TOMS468
Algorithm for Automatic Numerical Integration
Over a Finite Interval
TOMS468
is a FORTRAN77 library which
implements ACM TOMS algorithm 468, for estimating the
integral of a function over a finite interval.
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 quad ( a, b, result, k, epsil, npts, icheck, f )

where A and B are the limits of the interval,
RESULT is an array of length 8, which on output will
contain the integral estimate in entry RESULT(K),
K is set on output to indicate the appropriate entry
of RESULT, EPSIL is a requested relative accuracy,
NPTS is returned with the number of function evaluations,
ICHECK is an error flag which is 0 for normal return,
and F is the name of a usersupplied function which
evaluates the integrand at an arbitrary point X.
Languages:
TOMS468 is available in
a FORTRAN77 version.
Related Data and Programs:
INTLIB,
a FORTRAN90 library which
includes many routines for estimating 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.
TOMS351,
a FORTRAN77 library which
carries out Romberg integration of a function.
TOMS379,
a FORTRAN77 library which
carries out adaptive integration of a function.
Reference:

TNL Patterson,
The Optimal Addition of Points to Quadrature Formulae,
Mathematics of Computation,
Volume 22, 1968, pages 847856.

TNL Patterson,
Algorithm 468: Algorithm for Automatic Numerical Integration
Over a Finite Interval,
Communications of the ACM,
November 1973, Volume 16, Number 11, pages 694699.
Source Code:
Examples and Tests:
List of Routines:

QUAD is the basis quadrature routine.

QSUB uses QUAD in a nonadaptive subdivision scheme.

QSUBA uses QUAD in an adaptive subdivision scheme.
You can go up one level to
the FORTRAN77 source codes.
Last revised on 12 January 2006.