SPARSE_GRID_HERMITE
Sparse Grid Files
Gauss-Hermite

SPARSE_GRID_HERMITE 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-Hermite 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:

        -0.1797693134862000+309 -0.1797693134862000+309
         0.1797693134862000+309  0.1797693134862000+309
      

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

        1.047197551196598    
        0.5235987755982989    
        0.5235987755982989    
        0.5235987755982989    
        0.5235987755982989 
      

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

   0.000000000000000       0.000000000000000    
  -1.224744871391589       0.000000000000000    
   1.224744871391589       0.000000000000000    
   0.000000000000000      -1.224744871391589    
   0.000000000000000       1.224744871391589  
      

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:

GEN_HERMITE_RULE, a C++ program which can compute and print a generalized Gauss-Hermite quadrature rule.

HERMITE_RULE, a C++ program which can compute and print a Gauss-Hermite quadrature rule.

INT_EXACTNESS_GEN_HERMITE, a C++ program which tests the polynomial exactness of generalized Gauss-Hermite quadrature rules.

INT_EXACTNESS_HERMITE, a C++ program which tests the polynomial exactness of Gauss-Hermite quadrature rules.

SPARSE_GRID_HERMITE, a FORTRAN90 library which creates sparse grids based on Gauss-Hermite rules.

Sample Files:

Gauss-Hermite sparse grids in 2D.

• gh_d2_level0_x.txt, X file for dimension 2, level 0 Gauss-Hermite rule, 1 point.
• gh_d2_level0_w.txt, W file.
• gh_d2_level0_r.txt, R file.
• gh_d2_level1_x.txt, X file for dimension 2, level 1 Gauss-Hermite rule, 5 points.
• gh_d2_level1_w.txt, W file.
• gh_d2_level1_r.txt, R file.
• gh_d2_level2_x.txt, X file for dimension 2, level 2 Gauss-Hermite rule, 22 points.
• gh_d2_level2_w.txt, W file.
• gh_d2_level2_r.txt, R file.
• gh_d2_level3_x.txt, X file for dimension 2, level 3 Gauss-Hermite rule, 75 points.
• gh_d2_level3_w.txt, W file.
• gh_d2_level3_r.txt, R file.
• gh_d2_level4_x.txt, X file for dimension 2, level 4 Gauss-Hermite rule, 224 points.
• gh_d2_level4_w.txt, W file.
• gh_d2_level4_r.txt, R file.
• gh_d2_level5_x.txt, X file for dimension 2, level 5 Gauss-Hermite rule, 613 points.
• gh_d2_level5_w.txt, W file.
• gh_d2_level5_r.txt, R file.

Gauss-Hermite sparse grids in 3D.

• gh_d3_level0_x.txt, X file for dimension 3, level 0 Gauss-Hermite rule, 1 point.
• gh_d3_level0_w.txt, W file.
• gh_d3_level0_r.txt, R file.
• gh_d3_level1_x.txt, X file for dimension 3, level 1 Gauss-Hermite rule, 7 points.
• gh_d3_level1_w.txt, W file.
• gh_d3_level1_r.txt, R file.
• gh_d3_level2_x.txt, X file for dimension 3, level 2 Gauss-Hermite rule, 37 points.
• gh_d3_level2_w.txt, W file.
• gh_d3_level2_r.txt, R file.
• gh_d3_level3_x.txt, X file for dimension 3, level 3 Gauss-Hermite rule, 161 points.
• gh_d3_level3_w.txt, W file.
• gh_d3_level3_r.txt, R file.

Gauss-Hermite sparse grids in 6D.

• gh_d6_level0_x.txt, X file for dimension 6, level 0 Gauss-Hermite rule, 1 point.
• gh_d6_level0_w.txt, W file.
• gh_d6_level0_r.txt, R file.
• gh_d6_level1_x.txt, X file for dimension 6, level 1 Gauss-Hermite rule, 13 points.
• gh_d6_level1_w.txt, W file.
• gh_d6_level1_r.txt, R file.
• gh_d6_level2_x.txt, X file for dimension 6, level 2 Gauss-Hermite rule, 109 points.
• gh_d6_level2_w.txt, W file.
• gh_d6_level2_r.txt, R file.
• gh_d6_level3_x.txt, X file for dimension 6, level 3 Gauss-Hermite rule, 713 points.
• gh_d6_level3_w.txt, W file.
• gh_d6_level3_r.txt, R file.

You can go up one level to the DATASETS page.