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:

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 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;