TOMS612
Quadrature over a Triangle

TOMS612 is a FORTRAN77 library which approximates the integral of a function over a triangular region.

Languages:

TOMS612 is available in a FORTRAN77 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.

INTLIB, a FORTRAN90 library which numerically estimates integrals in one dimension.

LYNESS_RULE, a FORTRAN90 library which returns Lyness-Jespersen quadrature rules for the triangle.

MACHINE, a FORTRAN77 library which stores the appropriate values of machine constants for a given machine.

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

QUADPACK, a FORTRAN90 library which estimates integrals in one dimension.

QUADRULE, a FORTRAN90 library which defines quadrature rules on a variety of intervals with different weight functions.

STRI_QUAD, a FORTRAN90 library which can approximate the integral of a function over the surface of a sphere.

STROUD, a FORTRAN90 library which defines quadrature rules on a regions of a variety of shapes and dimensions.

TEST_NINT, a FORTRAN90 library which can be used to test N-dimensional quadrature routines.

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.

TOMS706, a FORTRAN77 library which estimates the integral of a function over a triangulated region.

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

Reference:

1. Elise deDoncker, Ian Robinson,
   Algorithm 612, TRIEX: Integration Over a Triangle Using Nonlinear Extrapolation,
   ACM Transactions on Mathematical Software,
   Volume 10, Number 1, March 1984, pages 17-22.
2. Phyllis Fox, Andrew Hall, Norman Schryer,
   Algorithm 528: Framework for a Portable Library,
   ACM Transactions on Mathematical Software,
   Volume 4, Number 2, June 1978, page 176-188.
3. James Lyness, Dennis Jespersen,
   Moderate Degree Symmetric Quadrature Rules for the Triangle,
   Journal of the Institute of Mathematics and its Applications,
   Volume 15, Number 1, February 1975, pages 19-32.

Source Code:

• toms612.f, the source code.
• toms612.sh, commands to compile the source code.

Examples and Tests:

• toms612_prb.f, a sample calling program.
• toms612_prb.sh, commands to compile and run the sample program.
• toms612_prb_output.txt, the output from a run of the sample program.

List of Routines:

• D1MACH returns double precision machine-dependent constants.
• TRIEX approximates the integral of a function over a triangle.
• DIVIN subdivides a triangle into four subtriangles.
• QUATRI returns a quadrature rule for a triangle.
• EPSALG carries out the epsilon algorithm.
• ORDER carries out a sorting algorithm.

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