SPARSE_GRID_GL
Sparse Grid Files
Gauss-Legendre

SPARSE_GRID_GL is a dataset directory which contains some examples of sparse grids, using the idea of a level to control the number of points, and assigning point locations using the Gauss-Legendre 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-Legendre 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-Legendre 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:

LEGENDRE_RULE, is a C++ program which computes a 1D Gauss-Legendre quadrature rule.

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.

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_GL, a C++ library which creates sparse grids based on Gauss-Legendre rules.

SPARSE_GRID_GL_DATASET, a C++ program which creates a sparse grid dataset based on Gauss-Legendre rules.

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-Legendre sparse grids in 2D.

• gl_d2_level0_x.txt, X file for dimension 2, level 0 Gauss-Legendre rule, 1 point.
• gl_d2_level0_x.png, a PNG image of the X data.
• gl_d2_level0_w.txt, W file.
• gl_d2_level0_r.txt, R file.
• gl_d2_level1_x.txt, X file for dimension 2, level 1 Gauss-Legendre rule, 5 points.
• gl_d2_level1_x.png, a PNG image of the X data.
• gl_d2_level1_w.txt, W file.
• gl_d2_level1_r.txt, R file.
• gl_d2_level2_x.txt, X file for dimension 2, level 2 Gauss-Legendre rule, 22 points.
• gl_d2_level2_x.png, a PNG image of the X data.
• gl_d2_level2_w.txt, W file.
• gl_d2_level2_r.txt, R file.
• gl_d2_level3_x.txt, X file for dimension 2, level 3 Gauss-Legendre rule, 75 points.
• gl_d2_level3_x.png, a PNG image of the X data.
• gl_d2_level3_w.txt, W file.
• gl_d2_level3_r.txt, R file.
• gl_d2_level4_x.txt, X file for dimension 2, level 4 Gauss-Legendre rule, 224 points.
• gl_d2_level4_x.png, a PNG image of the X data.
• gl_d2_level4_w.txt, W file.
• gl_d2_level4_r.txt, R file.
• gl_d2_level5_x.txt, X file for dimension 2, level 5 Gauss-Legendre rule, 613 points.
• gl_d2_level5_x.png, a PNG image of the X data.
• gl_d2_level5_w.txt, W file.
• gl_d2_level5_r.txt, R file.

Gauss-Legendre sparse grids in 6D.

• gl_d6_level0_x.txt, X file for dimension 6, level 0 Gauss-Legendre rule, 1 point.
• gl_d6_level0_w.txt, W file.
• gl_d6_level0_r.txt, R file.
• gl_d6_level1_x.txt, X file for dimension 6, level 1 Gauss-Legendre rule, 13 points.
• gl_d6_level1_w.txt, W file.
• gl_d6_level1_r.txt, R file.
• gl_d6_level2_x.txt, X file for dimension 6, level 2 Gauss-Legendre rule, 109 points.
• gl_d6_level2_w.txt, W file.
• gl_d6_level2_r.txt, R file.
• gl_d6_level3_x.txt, X file for dimension 6, level 3 Gauss-Legendre rule, 713 points.
• gl_d6_level3_w.txt, W file.
• gl_d6_level3_r.txt, R file.

Gauss-Legendre sparse grids in 10D.

• gl_d10_level0_x.txt, X file for dimension 10, level 0 Gauss-Legendre rule, 1 point.
• gl_d10_level0_w.txt, W file.
• gl_d10_level0_r.txt, R file.
• gl_d10_level1_x.txt, X file for dimension 10, level 1 Gauss-Legendre rule, 21 points.
• gl_d10_level1_w.txt, W file.
• gl_d10_level1_r.txt, R file.
• gl_d10_level2_x.txt, X file for dimension 10, level 2 Gauss-Legendre rule, 261 points.
• gl_d10_level2_w.txt, W file.
• gl_d10_level2_r.txt, R file.

You can go up one level to the DATASETS page.