toms353

toms353, a Fortran77 code 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: https://www.acm.org/pubs/calgo or NETLIB: https://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.

Licensing:

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

Languages:

toms353 is available in a Fortran77 version.

Related Data and Programs:

toms353_test

intlib, a Fortran90 code which contains routines which estimate the integral of a function.

quadpack, a Fortran90 code which includes many routines for estimating the integral of a function, including weight functions, singularities, and infinite intervals.

quad_rule, a Fortran90 library which defines many simple quadrature schemes.

stroud_rule, 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 code 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.