SPARSE_GRID_LAGUERRE is a C++ library which constructs sparse grids based on 1D Gauss-Laguerre rules.
Sparse grids are more naturally constructed from a nested family of quadrature rules. Gauss-Laguerre rules are not nested, but have higher accuracy. Thus, there can be a tradeoff. If we compare two sparse grids of the same "level", one using Gauss-Laguerre rules and the other a nested rule, then the Gauss-Laguerre sparse grid will have higher accuracy...but also a significantly greater number of points. When measuring efficiency, we really need to balance the cost in quadrature points against the accuracy, and so it is not immediately obvious which choice is best!
To slightly complicate matters, Gauss-Laguerre rules are not nested. A sparse grid constructed from Gauss-Laguerre rules will thus generally have more abscissas than a grid built of nested rules..
Here is a table showing the number of points in a sparse grid based on Gauss-Laguerre rules, indexed by the spatial dimension, and by the "level", which is simply an index for the family of sparse grids.
DIM: | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
LEVEL_MAX | ||||||
0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 3 | 7 | 10 | 13 | 16 | 19 |
2 | 7 | 29 | 58 | 95 | 141 | 196 |
3 | 15 | 95 | 255 | 515 | 906 | 1456 |
4 | 31 | 273 | 945 | 2309 | 4746 | 8722 |
5 | 63 | 723 | 3120 | 9065 | 21503 | 44758 |
6 | 127 | 1813 | 9484 | 32259 | 87358 | 204203 |
The code described and made available on this web page is distributed under the GNU LGPL license.
SPARSE_GRID_LAGUERRE is available in a C++ version and a FORTRAN90 version and a MATLAB version.
CC_DISPLAY, a MATLAB library which computes and displays Clenshaw Curtis grids in two dimensions, as well as sparse grids formed from sums of Clenshaw Curtis grids.
QUADRATURE_RULES, a dataset directory which defines quadrature rules; a number of examples of sparse grid quadrature rules are included.
QUADRULE, a C++ library which defines quadrature rules for various intervals and weight functions.
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 implements Novak and Ritter's method for estimating the integral of a function over a multidimensional hypercube using sparse grids.
SPARSE_GRID_CC, a dataset directory which contains the abscissas of sparse grids based on a Clenshaw Curtis rule.
SPARSE_GRID_CLOSED, a C++ library which defines define sparse grids based on closed nested quadrature rules.
SPARSE_GRID_DISPLAY, a MATLAB library which can display a 2D or 3D sparse grid.
SPARSE_GRID_F2, a dataset directory which contains the abscissas of sparse grids based on a Fejer Type 2 rule.
SPARSE_GRID_GL, a C++ library which computes a sparse grid based on 1D Gauss-Legendre rules.
SPARSE_GRID_GP, a dataset directory which contains the abscissas of sparse grids based on a Gauss Patterson rule.
SPARSE_GRID_HERMITE, a C++ library which creates sparse grids based on Gauss-Hermite rules.
SPARSE_GRID_LAGUERRE, a dataset directory which contains the abscissas of sparse grids based on a Gauss-Laguerre rule.
SPARSE_GRID_MIXED, a C++ library which constructs a sparse grid using different rules in each spatial dimension.
SPARSE_GRID_NCC, a dataset directory which contains the abscissas of sparse grids based on a Newton Cotes closed rule.
SPARSE_GRID_NCO, a dataset directory which contains the abscissas of sparse grids based on a Newton Cotes open rule.
SPARSE_GRID_OPEN, a C++ library which defines define sparse grids based on open nested quadrature rules.
TOMS847, a MATLAB program which uses sparse grids to carry out multilinear hierarchical interpolation. It is commonly known as SPINTERP, and is by Andreas Klimke.
You can go up one level to the C++ source codes.