CUBPACK
Adaptive Cubature for Simplices


CUBPACK 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.

Languages:

CUBPACK is available in a FORTRAN90 version.

Related Data and Programs:

DUNAVANT, a FORTRAN90 library which defines Dunavant rules for quadrature on a triangle.

FEKETE, a FORTRAN90 library which defines a Fekete rule for quadrature or interpolation over a triangle.

GM_RULE, a FORTRAN90 library which defines a Grundmann-Moeller rule for quadrature over a triangle, tetrahedron, or general M-dimensional simplex.

INTLIB, a FORTRAN90 library which estimates integrals in 1D.

KEAST, a FORTRAN90 library which defines a number of quadrature rules for a tetrahedron.

NCC_TETRAHEDRON, a FORTRAN90 library which defines Newton-Cotes closed quadrature rules on a tetrahedron.

NCC_TRIANGLE, a FORTRAN90 library which defines Newton-Cotes closed quadrature rules on a triangle.

NCO_TETRAHEDRON, a FORTRAN90 library which defines Newton-Cotes open quadrature rules on a tetrahedron.

NCO_TRIANGLE, a FORTRAN90 library which defines Newton-Cotes open quadrature rules on a triangle.

NINT_EXACTNESS, a FORTRAN90 program which demonstrates how to measure the polynomial exactness of a multidimensional quadrature rule.

NINT_EXACTNESS_TRI, a FORTRAN90 program which investigates the polynomial exactness of a quadrature rule for the triangle.

NINTLIB, a FORTRAN90 library which estimates integrals in multiple dimensions.

QUADPACK, a FORTRAN90 library which estimates integrals in 1D.

QUADRATURE_RULES, a dataset directory which contains sets of files that define quadrature rules over various 1D intervals or multidimensional hypercubes.

QUADRATURE_RULES_TET, a dataset directory which contains triples of files defining various quadrature rules on tetrahedrons.

QUADRATURE_RULES_TRI, a dataset directory which contains quadrature rules to be applied to triangular regions.

QUADRATURE_TEST, 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.

QUADRULE, a FORTRAN90 library which defines a number of quadrature rules for approximate integration.

SIMPACK, 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.

STROUD, a FORTRAN90 library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

TEST_INT, a FORTRAN90 library which contains functions that may be used as test integrands for quadrature rules in 1D.

TEST_NINT, a FORTRAN90 library containing a number of functions that may be used as test integrands for quadrature rules in multiple dimensions.

TEST_TRI_INT, a FORTRAN90 library which can be used to test algorithms for quadrature over a triangle.

TOMS351, a FORTRAN77 library which estimates an integral using Romberg integration.

TOMS379, a FORTRAN77 library which estimates an integral.

TOMS418, a FORTRAN77 library which estimates the integral of a function with a sine or cosine factor.

TOMS424, a FORTRAN77 library which estimates the integral of a function using Clenshaw-Curtis quadrature.

TOMS468, a FORTRAN77 library which carries out the "automatic" integration of a function.

WANDZURA, a FORTRAN90 library for defining Wandzura rules for quadrature on a triangle.

Author:

Alan Genz and Ronald Cools.

Reference:

  1. Alan Genz, Ronald Cools,
    An Adaptive Cubature Algorithm for Simplices,
    ACM Transactions on Mathematical Software,
    Volume 29, Number 3, September 2003, pages 297-308.
  2. Alan Genz, Ronald Cools,
    Algorithm 824: CUBPACK: a Package for Automatic Cubature; Framework Description,
    ACM Transactions on Mathematical Software,
    Volume 29, Number 3, September 2003, pages 287-296.

Source Code:

Examples and Tests:

DETAILS simply prints information about CUBPACK.

EX_QAG approximates an integral over an interval, like NAG's QAG routine.

EX_QAGS approximates an integral over an interval, like NAG's QAGS routine.

EX_TRIEX approximates an integral over a triangle, like the TRIEX routine.

EX_DECUHR2D approximates an integral over a square, like the DECUHR2D routine.

EX_CUTET approximates an integral over a tetrahedron, like CUTET.

EX_DECUHR3D approximates an integral over a cube, like DECUHR3D.

SIMPLEXPAPERTEST approximates an integral over a 5D region

You can go up one level to the FORTRAN90 source codes.


Last revised on 17 January 2011.