TSG
TASMANIAN Sparse Grid Library


TSG MATLAB examples and an interface library which demonstrate the use of the TasmanianSparseGrid (TSG) package, which implements routines for working with sparse grids, to efficiently estimate integrals or compute interpolants of scalar functions of multidimensional arguments.

TSG can create three kinds of rules:

TSG is a family of algorithms for constructing multidimensional quadrature and interpolation rules from tensor products of 1-dimensional versions of such rules.

TSG includes a large variety of 1-dimensional rules, which are generally defined, by default, over the interval [-1,+1]. In that case, the multidimensional quadrature and interpolation rules will be defined over the hypercube [-1,+1]^d, but a simple linear transformation can be carried out by TSG to redefine the linearly redefine the region.

The one-dimensional rules that can be used include:

The TasmanianSparseGrid library is available for download from http://tasmanian.ornl.gov/ .

The MATLAB programs must actually work with the compiled C++ version of the TasmanianSparseGrid library. They do this by interfacing with a compiled C++ program called tasg, communicating via the MATLAB system() command, with data passed by writing and reading files from a workfile directory whose location is specified by the user.

Licensing:

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

Languages:

TSG is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Programs:

SGMGA, a MATLAB library which creates sparse grids based on a mixture of 1D quadrature rules, allowing anisotropic weights for each dimension.

SPARSE_GRID_CC, a MATLAB library which creates sparse grids based on Clenshaw-Curtis rules.

SPARSE_GRID_HW, a MATLAB library which creates sparse grids based on Gauss-Legendre, Gauss-Hermite, Gauss-Patterson, or a nested variation of Gauss-Hermite rules, by Florian Heiss and Viktor Winschel.

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;

SPQUAD, a MATLAB library which computes the points and weights of a sparse grid quadrature rule for an M-dimensional integral, based on the Clenshaw-Curtis quadrature rule, by Greg von Winckel.

TOMS847, a MATLAB library which carries out piecewise multilinear hierarchical sparse grid interpolation; this library is commonly called SPINTERP (version 2.1); this is ACM TOMS Algorithm 847, by Andreas Klimke;

Author:

Miroslav Stoyanov, Oak Ridge National Laboratory, mkstoyanov@gmail.com.

References:

  1. Miro Stoyanov,
    User Manual: TASMANIAN Sparse Grids,
    ORNL Report,
    Oak Ridge National Laboratory, August 2013.

Examples and Tests:

Source Code:

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


Last revised on 25 February 2014.