SPARSE_GRID_F2
Sparse Grid Files
Fejer Type 2


SPARSE_GRID_F2 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 Fejer Type 2 rule.

Each sparse grid is stored using the "quadrature rule" format, that is, as three files:

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 Fejer Type 2 sparse grid rule of dimension 2 and level 1:


  -1.333333333333334    
   1.333333333333333    
   1.333333333333333    
   1.333333333333333    
   1.333333333333333      
      

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


  0.6123233995736766E-16  0.6123233995736766E-16
 -0.7071067811865475      0.6123233995736766E-16
  0.7071067811865475      0.6123233995736766E-16
  0.6123233995736766E-16 -0.7071067811865475    
  0.6123233995736766E-16  0.7071067811865475   
      

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_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:

F2_D2_LEVEL0, dimension 2, level 0 Fejer Type 2 rule, 1 point.

F2_D2_LEVEL1, dimension 2, level 1 Fejer Type 2 rule, 5 points.

F2_D2_LEVEL2 dimension 2, level 2 Fejer Type 2 rule, 17 points.

F2_D2_LEVEL3, dimension 2, level 3 Fejer Type 2 rule, 49 points.

F2_D2_LEVEL4, dimension 2, level 4 Fejer Type 2 rule, 129 points.

F2_D2_LEVEL5, dimension 2, level 5 Fejer Type 2 rule, 321 points.

F2_D2_LEVEL6, dimension 2, level 6 Fejer Type 2 rule, 769 points.

F2_D2_LEVEL7, dimension 2, level 7 Fejer Type 2 rule, 1793 points.

F2_D6_LEVEL0, dimension 6, level 0 Fejer Type 2 rule, 1 point.

F2_D6_LEVEL1, dimension 6, level 1 Fejer Type 2 rule, 13 points.

F2_D6_LEVEL2 dimension 6, level 2 Fejer Type 2 rule, 97 points.

F2_D6_LEVEL3, dimension 6, level 3 Fejer Type 2 rule, 545 points.

F2_D6_LEVEL4, dimension 6, level 4 Fejer Type 2 rule, 2561 points.

F2_D6_LEVEL5, dimension 6, level 5 Fejer Type 2 rule, 10625 points.

You can go up one level to the DATASETS page.


Last revised on 01 February 2009.