</html>