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cubpack.html
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cubpack.html
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<html>
<head>
<title>
CUBPACK - Adaptive Cubature for Simplices
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
CUBPACK <br> Adaptive Cubature for Simplices
</h1>
<hr>
<p>
<b>CUBPACK</b>
is a FORTRAN90 library which
estimates the integral of a function
(or vector of functions) over a collection of N-dimensional
hyperrectangles and simplices,
by Alan Genz and Ronald Cools.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/dunavant/dunavant.html">
DUNAVANT</a>,
a FORTRAN90 library which
defines Dunavant rules for quadrature
on a triangle.
</p>
<p>
<a href = "../../f_src/fekete/fekete.html">
FEKETE</a>,
a FORTRAN90 library which
defines
a Fekete rule for quadrature or interpolation over a triangle.
</p>
<p>
<a href = "../../f_src/gm_rule/gm_rule.html">
GM_RULE</a>,
a FORTRAN90 library which
defines a Grundmann-Moeller
rule for quadrature over a triangle, tetrahedron, or general
M-dimensional simplex.
</p>
<p>
<a href = "../../f_src/intlib/intlib.html">
INTLIB</a>,
a FORTRAN90 library which
estimates integrals in 1D.
</p>
<p>
<a href = "../../f_src/keast/keast.html">
KEAST</a>,
a FORTRAN90 library which
defines a number of quadrature rules
for a tetrahedron.
</p>
<p>
<a href = "../../f_src/ncc_tetrahedron/ncc_tetrahedron.html">
NCC_TETRAHEDRON</a>,
a FORTRAN90 library which
defines Newton-Cotes closed quadrature
rules on a tetrahedron.
</p>
<p>
<a href = "../../f_src/ncc_triangle/ncc_triangle.html">
NCC_TRIANGLE</a>,
a FORTRAN90 library which
defines Newton-Cotes closed quadrature
rules on a triangle.
</p>
<p>
<a href = "../../f_src/nco_tetrahedron/nco_tetrahedron.html">
NCO_TETRAHEDRON</a>,
a FORTRAN90 library which
defines Newton-Cotes open quadrature
rules on a tetrahedron.
</p>
<p>
<a href = "../../f_src/nco_triangle/nco_triangle.html">
NCO_TRIANGLE</a>,
a FORTRAN90 library which
defines Newton-Cotes open quadrature
rules on a triangle.
</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/nint_exactness_tri/nint_exactness_tri.html">
NINT_EXACTNESS_TRI</a>,
a FORTRAN90 program which
investigates the polynomial
exactness of a quadrature rule for the triangle.
</p>
<p>
<a href = "../../f_src/nintlib/nintlib.html">
NINTLIB</a>,
a FORTRAN90 library which
estimates integrals in multiple dimensions.
</p>
<p>
<a href = "../../f_src/quadpack/quadpack.html">
QUADPACK</a>,
a FORTRAN90 library which
estimates integrals in 1D.
</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 = "../../datasets/quadrature_rules_tet/quadrature_rules_tet.html">
QUADRATURE_RULES_TET</a>,
a dataset directory which
contains triples of files defining various quadrature
rules on tetrahedrons.
</p>
<p>
<a href = "../../datasets/quadrature_rules_tri/quadrature_rules_tri.html">
QUADRATURE_RULES_TRI</a>,
a dataset directory which
contains quadrature rules to be applied to triangular
regions.
</p>
<p>
<a href = "../../f_src/quadrature_test/quadrature_test.html">
QUADRATURE_TEST</a>,
a FORTRAN90 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 FORTRAN90 library which
defines a number of
quadrature rules for approximate integration.
</p>
<p>
<a href = "../../f77_src/simpack/simpack.html">
SIMPACK</a>,
a FORTRAN77 library which
approximate 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
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_int/test_int.html">
TEST_INT</a>,
a FORTRAN90 library which
contains functions that may be used as test integrands for
quadrature rules in 1D.
</p>
<p>
<a href = "../../f_src/test_nint/test_nint.html">
TEST_NINT</a>,
a FORTRAN90 library containing a
number of functions that may be used as test integrands for
quadrature rules in multiple dimensions.
</p>
<p>
<a href = "../../f_src/test_tri_int/test_tri_int.html">
TEST_TRI_INT</a>,
a FORTRAN90 library which
can be used to test algorithms
for quadrature over a triangle.
</p>
<p>
<a href = "../../f77_src/toms351/toms351.html">
TOMS351</a>,
a FORTRAN77 library which
estimates an integral using Romberg
integration.
</p>
<p>
<a href = "../../f77_src/toms379/toms379.html">
TOMS379</a>,
a FORTRAN77 library which
estimates an integral.
</p>
<p>
<a href = "../../f77_src/toms418/toms418.html">
TOMS418</a>,
a FORTRAN77 library which
estimates the integral of a function
with a sine or cosine factor.
</p>
<p>
<a href = "../../f77_src/toms424/toms424.html">
TOMS424</a>,
a FORTRAN77 library which
estimates the integral of a function
using Clenshaw-Curtis quadrature.
</p>
<p>
<a href = "../../f77_src/toms468/toms468.html">
TOMS468</a>,
a FORTRAN77 library which
carries out the "automatic" integration of a function.
</p>
<p>
<a href = "../../f_src/wandzura/wandzura.html">
WANDZURA</a>,
a FORTRAN90 library
for defining Wandzura rules for quadrature
on a triangle.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Alan Genz and Ronald Cools.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Alan Genz, Ronald Cools,<br>
An Adaptive Cubature Algorithm for Simplices,<br>
ACM Transactions on Mathematical Software,<br>
Volume 29, Number 3, September 2003, pages 297-308.
</li>
<li>
Alan Genz, Ronald Cools,<br>
Algorithm 824:
CUBPACK: a Package for Automatic Cubature;
Framework Description,<br>
ACM Transactions on Mathematical Software,<br>
Volume 29, Number 3, September 2003, pages 287-296.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "buckley.f90">buckley.f90</a>
contains modules describing numeric precision;
</li>
<li>
<a href = "check.f90">check.f90</a>
checks the validity of the
input parameters to CUBATR on start or restart;
</li>
<li>
<a href = "cui.f90">cui.f90</a>
contains the CUBPACK user interface;
</li>
<li>
<a href = "divide.f90">divide.f90</a>
divides a region into subregions with equal volume;
</li>
<li>
<a href = "ds__output.txtines.f90">ds__output.txtines.f90</a>
contains _output.txtines involving the data structure;
</li>
<li>
<a href = "error_handling.f90">error_handling.f90</a>
contains _output.txtines to handle errors;
</li>
<li>
<a href = "global_all.f90">global_all.f90</a>
controls the computation of integrals over a collection of regions;
</li>
<li>
<a href = "internal_types.f90">internal_types.f90</a>
a module that declares some data types;
</li>
<li>
<a href = "region_processor.f90">region_processor.f90</a>
improves the estimate of an integral over a region;
</li>
<li>
<a href = "rule_1.f90">rule_1.f90</a>
returns integration rules for an interval;
</li>
<li>
<a href = "rule_c2.f90">rule_c2.f90</a>
computes integration rules and error estimates over a square;
</li>
<li>
<a href = "rule_c3.f90">rule_c3.f90</a>
computes integration rules and error estimates over a cube;
</li>
<li>
<a href = "rule_cn.f90">rule_cn.f90</a>
computes integration rules and error estimates over
a hyper-rectangular region;
</li>
<li>
<a href = "rule_general.f90">rule_general.f90</a>
computes integration rules and error estimates;
</li>
<li>
<a href = "rule_t2.f90">rule_t2.f90</a>
computes integration rules over a triangle;
</li>
<li>
<a href = "rule_t3.f90">rule_t3.f90</a>
computes integration rules over a tetrahedron;
</li>
<li>
<a href = "rule_tn.f90">rule_tn.f90</a>
computes integration rules over a hyper-symplex region;
</li>
<li>
<a href = "volume.f90">volume.f90</a>
computes the volume of a polytope;
</li>
<li>
<a href = "cubpack.sh">cubpack.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>DETAILS</b> simply prints information a_output.txt CUBPACK.
<ul>
<li>
<a href = "details.f90">details.f90</a>;
</li>
<li>
<a href = "details.sh">details.sh</a>,
commands to compile, link and run the program;
</li>
<li>
<a href = "details_output.txt">details_output.txt</a>, the output.
</li>
</ul>
</p>
<p>
<b>EX_QAG</b> approximates an integral over an interval, like NAG's
QAG _output.txtine.
<ul>
<li>
<a href = "ex_qag.f90">ex_qag.f90</a>;
</li>
<li>
<a href = "ex_qag.sh">ex_qag.sh</a>,
commands to compile, link and run the program;
</li>
<li>
<a href = "ex_qag_output.txt">ex_qag_output.txt</a>, the output.
</li>
</ul>
</p>
<p>
<b>EX_QAGS</b> approximates an integral over an interval, like NAG's
QAGS _output.txtine.
<ul>
<li>
<a href = "ex_qags.f90">ex_qags.f90</a>;
</li>
<li>
<a href = "ex_qags.sh">ex_qags.sh</a>,
commands to compile, link and run the program;
</li>
<li>
<a href = "ex_qags_output.txt">ex_qags_output.txt</a>, the output.
</li>
</ul>
</p>
<p>
<b>EX_TRIEX</b> approximates an integral over a triangle, like the
TRIEX _output.txtine.
<ul>
<li>
<a href = "ex_triex.f90">ex_triex.f90</a>;
</li>
<li>
<a href = "ex_triex.sh">ex_triex.sh</a>,
commands to compile, link and run the program;
</li>
<li>
<a href = "ex_triex_output.txt">ex_triex_output.txt</a>, the output.
</li>
</ul>
</p>
<p>
<b>EX_DECUHR2D</b> approximates an integral over a square, like the
DECUHR2D _output.txtine.
<ul>
<li>
<a href = "ex_decuhr2d.f90">ex_decuhr2d.f90</a>;
</li>
<li>
<a href = "ex_decuhr2d.sh">ex_decuhr2d.sh</a>,
commands to compile, link and run the program;
</li>
<li>
<a href = "ex_decuhr2d_output.txt">ex_decuhr2d_output.txt</a>, the output.
</li>
</ul>
</p>
<p>
<b>EX_CUTET</b> approximates an integral over a tetrahedron, like the
CUTET _output.txtine.
<ul>
<li>
<a href = "ex_cutet.f90">ex_cutet.f90</a>;
</li>
<li>
<a href = "ex_cutet.sh">ex_cutet.sh</a>,
commands to compile, link and run the program;
</li>
<li>
<a href = "ex_cutet_output.txt">ex_cutet_output.txt</a>, the output.
</li>
</ul>
</p>
<p>
<b>EX_DECUHR3D</b> approximates an integral over a cube, like the
DECUHR3D _output.txtine.
<ul>
<li>
<a href = "ex_decuhr3d.f90">ex_decuhr3d.f90</a>;
</li>
<li>
<a href = "ex_decuhr3d.sh">ex_decuhr3d.sh</a>,
commands to compile, link and run the program;
</li>
<li>
<a href = "ex_decuhr3d_output.txt">ex_decuhr3d_output.txt</a>, the output.
</li>
</ul>
</p>
<p>
<b>SIMPLEXPAPERTEST</b> approximates an integral over a 5D region
<ul>
<li>
<a href = "simplexpapertest.f90">simplexpapertest.f90</a>;
</li>
<li>
<a href = "simplexpapertest.sh">simplexpapertest.sh</a>,
commands to compile, link and run the program;
</li>
<li>
<a href = "simplexpapertest_output.txt">simplexpapertest_output.txt</a>, the output.
</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 January 2011.
</i>
<!-- John Burkardt -->
</body>
</html>