SPARSE_GRID_GPE
Gauss Patterson Exponential Growth Sparse Grids

SPARSE_GRID_GPE is a dataset directory which contains examples of sparse grids based on the Gauss Patterson Exponential growth rule.

Each sparse grid is stored using the "quadrature rule" format, that is, as three files:

• an "R" or "region" file, which lists two points that bound the region;
• a "W" or "weight" file, which lists the weight for each abscissa;
• an "X" or "abscissa" file, which lists the abscissas of the rule.

The abscissas are ordered to respect the natural nesting of the sparse grids by level. That is, the file of level 3 points begins by listing the points in the level 2 grid.

Licensing:

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

Related Data and Programs:

SPARSE_GRID_GPS, a dataset directory which contains multidimensional Smolyak sparse grids based on the 1D Gauss-Patterson Slow growth rule;

Sample Files:

Gauss-Patterson sparse grids in 2D.

• gpe_d2_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• gpe_d2_level0_w.txt, the weights.
• gpe_d2_level0_r.txt, the region.
• gpe_d2_level0.png, an image.
• gpe_d2_level1_x.txt, X file for dimension 2, level 1 Gauss-Patterson rule, 5 points.
• gpe_d2_level1.png, an image.
• gpe_d2_level1_w.txt, W file.
• gpe_d2_level1_r.txt, R file.
• gpe_d2_level2_x.txt, X file for dimension 2, level 2 Gauss-Patterson rule, 17 points.
• gpe_d2_level2.png, an image.
• gpe_d2_level2_w.txt, W file.
• gpe_d2_level2_r.txt, R file.
• gpe_d2_level3_x.txt, X file for dimension 2, level 3 Gauss-Patterson rule, 49 points.
• gpe_d2_level3.png, an image.
• gpe_d2_level3_w.txt, W file.
• gpe_d2_level3_r.txt, R file.
• gpe_d2_level4_x.txt, X file for dimension 2, level 4 Gauss-Patterson rule, 129 points.
• gpe_d2_level4.png, an image.
• gpe_d2_level4_w.txt, W file.
• gpe_d2_level4_r.txt, R file.
• gpe_d2_level5_x.txt, X file for dimension 2, level 5 Gauss-Patterson rule, 321 points.
• gpe_d2_level5.png, an image.
• gpe_d2_level5_w.txt, W file.
• gpe_d2_level5_r.txt, R file.
• gpe_d2_level6_x.txt, X file for dimension 2, level 6 Gauss-Patterson rule, 769 points.
• gpe_d2_level6.png, an image.
• gpe_d2_level6_w.txt, W file.
• gpe_d2_level6_r.txt, R file.
• gpe_d2_level7_x.txt, X file for dimension 2, level 7 Gauss-Patterson rule, 1793 points.
• gpe_d2_level7_w.txt, W file.
• gpe_d2_level7_r.txt, R file.

Gauss-Patterson Sparse Quadrature Rules in 6D, defined on the [-1,1] hypercube:

• gpe_d6_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• gpe_d6_level0_w.txt, the weights.
• gpe_d6_level0_r.txt, the region.
• gpe_d6_level1_x.txt, the abscissas for the level 1, order 13 sparse rule.
• gpe_d6_level1_w.txt, the weights.
• gpe_d6_level1_r.txt, the region.
• gpe_d6_level2_x.txt, the abscissas for the level 2, order 97 sparse rule.
• gpe_d6_level2_w.txt, the weights.
• gpe_d6_level2_r.txt, the region.
• gpe_d6_level3_x.txt, the abscissas for the level 3, order 545 sparse rule.
• gpe_d6_level3_w.txt, the weights.
• gpe_d6_level3_r.txt, the region.
• gpe_d6_level4_x.txt, the abscissas for the level 4, order 2561 sparse rule.
• gpe_d6_level4_w.txt, the weights.
• gpe_d6_level4_r.txt, the region.
• gpe_d6_level5_x.txt, the abscissas for the level 5, order 10625 sparse rule.
• gpe_d6_level5_w.txt, the weights.
• gpe_d6_level5_r.txt, the region.
• gpe_d6_level6_x.txt, the abscissas for the level 6, order 40193 sparse rule.
• gpe_d6_level6_w.txt, the weights.
• gpe_d6_level6_r.txt, the region.

Gauss-Patterson Sparse Quadrature Rules in 10D, defined on the [-1,1] hypercube:

• gpe_d10_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• gpe_d10_level0_w.txt, the weights.
• gpe_d10_level0_r.txt, the region.
• gpe_d10_level1_x.txt, the abscissas for the level 1, order 21 sparse rule.
• gpe_d10_level1_w.txt, the weights.
• gpe_d10_level1_r.txt, the region.
• gpe_d10_level2_x.txt, the abscissas for the level 2, order 241 sparse rule.
• gpe_d10_level2_w.txt, the weights.
• gpe_d10_level2_r.txt, the region.
• gpe_d10_level3_x.txt, the abscissas for the level 3, order 2001 sparse rule.
• gpe_d10_level3_w.txt, the weights.
• gpe_d10_level3_r.txt, the region.
• gpe_d10_level4_x.txt, the abscissas for the level 4, order 13441 sparse rule.
• gpe_d10_level4_w.txt, the weights.
• gpe_d10_level4_r.txt, the region.
• gpe_d10_level5_x.txt, the abscissas for the level 5, order 77505 sparse rule.
• gpe_d10_level5_w.txt, the weights.
• gpe_d10_level5_r.txt, the region.

You can go up one level to the DATASETS page.