TSG
TASMANIAN Sparse Grid Library

TSG includes C++ programs 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:

• Global grids, for globally smooth functions;
• Local polynomial grids, a piecewise polynomial approach for non-smooth functions
• Wavelet grids, also for non-smooth functions, but this option can sometimes achieve better accuracy with fewer points.

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:

• Chebyshev;
• Clenshaw Curtis;
• Fejer Type 2;
• Gauss Chebyshev Type 1;
• Gauss Chebyshev Type 2;
• Gauss Gegenbauer;
• Gauss Hermite;
• Gauss Jacobi;
• Gauss Laguerre;
• Gauss Legendre;
• Local polynomial;
• Local polynomial zero;
• Local wavelet.

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

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:

SGMG, a C++ library which creates a sparse grid dataset based on a mixed set of 1D factor rules, and experiments with the use of a linear growth rate for the quadrature rules.

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

SMOLPACK, a C library which estimates the integral of a function over a M-dimensional hypercube using a sparse grid, by Knut Petras;

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

SPARSE_GRID_HW, a C++ 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;

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:

TSG_PRB is a version of the example calling program provided with the TasmanianSparseGrids software library.

• tsg_prb.cpp, the calling program;
• tsg_prb.sh, commands to compile, link and run the calling program;
• tsg_prb_output.txt, the output file.

You can go up one level to the C++ source codes.