TOMS379
SQUANK (Simpson Quadrature Used Adaptively - Noise Killed)

TOMS379 is a FORTRAN77 program, using single precision arithmetic, which implements ACM TOMS algorithm 379, for estimating the integral of a function over a finite interval.

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.

Related Data and Programs:

INTLIB is a FORTRAN90 library of routines which includes many routines for estimating the integral of a function.

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

QUADRULE is a FORTRAN90 library of routines which defines many simple quadrature schemes.

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

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

TOMS351 is a FORTRAN77 library of routines which carries out Romberg integration of a function.

TOMS468 is a FORTRAN77 library of routines which carries out automatic integration of a function.

Usage:

value = squank ( a, big, error, fifth, rum, no, fun )

where SQUANK is the estimate for the integral, A and BIG are the limits of the interval, ERROR is a requested absolute accuracy, FIFTH is the size of the fifth order adjustment term, RUM is the estimated error, NO is the number of function evaluations, and FUN is the name of a user-supplied function which evaluates the integrand at an arbitrary point X.

Reference:

1. James Lyness,
   Algorithm 379: SQUANK (Simpson Quadrature Used Adaptively - Noise Killed),
   Communications of the ACM,
   Volume 13, Number 4, April 1970, pages 260-263.

Source Code:

• toms379.f, the source code.
• toms379.csh, commands to compile the source code.

Examples and Tests:

• toms379_prb.f, a sample calling program.
• toms379_prb.csh, commands to compile and run the sample program.
• toms379_prb.out, the output from a run of the sample program.

List of Routines:

• SQUANK applies Simpson quadrature adaptively to estimate an integral.

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