TOMS353
Filon Quadrature

TOMS353 is a FORTRAN77 library which implements ACM TOMS algorithm 353, which estimates integrals of F(X)*COS(M*PI*X) or F(X)*SIN(M*PI*X) from 0 to 1, using Filon quadrature.

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.

Usage:

call fser1 (f, eps, max, m, c, s, lc, ls )

where F is the name of the FORTRAN function that evaluates the main integrand factor F(X), EPS is the desired accuracy, MAX is the maximum number of interval halvings allowed, M is the integer multiplier in the argument M*PI*X of the SIN or COS factors, C and/or S are returned as estimates of the integral from 0 to 1 of F(X)*COS(M*PI*X) and F(X)*SIN(M*PI*X), LC and LS are input by the user as 1 or 0, depending on whether the cosine and sine integrals are or are not to be computed.

Related Data and Programs:

INTLIB, a FORTRAN90 library which contains routines which estimate the integral of a function.

QUADPACK, a FORTRAN90 library which includes many routines for estimating the integral of a function, including weight functions, singularities, and infinite intervals.

QUADRULE, a FORTRAN90 library which defines many simple quadrature schemes.

STROUD, a FORTRAN90 library which defines quadrature schemes for a number of geometrically interesting regions.

TEST_INT, a FORTRAN90 library which contains routines which define integrands suitable for testing integration software.

TOMS418, a FORTRAN77 library which uses Filon quadrature for integrands with a SIN or COS factor.

TOMS468, a FORTRAN77 library which carries out the automatic integration of a function.

Reference:

1. Stephen Chase, Lloyd Fosdick,
   An Algorithm for Filon Quadrature,
   Communications of the ACM,
   Volume 12, Number 8, pages 453-457, August 1969.
2. Stephen Chase, Lloyd Fosdick,
   Algorithm 353: Filon Quadrature,
   Communications of the ACM,
   Volume 12, Number 8, pages 457-458, August 1969.
3. Bo Einarsson,
   Remark on Algorithm 353: Filon Quadrature,
   Communications of the ACM,
   April 1970, Volume 13, Issue 4, page 263.

Source Code:

• toms353.f, the source code.
• toms353.sh, commands to compile the source code.

Examples and Tests:

• toms353_prb.f, a sample calling program.
• toms353_prb.sh, commands to compile and run the sample program.
• toms353_prb_output.txt, the output from a run of the sample program.

List of Routines:

• FSER1 estimates an integral using Filon quadrature.

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