SPARSE_GRID_GP
Sparse Grid Files
Gauss Patterson

SPARSE_GRID_GP is a dataset directory which contains examples of sparse grids, using the idea of a level to control the number of points, and assigning point locations using the Gauss Patterson 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.

Example:

Here is the text of an "R" file storing two points that define the endpoints of the region, for a sparse grid rule of dimension 2 and level 1:

     -1.000000     -1.000000
      1.000000     +1.000000
      

Here is the text of an "W" file storing the weights of a Gauss-Patterson sparse grid rule of dimension 2 and level 1:

     -0.444444
      1.111111
      1.111111
      1.111111
      1.111111
      

Here is the text of an "X" file storing the abscissas of a Gauss-Patterson sparse grid rule of dimension 2 and level 1:

      0.000000      0.000000
     -0.774596      0.000000
      0.774596      0.000000
      0.000000     -0.774596
      0.000000      0.774596
      

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:

NINT_EXACTNESS_MIXED is a C++ program which measures the polynomial exactness of a multidimensional quadrature rule based on a mixture of 1D quadrature rule factors.

PATTERSON_RULE, is a C++ program which computes a 1D Gauss-Patterson quadrature rule.

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

SP_LEVEL_OPEN, a C++ program which creates a sparse grid dataset based on open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).

SPARSE_GRID_DISPLAY, a MATLAB program which reads a file of points on a sparse grid, displays the grid and save the image in a PNG file;

SPARSE_GRID_MIXED, a C++ library which creates a sparse grid dataset based on a mixed set of 1D factor rules.

SPINTERP, a MATLAB library which carries out piecewise multilinear hierarchical sparse grid interpolation, by Andreas Klimke; ACM TOMS Algorithm 847.

TABLE, a data directory which contains examples of TABLE files, a simple format for N points in M dimensions;

Sample Files:

Gauss-Patterson sparse grids in 2D.

• gp_d2_level0_x.txt, X file for dimension 2, level 0 Gauss-Patterson rule, 1 point.
• gp_d2_level0_x.png, a PNG image of the X data.
• gp_d2_level0_w.txt, W file.
• gp_d2_level0_r.txt, R file.
• gp_d2_level1_x.txt, X file for dimension 2, level 1 Gauss-Patterson rule, 5 points.
• gp_d2_level1_x.png, a PNG image of the X data.
• gp_d2_level1_w.txt, W file.
• gp_d2_level1_r.txt, R file.
• gp_d2_level2_x.txt, X file for dimension 2, level 2 Gauss-Patterson rule, 17 points.
• gp_d2_level2_x.png, a PNG image of the X data.
• gp_d2_level2_w.txt, W file.
• gp_d2_level2_r.txt, R file.
• gp_d2_level3_x.txt, X file for dimension 2, level 3 Gauss-Patterson rule, 49 points.
• gp_d2_level3_x.png, a PNG image of the X data.
• gp_d2_level3_w.txt, W file.
• gp_d2_level3_r.txt, R file.
• gp_d2_level4_x.txt, X file for dimension 2, level 4 Gauss-Patterson rule, 129 points.
• gp_d2_level4_x.png, a PNG image of the X data.
• gp_d2_level4_w.txt, W file.
• gp_d2_level4_r.txt, R file.
• gp_d2_level5_x.txt, X file for dimension 2, level 5 Gauss-Patterson rule, 321 points.
• gp_d2_level5_x.png, a PNG image of the X data.
• gp_d2_level5_w.txt, W file.
• gp_d2_level5_r.txt, R file.

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

• gp_d6_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• gp_d6_level0_w.txt, the weights.
• gp_d6_level0_r.txt, the region.
• gp_d6_level1_x.txt, the abscissas for the level 1, order 13 sparse rule.
• gp_d6_level1_w.txt, the weights.
• gp_d6_level1_r.txt, the region.
• gp_d6_level2_x.txt, the abscissas for the level 2, order 97 sparse rule.
• gp_d6_level2_w.txt, the weights.
• gp_d6_level2_r.txt, the region.
• gp_d6_level3_x.txt, the abscissas for the level 3, order 545 sparse rule.
• gp_d6_level3_w.txt, the weights.
• gp_d6_level3_r.txt, the region.
• gp_d6_level4_x.txt, the abscissas for the level 4, order 2561 sparse rule.
• gp_d6_level4_w.txt, the weights.
• gp_d6_level4_r.txt, the region.
• gp_d6_level5_x.txt, the abscissas for the level 5, order 10625 sparse rule.
• gp_d6_level5_w.txt, the weights.
• gp_d6_level5_r.txt, the region.

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

• gp_d10_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• gp_d10_level0_w.txt, the weights.
• gp_d10_level0_r.txt, the region.
• gp_d10_level1_x.txt, the abscissas for the level 1, order 21 sparse rule.
• gp_d10_level1_w.txt, the weights.
• gp_d10_level1_r.txt, the region.
• gp_d10_level2_x.txt, the abscissas for the level 2, order 241 sparse rule.
• gp_d10_level2_w.txt, the weights.
• gp_d10_level2_r.txt, the region.
• gp_d10_level3_x.txt, the abscissas for the level 3, order 2001 sparse rule.
• gp_d10_level3_w.txt, the weights.
• gp_d10_level3_r.txt, the region.
• gp_d10_level4_x.txt, the abscissas for the level 4, order 13441 sparse rule.
• gp_d10_level4_w.txt, the weights.
• gp_d10_level4_r.txt, the region.
• gp_d10_level5_x.txt, the abscissas for the level 5, order 77505 sparse rule.
• gp_d10_level5_w.txt, the weights.
• gp_d10_level5_r.txt, the region.

You can go up one level to the DATASETS page.