toms612

toms612, a Fortran77 code which approximates the integral of a function over a triangular region. The code is commonly known as triex(); This is a version of ACM TOMS algorithm 612.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

toms612 is available in a Fortran77 version.

Related Data and Programs:

toms612_test

dunavant, a Fortran90 code 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.

quad_rule, 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_rule, 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 code which estimates an integral using Romberg integration.

toms379, a Fortran77 code which estimates an integral.

toms418, a Fortran77 code 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.