SPARSE_GRID_NCO
Sparse Grid Files
Newton Cotes Open

SPARSE_GRID_NCO 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 Newton Cotes Open 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 Newton Cotes Open sparse grid rule of dimension 2 and level 1:

  -6.666666666666666    
   2.666666666666666    
   2.666666666666666    
   2.666666666666666    
   2.666666666666666    
      

Here is the text of an "X" file storing the abscissas of a Newton Cotes Open sparse grid rule of dimension 2 and level 1:

   0.000000000000000       0.000000000000000    
 -0.5000000000000000       0.000000000000000    
  0.5000000000000000       0.000000000000000    
   0.000000000000000     -0.5000000000000000    
   0.000000000000000      0.5000000000000000   
      

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

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

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:

NCO_D2_LEVEL0, dimension 2, level 0 Newton Cotes Open rule, 1 point.

• nco_d2_level0_x.txt, X file.
• nco_d2_level0_x.png, a PNG image of the X data.
• nco_d2_level0_w.txt, W file.
• nco_d2_level0_r.txt, R file.

NCO_D2_LEVEL1, dimension 2, level 1 Newton Cotes Open rule, 5 points.

• nco_d2_level1_x.txt, X file.
• nco_d2_level1_x.png, a PNG image of the X data.
• nco_d2_level1_w.txt, W file.
• nco_d2_level1_r.txt, R file.

NCO_D2_LEVEL2 dimension 2, level 2 Newton Cotes Open rule, 17 points.

• nco_d2_level2_x.txt, X file.
• nco_d2_level2_x.png, a PNG image of the X data.
• nco_d2_level2_w.txt, W file.
• nco_d2_level2_r.txt, R file.

NCO_D2_LEVEL3, dimension 2, level 3 Newton Cotes Open rule, 49 points.

• nco_d2_level3_x.txt, X file.
• nco_d2_level3_x.png, a PNG image of the X data.
• nco_d2_level3_w.txt, W file.
• nco_d2_level3_r.txt, R file.

NCO_D2_LEVEL4, dimension 2, level 4 Newton Cotes Open rule, 129 points.

• nco_d2_level4_x.txt, X file.
• nco_d2_level4_x.png, a PNG image of the X data.
• nco_d2_level4_w.txt, W file.
• nco_d2_level4_r.txt, R file.

NCO_D2_LEVEL5, dimension 2, level 5 Newton Cotes Open rule, 321 points.

• nco_d2_level5_x.txt, X file.
• nco_d2_level5_x.png, a PNG image of the X data.
• nco_d2_level5_w.txt, W file.
• nco_d2_level5_r.txt, R file.

NCO_D2_LEVEL6, dimension 2, level 6 Newton Cotes Open rule, 769 points.

• nco_d2_level6_x.txt, X file.
• nco_d2_level6_w.txt, W file.
• nco_d2_level6_r.txt, R file.

You can go up one level to the DATASETS page.