SIMPACK
Quadrature over Multidimensional Simplexes

SIMPACK is a FORTRAN77 library which approximates the integral of a vector of functions over a multidimensional simplex, or a region which is the sum of multidimensional simplexes, by Alan Genz.

Languages:

SIMPACK is available in a FORTRAN77 version.

Related Data and Programs:

CUBPACK, a FORTRAN90 library which estimates the integral of a function (or vector of functions) over a collection of M-dimensional hyperrectangles and simplices.

GM_RULE, a FORTRAN77 library which defines a Grundmann-Moeller rule for quadrature over a triangle, tetrahedron, or general M-dimensional simplex.

INTLIB, a FORTRAN90 library which contains routines for numerical estimation of integrals in 1D.

NINTLIB, a FORTRAN77 library which contains routines for numerical estimation of integrals in M dimensions.

QUADPACK, a FORTRAN77 library which contains a variety of routines for numerical estimation of integrals in 1D.

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

SIMPLEX_COORDINATES, a FORTRAN77 library which computes the Cartesian coordinates of the vertices of a regular simplex in M 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 which contains functions that may be used as test integrands for quadrature rules in M dimensions.

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

Author:

Alan Genz,
Department of Mathematics,
Washington State University,
Pullman, WA 99164-3113, USA,
Email: alangenz@wsu.edu.

Reference:

1. Alan Genz, Ron Cools,
   An Adaptive Numerical Cubature Algorithm for Simplices,
   Technical Report TW273,
   Department of Computer Science,
   Katholieke Universiteit Leuven, 1997.
2. Axel Grundmann, Michael Moeller,
   Invariant Integration Formulas for the N-Simplex by Combinatorial Methods,
   SIAM Journal on Numerical Analysis,
   Volume 15, Number 2, April 1978, pages 282-290.
3. Arthur Stroud,
   A Fifth Degree Integration Formula for the n-Simplex,
   SIAM Journal on Numerical Analysis,
   Volume 6, Number 1, March 1969, pages 90-98.
4. Ivan Mysovskikh,
   On a cubature formula for the simplex,
   Voprosy Vycislitelnoj i Prikl. Mat.,
   Volume 51, 1978, pages 74-90.

Source Code:

• simpack.f, the source code.
• simpack.sh, commands to compile the source code.

Examples and Tests:

• simpack_prb.f, a sample calling program.
• simpack_prb.sh, commands to compile and run the sample program.
• simpack_prb_output.txt, the output from a run of the sample program.

List of Routines:

• SMPINT integrates a vector function of a collection of simplexes.
• SMPCHC checks the input parameters to SMPINT.
• SMPSAD integrates a vector function over a hyperrectangle.
• SMPVOL computes the scaled volume of a simplex.
• SMPRUL computes the integration rules.
• SMPROD computes a weighted dot product.
• SMPRMS initializes a basic rule and some null rules.
• SMPCPY sets a vector to a constant.
• SMPSMS computes a symmetric sum over a simplex.
• SMPSTR maintains a heap to keep track of subregions.
• SMPDFS determines how to subdivide the subregion.

You can go up one level to the FORTRAN77 source codes.