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:

• QUADRATURE_RULES is a dataset directory containing examples of how a quadrature rule can be defined by three simple files.
• SMOLPACK is a C library of routines which implements Novak and Ritter's method for estimating the integral of a function over a multidimensional hypercube using sparse grids.
• SPARSE_GRID_DISPLAY is a library of MATLAB routines which can display a 2D or 3D sparse grid.
• SPARSE_GRID_HERMITE is a library of FORTRAN90 routines which can construct a Gauss-Hermite sparse grid.
• SPARSE_GRID_HERMITE_DATASET is an executable FORTRAN90 program which can generate a Gauss-Hermite sparse grid based on user input.
• SPINTERP is a MATLAB library of routines by Andreas Klimke which use a sparse grid to perform multilinear hierarchical interpolation.
• TABLE is the file format used to store this data;

• QUADRATURE_RULES is a dataset directory of files that define quadrature rules; a number of examples of sparse grid quadrature rules are included.
• SPARSE_GRID_CC some sample sparse grids from the Clenshaw Curtis rule.
• SPARSE_GRID_F2 some sample sparse grids from the Fejer Type 2 rule.
• SPARSE_GRID_GP some sample sparse grids from the Gauss-Patterson rule.
• SPARSE_GRID_HERMITE some sample sparse grids from the Gauss-Hermite rule.
• SPARSE_GRID_LAGUERRE some sample sparse grids from the Gauss-Laguerre rule.
• SPARSE_GRID_NCC some sample sparse grids from the Newton Cotes Closed rule.
• SPARSE_GRID_NCO some sample sparse grids from the Newton Cotes Open rule.

Sample Files:

Gauss-Hermite sparse grids in 2D.

• herm_d2_level0_x.txt, X file for dimension 2, level 0 Gauss-Hermite rule, 1 point.
• herm_d2_level0_w.txt, W file.
• herm_d2_level0_r.txt, R file.
• herm_d2_level1_x.txt, X file for dimension 2, level 1 Gauss-Hermite rule, 5 points.
• herm_d2_level1_w.txt, W file.
• herm_d2_level1_r.txt, R file.
• herm_d2_level2_x.txt, X file for dimension 2, level 2 Gauss-Hermite rule, 22 points.
• herm_d2_level2_w.txt, W file.
• herm_d2_level2_r.txt, R file.
• herm_d2_level3_x.txt, X file for dimension 2, level 3 Gauss-Hermite rule, 75 points.
• herm_d2_level3_w.txt, W file.
• herm_d2_level3_r.txt, R file.
• herm_d2_level4_x.txt, X file for dimension 2, level 4 Gauss-Hermite rule, 224 points.
• herm_d2_level4_w.txt, W file.
• herm_d2_level4_r.txt, R file.
• herm_d2_level5_x.txt, X file for dimension 2, level 5 Gauss-Hermite rule, 613 points.
• herm_d2_level5_w.txt, W file.
• herm_d2_level5_r.txt, R file.

Gauss-Hermite sparse grids in 3D.

• herm_d3_level0_x.txt, X file for dimension 3, level 0 Gauss-Hermite rule, 1 point.
• herm_d3_level0_w.txt, W file.
• herm_d3_level0_r.txt, R file.
• herm_d3_level1_x.txt, X file for dimension 3, level 1 Gauss-Hermite rule, 7 points.
• herm_d3_level1_w.txt, W file.
• herm_d3_level1_r.txt, R file.
• herm_d3_level2_x.txt, X file for dimension 3, level 2 Gauss-Hermite rule, 37 points.
• herm_d3_level2_w.txt, W file.
• herm_d3_level2_r.txt, R file.
• herm_d3_level3_x.txt, X file for dimension 3, level 3 Gauss-Hermite rule, 161 points.
• herm_d3_level3_w.txt, W file.
• herm_d3_level3_r.txt, R file.

Gauss-Hermite sparse grids in 6D.

• herm_d6_level0_x.txt, X file for dimension 6, level 0 Gauss-Hermite rule, 1 point.
• herm_d6_level0_w.txt, W file.
• herm_d6_level0_r.txt, R file.
• herm_d6_level1_x.txt, X file for dimension 6, level 1 Gauss-Hermite rule, 13 points.
• herm_d6_level1_w.txt, W file.
• herm_d6_level1_r.txt, R file.
• herm_d6_level2_x.txt, X file for dimension 6, level 2 Gauss-Hermite rule, 109 points.
• herm_d6_level2_w.txt, W file.
• herm_d6_level2_r.txt, R file.
• herm_d6_level3_x.txt, X file for dimension 6, level 3 Gauss-Hermite rule, 713 points.
• herm_d6_level3_w.txt, W file.
• herm_d6_level3_r.txt, R file.

You can go up one level to the DATASETS page.