NINTLIB is a FORTRAN90 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.
CUBPACK, a FORTRAN90 library which estimates the integral of a function over a collection of N-dimensional hyperrectangles and simplices.
FEKETE, a FORTRAN90 library which defines Fekete rules for interpolation or quadrature on a triangle.
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 FORTRAN90 program which measures the polynomial exactness of a multidimensional quadrature rule.
PRODUCT_RULE, a FORTRAN90 program which constructs a product rule from 1D factor rules.
QUADRATURE_RULES, a dataset directory which contains sets of files that define quadrature rules over various 1D intervals or multidimensional hypercubes.
QUADRULE, a FORTRAN90 library which defines a variety of (mostly 1-dimensional) quadrature rules.
SIMPACK, a FORTRAN77 library which approximates the integral of a function or vector of functions over a multidimensional simplex, or a region which is the sum of multidimensional simplexes.
STROUD, a FORTRAN90 library which defines a variety of quadrature rules over various "interesting" geometric shapes.
TEST_INT_2D, a FORTRAN90 library which defines test integrands for 2D quadrature rules.
TEST_NINT, a FORTRAN90 library which defines test functioins for multi-dimensional quadrature routines.
TESTPACK, a FORTRAN90 library which defines a set of integrands used to test multidimensional quadrature.
You can go up one level to the FORTRAN90 source codes.