SPARSE_GRID_CCE
Clenshaw Curtis Exponential Growth Sparse Grids

SPARSE_GRID_CCE is a dataset directory which contains examples of multidimensional sparse grid quadrature rules based on Clenshaw Curtis Exponential growth rule.

A quadrature rule is a set of n points x and associated weights w so that the integral of a function f(x) over some particular region can be approximated by:

Integral f(x) dx = Sum ( 1 <= i <= n ) w(i) * f(x(i))

For this directory, a quadrature rule is stored as three files, containing the weights, the points, and a file containing two points defining the corners of the rectangular region. The dimension of the region is deduced implicitly from the dimension of the points.

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:

SPARSE_GRID_CCL, a dataset directory which contains M-dimensional Smolyak sparse grids based on the 1D Clenshaw Curtis Linear (CCL) growth rule;

SPARSE_GRID_CCS, a dataset library which contains sparse grids based on Clenshaw-Curtis Slow-exponential (CCS) growth rules.

Sample Files:

CCE grids in 1D:

• cce_d1_level0_x.txt, the abscissas for the level 0, order 1 rule.
• cce_d1_level0_w.txt, the weightse.
• cce_d1_level0_r.txt, the range.
• cce_d1_level1_x.txt, the abscissas for the level 1, order 3 rule.
• cce_d1_level1_w.txt, the weights.
• cce_d1_level1_r.txt, the range.
• cce_d1_level2_x.txt, the abscissas for the level 2, order 5 rule.
• cce_d1_level2_w.txt, the weights.
• cce_d1_level2_r.txt, the range.
• cce_d1_level3_x.txt, the abscissas for the level 3, order 9 rule.
• cce_d1_level3_w.txt, the weights.
• cce_d1_level3_r.txt, the range.
• cce_d1_level4_x.txt, the abscissas for the level 4, order 17 rule.
• cce_d1_level4_w.txt, the weightse.
• cce_d1_level4_r.txt, the range.
• cce_d1_level5_x.txt, the abscissas for the level 5, order 33 rule.
• cce_d1_level5_w.txt, the weights.
• cce_d1_level5_r.txt, the range.
• cce_d1_level6_x.txt, the abscissas.
• cce_d1_level6_w.txt, the weights.
• cce_d1_level6_r.txt, the range.

CCE grids in 2D:

• cce_d2_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• cce_d2_level0_w.txt, the weights.
• cce_d2_level0_r.txt, the region.
• cce_d2_level0.png, an image of the grid.
• cce_d2_level1_x.txt, the abscissas for the level 1, order 5 sparse rule.
• cce_d2_level1_w.txt, the weights.
• cce_d2_level1_r.txt, the region.
• cce_d2_level1.png,
• cce_d2_level2_x.txt, the abscissas for the level 2, order 13 sparse rule.
• cce_d2_level2_w.txt, the weights.
• cce_d2_level2_r.txt, the region.
• cce_d2_level2.png, an image of the grid.
• cce_d2_level3_x.txt, the abscissas for the level 3, order 29 sparse rule.
• cce_d2_level3_w.txt, the weights.
• cce_d2_level3_r.txt, the region.
• cce_d2_level3.png, an image of the grid.
• cce_d2_level4_x.txt, the abscissas for the level 4, order 65 sparse rule.
• cce_d2_level4_w.txt, the weights.
• cce_d2_level4_r.txt, the region.
• cce_d2_level4.png, an image of the grid.
• cce_d2_level5_x.txt, the abscissas for the level 5, order 145 sparse rule.
• cce_d2_level5_w.txt, the weights.
• cce_d2_level5_r.txt, the region.
• cce_d2_level5.png, an image of the grid.
• cce_d2_level6_x.txt, the abscissas for the level 6, order 321 sparse rule.
• cce_d2_level6_w.txt, the weights.
• cce_d2_level6_r.txt, the region.
• cce_d2_level6.png, an image of the grid.
• cce_d2_level7_x.txt, the abscissas for the level 7, order 705 sparse rule.
• cce_d2_level7_w.txt, the weights.
• cce_d2_level7_r.txt, the region.
• cce_d2_level7.png, an image of the grid.
• cce_d2_level8_x.txt, the abscissas for the level 8, order 1,537 sparse rule.
• cce_d2_level8_w.txt, the weights.
• cce_d2_level8_r.txt, the region.
• cce_d2_level9_x.txt, the abscissas for the level 9, order 3,329 sparse rule.
• cce_d2_level9_w.txt, the weights.
• cce_d2_level9_r.txt, the region.
• cce_d2_level10_x.txt, the abscissas for the level 10, order 7,169 sparse rule.
• cce_d2_level10_w.txt, the weights.
• cce_d2_level10_r.txt, the region.

CCE grids in 3D:

• cce_d3_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• cce_d3_level0_w.txt, the weights.
• cce_d3_level0_r.txt, the region.
• cce_d3_level0.png, a snapshot of a view of the 3D region.
• cce_d3_level1_x.txt, the abscissas for the level 1, order 7 sparse rule.
• cce_d3_level1_w.txt, the weights.
• cce_d3_level1_r.txt, the region.
• cce_d3_level1.png, a snapshot of a view of the 3D region.
• cce_d3_level2_x.txt, the abscissas for the level 2, order 25 sparse rule.
• cce_d3_level2_w.txt, the weights.
• cce_d3_level2_r.txt, the region.
• cce_d3_level2.png, a snapshot of a view of the 3D region.
• cce_d3_level3_x.txt, the abscissas for the level 3, order 69 sparse rule.
• cce_d3_level3_w.txt, the weights.
• cce_d3_level3_r.txt, the region.
• cce_d3_level3.png, a snapshot of a view of the 3D region.
• cce_d3_level4_x.txt, the abscissas for the level 4, order 177 sparse rule.
• cce_d3_level4_w.txt, the weights.
• cce_d3_level4_r.txt, the region.
• cce_d3_level4.png, a snapshot of a view of the 3D region.
• cce_d3_level5_x.txt, the abscissas for the level 5, order 441 sparse rule.
• cce_d3_level5_w.txt, the weights.
• cce_d3_level5_r.txt, the region.
• cce_d3_level5.png, a snapshot of a view of the 3D region.
• cce_d3_level6_x.txt, the abscissas for the level 6, order 1,073 sparse rule.
• cce_d3_level6_w.txt, the weights.
• cce_d3_level6_r.txt, the region.
• cce_d3_level6.png, a snapshot of a view of the 3D region.
• cce_d3_level7_x.txt, the abscissas for the level 7, order 2,561 sparse rule.
• cce_d3_level7_w.txt, the weights.
• cce_d3_level7_r.txt, the region.
• cce_d3_level7.png, a snapshot of a view of the 3D region.

CCE grids in 4D:

• cce_d4_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• cce_d4_level0_w.txt, the weights.
• cce_d4_level0_r.txt, the region.
• cce_d4_level1_x.txt, the abscissas for the level 1, order 9 sparse rule.
• cce_d4_level1_w.txt, the weights.
• cce_d4_level1_r.txt, the region.
• cce_d4_level2_x.txt, the abscissas for the level 2, order 41 sparse rule.
• cce_d4_level2_w.txt, the weights.
• cce_d4_level2_r.txt, the region.
• cce_d4_level3_x.txt, the abscissas for the level 3, order 137 sparse rule.
• cce_d4_level3_w.txt, the weights.
• cce_d4_level3_r.txt, the region.
• cce_d4_level4_x.txt, the abscissas for the level 4, order 401 sparse rule.
• cce_d4_level4_w.txt, the weights.
• cce_d4_level4_r.txt, the region.
• cce_d4_level5_x.txt, the abscissas for the level 5, order 1,105 sparse rule.
• cce_d4_level5_w.txt, the weights.
• cce_d4_level5_r.txt, the region.
• cce_d4_level6_x.txt, the abscissas for the level 6, order 2,929 sparse rule.
• cce_d4_level6_w.txt, the weights.
• cce_d4_level6_r.txt, the region.

CCE grids in 5D:

• cce_d5_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• cce_d5_level0_w.txt, the weights.
• cce_d5_level0_r.txt, the region.
• cce_d5_level1_x.txt, the abscissas for the level 1, order 11 sparse rule.
• cce_d5_level1_w.txt, the weights.
• cce_d5_level1_r.txt, the region.
• cce_d5_level2_x.txt, the abscissas for the level 2, order 61 sparse rule.
• cce_d5_level2_w.txt, the weights.
• cce_d5_level2_r.txt, the region.
• cce_d5_level3_x.txt, the abscissas for the level 3, order 241 sparse rule.
• cce_d5_level3_w.txt, the weights.
• cce_d5_level3_r.txt, the region.
• cce_d5_level4_x.txt, the abscissas for the level 4, order 801 sparse rule.
• cce_d5_level4_w.txt, the weights.
• cce_d5_level4_r.txt, the region.
• cce_d5_level5_x.txt, the abscissas for the level 5, order 2,433 sparse rule.
• cce_d5_level5_w.txt, the weights.
• cce_d5_level5_r.txt, the region.

CCE grids in 6D:

• cce_d6_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• cce_d6_level0_w.txt, the weights.
• cce_d6_level0_r.txt, the region.
• cce_d6_level1_x.txt, the abscissas for the level 1, order 13 sparse rule.
• cce_d6_level1_w.txt, the weights.
• cce_d6_level1_r.txt, the region.
• cce_d6_level2_x.txt, the abscissas for the level 2, order 85 sparse rule.
• cce_d6_level2_w.txt, the weights.
• cce_d6_level2_r.txt, the region.
• cce_d6_level3_x.txt, the abscissas for the level 3, order 389 sparse rule.
• cce_d6_level3_w.txt, the weights.
• cce_d6_level3_r.txt, the region.
• cce_d6_level4_x.txt, the abscissas for the level 4, order 1,457 sparse rule.
• cce_d6_level4_w.txt, the weights.
• cce_d6_level4_r.txt, the region.
• cce_d6_level5_x.txt, the abscissas for the level 5, order 4,865 sparse rule.
• cce_d6_level5_w.txt, the weights.
• cce_d6_level5_r.txt, the region.
• cce_d6_level6_x.txt, the abscissas for the level 6, order 15,121 sparse rule.
• cce_d6_level6_w.txt, the weights.
• cce_d6_level6_r.txt, the region.
• cce_d6_level7_x.txt, the abscissas for the level 7, order 44,689 sparse rule.
• cce_d6_level7_w.txt, the weights.
• cce_d6_level7_r.txt, the region.

CCE grids in 10D:

• cce_d10_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• cce_d10_level0_w.txt, the weights.
• cce_d10_level0_r.txt, the region.
• cce_d10_level1_x.txt, the abscissas for the level 1, order 21 sparse rule.
• cce_d10_level1_w.txt, the weights.
• cce_d10_level1_r.txt, the region.
• cce_d10_level2_x.txt, the abscissas for the level 2, order 221 sparse rule.
• cce_d10_level2_w.txt, the weights.
• cce_d10_level2_r.txt, the region.
• cce_d10_level3_x.txt, the abscissas for the level 3, order 1,581 sparse rule.
• cce_d10_level3_w.txt, the weights.
• cce_d10_level3_r.txt, the region.
• cce_d10_level4_x.txt, the abscissas for the level 4, order 8,801 sparse rule.
• cce_d10_level4_w.txt, the weights.
• cce_d10_level4_r.txt, the region.
• cce_d10_level5_x.txt, the abscissas for the level 5, order 41,265 sparse rule.
• cce_d10_level5_w.txt, the weights.
• cce_d10_level5_r.txt, the region.
• cce_d10_level6_x.txt, the abscissas for the level 6, order 171,425 sparse rule.
• cce_d10_level6_w.txt, the weights.
• cce_d10_level6_r.txt, the region.

CCE grids in 20D:

• cce_d20_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• cce_d20_level0_w.txt, the weights.
• cce_d20_level0_r.txt, the region.
• cce_d20_level1_x.txt, the abscissas for the level 1, order 41 sparse rule.
• cce_d20_level1_w.txt, the weights.
• cce_d20_level1_r.txt, the region.
• cce_d20_level2_x.txt, the abscissas for the level 2, order 841 sparse rule.
• cce_d20_level2_w.txt, the weights.
• cce_d20_level2_r.txt, the region.
• cce_d20_level3_x.txt, the abscissas for the level 3, order 11,561 sparse rule.
• cce_d20_level3_w.txt, the weights.
• cce_d20_level3_r.txt, the region.
• cce_d20_level4_x.txt, the abscissas for the level 4, order 120,401 sparse rule.
• cce_d20_level4_w.txt, the weights.
• cce_d20_level4_r.txt, the region.

CCE grids in 100D:

• cce_d100_level0_x.txt, the abscissas for the level 0, order 1 sparse rule.
• cce_d100_level0_w.txt, the weights.
• cce_d100_level0_r.txt, the region.
• cce_d100_level1_x.txt, the abscissas for the level 1, order 201 sparse rule.
• cce_d100_level1_w.txt, the weights.
• cce_d100_level1_r.txt, the region.
• cce_d100_level2_x.txt, the abscissas for the level 2, order 20,201 sparse rule.
• cce_d100_level2_w.txt, the weights.
• cce_d100_level2_r.txt, the region.

You can go up one level to the DATASETS page.