N-dimensional quadrature

NINTLIB is a FORTRAN77 library which estimates integrals over multi-dimensional regions.

Please note that these routines are simple and academic. A good program for computing an integral in multiple dimensions must include error estimation and adaptivity. Simple straightforward approaches to reducing the error will cause a ruinous explosion in the number of function evaluations required.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


NINTLIB is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

INTEGRAL_TEST, a FORTRAN90 program which tests the suitability of a set of N points for use in an equal-weight quadrature rule over the M-dimensional unit hypercube.

INTLIB, a FORTRAN90 library which esitmates the integral of a function over a one-dimensional interval.

QUADRULE, a FORTRAN90 library which defines a variety of (mostly 1-dimensional) quadrature rules.

STROUD, a FORTRAN90 library which defines a variety of quadrature rules over various "interesting" geometric shapes.

TEST_NINT, a FORTRAN90 library which tests M-dimensional quadrature routines.


  1. Philip Davis, Philip Rabinowitz,
    Methods of Numerical Integration,
    Second Edition,
    Dover, 2007,
    ISBN: 0486453391,
    LC: QA299.3.D28.

Source Code:

Examples and Tests:

List of Routines:

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

Last revised on 26 February 2007.