sandia_cubature, a FORTRAN90 code which implements quadrature rules for certain multidimensional regions and weight functions.
We consider the following integration regions:
The available rules for region EN_HER all have odd precision, ranging from 1 to 11. Some of these rules are valid for any spatial dimension N. However, many of these rules are restricted to a limited range, such as 2 <= N < 6. Some of the rules have two forms; in that case, the particular form is selectable by setting an input argument OPTION to 1 or 2. Finally, note that in multidimensional integration, the dependence of the order O (number of abscissas) on the spatial dimension N is critical. Rules for which the order is a multiple of 2^N are not practical for large values of N. The source code for each rule lists its formula for the order as a function of N.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
sandia_cubature is available in a C++ version and a Fortran90 version and a MATLAB version.
sandia_rules, a FORTRAN90 library which produces 1D quadrature rules of Chebyshev, Clenshaw Curtis, Fejer 2, Gegenbauer, generalized Hermite, generalized Laguerre, Hermite, Jacobi, Laguerre, Legendre and Patterson types.
stroud, a FORTRAN90 library which defines quadrature rules for a variety of multidimensional reqions.