Multi-dimensional quadrature

NINTLIB, a MATLAB 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 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 multi-dimensional unit hypercube.

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

NINT_EXACTNESS, a MATLAB program which demonstrates how to measure the polynomial exactness of a multidimensional quadrature rule.


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

QUADRATURE_TEST, a MATLAB program which reads the definition of a multidimensional quadrature rule from three files, applies the rule to a number of test integrals, and prints the results.

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

QUADRULE_FAST, a MATLAB library which defines efficient versions of a few 1D quadrature rules.

STROUD, a MATLAB library which defines quadrature rules over various "interesting" geometric shapes.

TEST_INT_2D, a MATLAB library which defines test integrands for 2D quadrature rules.

TEST_NINT, a MATLAB library which tests multi-dimensional quadrature routines.

TESTPACK, a MATLAB library which defines a set of integrands used to test multidimensional quadrature.


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

Source Code:

Last revised on 15 February 2019.