Sparse Grids for Uniform and Normal Weights
Heiss and Winschel

SPARSE_GRID_HW is a FORTRAN90 library which can compute sparse grids for multidimensional integration, based on 1D rules for the unit interval with unit weight function, or for the real line with the Gauss-Hermite weight function. The original MATLAB code is by Florian Heiss and Viktor Winschel.

The original version of this software, and other information, is available at .

Four built-in 1D families of quadrature rules are supplied, and the user can extend the package by supplying any family of 1D quadrature rules.

The built-in families are identified by a 3-letter key which is also the name of the routine that returns members of the family:

The user can build new sparse grids by supplying a 1D quadrature family. Examples provided include:


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


SPARSE_GRID_HW is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version

Related Data and Programs:

GRID_DISPLAY, a MATLAB library which can display a 1D, 2D or 3D grid.

NINT_EXACTNESS_MIXED, a FORTRAN90 program which measures the polynomial exactness of a multidimensional quadrature rule based on a mixture of 1D quadrature rule factors.

PRODUCT_RULE, a FORTRAN90 program which constructs a product quadrature rule from identical 1D factor rules.

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

SANDIA_RULES, a FORTRAN90 library which generates Gauss quadrature rules of various orders and types.

SANDIA_SPARSE, a FORTRAN90 library which computes the points and weights of a Smolyak sparse grid, based on a variety of 1-dimensional quadrature rules.

SMOLPACK, a C library which implements Novak and Ritter's method for estimating the integral of a function over a multidimensional hypercube using sparse grids, by Knut Petras.

SPARSE_GRID_HERMITE, a FORTRAN90 library which creates sparse grids based on Gauss-Hermite rules.

SPINTERP, a MATLAB library which carries out piecewise multilinear hierarchical sparse grid interpolation; an earlier version of this software is ACM TOMS Algorithm 847, by Andreas Klimke;


Original MATLAB code by Florian Heiss and Viktor Winschel. FORTRAN90 version by John Burkardt.


Source Code:

Examples and Tests:

List of Routines:

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

Last revised on 26 February 2014.