TOMS612
Quadrature over a Triangle

TOMS612 is a FORTRAN77 program, using double precision arithmetic, which approximates the integral of a function over a triangular region.

Related Data and Programs:

DUNAVANT is a FORTRAN90 library of routines for defining Dunavant rules for quadrature on a triangle.

FEKETE is a FORTRAN90 library of routines for defining a Fekete rule for quadrature or interpolation over a triangle.

INTLIB is a FORTRAN90 library of routines for numerically estimating integrals in one dimension.

MACHINE is a FORTRAN77 library of routines which store the appropriate values of machine constants for a given machine.

NINTLIB is a FORTRAN90 library of routines for numerically estimating integrals in multiple dimensions.

QUADPACK is a FORTRAN90 library of routines for estimating integrals in one dimension.

QUADRULE is a FORTRAN90 library of routines for defining quadrature rules on a variety of intervals with different weight functions.

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

STROUD is a FORTRAN90 library of routines for defining quadrature rules on a regions of a variety of shapes and dimensions.

TEST_NINT is a FORTRAN90 library of functions that can be used to test N-dimensional quadrature routines.

TEST_TRI_INT is a FORTRAN90 library of functions that can be used to test algorithms for quadrature over a triangle.

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

TOMS379 is a FORTRAN77 library which estimates an integral.

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

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

TOMS468 is a FORTRAN77 library for the "automatic" integration of a function.

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

TRIANGULATION is a FORTRAN90 library of routines for triangulations, which includes some quadrature rules on triangles.

WANDZURA is a FORTRAN90 library of routines for defining 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.

Source Code:

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

Examples and Tests:

• toms612_prb.f, a sample calling program.
• toms612_prb.csh, commands to compile and run the sample program.
• toms612_prb.out, 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.