QUADPACK
Numerical Integration


QUADPACK is a FORTRAN90 library which estimates integrals using numerical quadrature, by Piessens, deDoncker-Kapenga, Ueberhuber, and Kahaner

There are routines for nonadaptive or adaptive integration, finite, semi-infinite or fully infinite integration regions, integrands with singularities, and integrands that include a factor of SIN(X) or COS(X).

Many subroutines come in two versions, a "simple" interface and an "extended" interface. Compare, for example, the routines QAWF and QAWFE. The first one simply makes sensible choices for many parameter values. The second one gives the user full control over all the parameters.

Routines for a finite region:

How to decide what routine to use, if your integration region is finite:

Routines for an infinite region:

Languages:

QUADPACK is available in a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

INTLIB, a FORTRAN90 library which numerically estimates integrals.

KRONROD, a FORTRAN90 library which can compute a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.

NMS, a FORTRAN90 library which includes QUADPACK.

PRODUCT_RULE, a FORTRAN90 program which can create a multidimensional quadrature rule as a product of one dimensional rules.

QUADPACK_DOUBLE, a FORTRAN90 library which estimates integrals using numerical quadrature, using double precision arithmetic, by Piessens, deDoncker-Kapenga, Ueberhuber, and Kahaner.

QUADRULE, a FORTRAN90 library which defines quadrature rules for various intervals and weight functions.

SLATEC, a FORTRAN90 library which includes QUADPACK.

STROUD, a FORTRAN90 library which defines quadrature rules for various geometric shapes.

TANH_QUAD, a FORTRAN90 library which sets up the tanh quadrature rule;

TEST_INT, a FORTRAN90 library which defines some test integration problems.

TEST_INT_HERMITE, a FORTRAN90 library which defines some test integration problems over infinite intervals.

TEST_INT_LAGUERRE, a FORTRAN90 library which defines test integrands for integration over [-ALPHA,+Infinity).

TOMS351, a FORTRAN77 library which estimates an integral using Romberg integration.

TOMS379, a FORTRAN77 library which estimates an integral.

TOMS418, a FORTRAN77 library which estimates the integral of a function with a sine or cosine factor.

TOMS424, a FORTRAN77 library which estimates the integral of a function using Clenshaw-Curtis quadrature.

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

Author:

Robert Piessens, Elise deDoncker-Kapenga, Christian Ueberhuber, David Kahaner.

Reference:

  1. Robert Piessens, Elise deDoncker-Kapenga, Christian Ueberhuber, David Kahaner,
    QUADPACK: A Subroutine Package for Automatic Integration,
    Springer, 1983,
    ISBN: 3540125531,
    LC: QA299.3.Q36.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 29 October 2010.