TOMS439
Product Type Three-point Guass-Legendre Simpson's Integration

TOMS439 is a FORTRAN77 library which implements ACM TOMS algorithm 439, which carries out a product type three point Gauss-Legendre-Simpson's integration rule to estimate the integral from A to B of F(X) * G(X).

While the text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html, most of the early algorithms are not available. This is one of them. I typed it in.

Usage:

call p3pgs ( a, b, n, fn, gn, vint )

where A and B are the left and right endpoints of the interval, N is the number of times the rule is to be compounded, FN and GN are external functions for evaluating the integrand factors, and VINT is returned as the estimated value of the integral of FN(X) * GN(X) from A to B.

Languages:

TOMS439 is available in a FORTRAN77 version.

Related Data and Programs:

INTLIB, a FORTRAN90 library which estimates integrals.

QUADRULE, a FORTRAN90 library which can define various quadrature rules to estimate integrals.

TEST_INT, a FORTRAN90 library which defines a number of scalar functions of to test routines that estimate integrals.

TOMS436, a FORTRAN77 library which carries out product type trapezoidal integration.

TOMS437, a FORTRAN77 library which carries out product type Simpson's integration.

TOMS438, a FORTRAN77 library which carries out product type two-point Gauss-Legendre-Simpson's integration.

Reference:

1. Robert Boland,
   Algorithm 439: Product Type Three-point Guass-Legendre Simpson's Integration,
   Communications of the ACM,
   Volume 15, Number 12, December 1972, pages 1072.

Source Code:

• toms439.f, the source code.
• toms439.sh, commands to compile the source code.

Examples and Tests:

• toms439_prb.f, a sample calling program.
• toms439_prb.sh, commands to compile and run the sample program.
• toms439_prb_output.txt, the output from a run of the sample program.

List of Routines:

• P3PGS carries out a product type three-point Gauss-Legendre-Simpson's integration.

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