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SPARSE_GRID_CC_DATASET\ Create Clenshaw-Curtis Sparse Grid Dataset {#sparse_grid_cc_dataset-create-clenshaw-curtis-sparse-grid-dataset align=”center”} ==========================================


SPARSE_GRID_CC_DATASET is a C++ program which creates a Clenshaw-Curtis sparse grid dataset.

Usage: {#usage align=”center”}

sparse_grid_cc_dataset dim_num level_max

where

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.

Licensing: {#licensing align=”center”}

The code described and made available on this web page is distributed under the GNU LGPL license.

Languages: {#languages align=”center”}

SPARSE_GRID_CC_DATASET is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

CC_DISPLAY, a MATLAB library which can compute and display Clenshaw Curtis grids in two dimensions, as well as sparse grids formed from sums of Clenshaw Curtis grids.

QUADRATURE_RULES, a dataset directory of files which defines quadrature rules; a number of examples of sparse grid quadrature rules are included.

SGMGA, a C++ library which creates sparse grids based on a mixture of 1D quadrature rules, allowing anisotropic weights for each dimension.

SMOLPACK, a C library which implements Novak and Ritter’s method for estimating the integral of a function over a multidimensional hypercube using sparse grids.

SPARSE_GRID_CC, a C++ library which creates a Clenshaw-Curtis sparse grid.

SPARSE_GRID_CC, a dataset directory which contains examples of Clenshaw-Curtis sparse grids.

SPARSE_GRID_F2, a dataset directory which conains the abscissas of sparse grids based on a Fejer Type 2 rule.

SPARSE_GRID_GL_DATASET, a C++ program which creates a Gauss-Legendre sparse grid and writes the data to three files.

SPARSE_GRID_GP, a dataset directory which contains the abscissas of sparse grids based on a Gauss Patterson rule.

SPARSE_GRID_HERMITE_DATASET, a C++ program which creates a Gauss-Hermite sparse grid and write the data to three files.

SPARSE_GRID_LAGUERRE_DATASET, a C++ program which creates a Gauss-Laguerre sparse grid and write the data to three files.

SPARSE_GRID_MIXED_DATASET, a C++ program which creates a sparse grid dataset based on a mixture of 1D rules.

SPARSE_GRID_NCC, a dataset directory which contains the abscissas of sparse grids based on a Newton Cotes closed rule.

SPARSE_GRID_NCO, a dataset directory which contains the abscissas of sparse grids based on a Newton Cotes open rule.

SPARSE_GRID_OPEN_DATASET, a C++ program which creates a sparse grid dataset based on open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).

TOMS847, a MATLAB program which uses sparse grids to carry out multilinear hierarchical interpolation. It is commonly known as SPINTERP, and is by Andreas Klimke.

Reference: {#reference align=”center”}

  1. Volker Barthelmann, Erich Novak, Klaus Ritter,\ High Dimensional Polynomial Interpolation on Sparse Grids,\ Advances in Computational Mathematics,\ Volume 12, Number 4, 2000, pages 273-288.
  2. Thomas Gerstner, Michael Griebel,\ Numerical Integration Using Sparse Grids,\ Numerical Algorithms,\ Volume 18, Number 3-4, 1998, pages 209-232.
  3. Albert Nijenhuis, Herbert Wilf,\ Combinatorial Algorithms for Computers and Calculators,\ Second Edition,\ Academic Press, 1978,\ ISBN: 0-12-519260-6,\ LC: QA164.N54.
  4. Fabio Nobile, Raul Tempone, Clayton Webster,\ A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data,\ SIAM Journal on Numerical Analysis,\ Volume 46, Number 5, 2008, pages 2309-2345.
  5. Sergey Smolyak,\ Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions,\ Doklady Akademii Nauk SSSR,\ Volume 4, 1963, pages 240-243.
  6. Dennis Stanton, Dennis White,\ Constructive Combinatorics,\ Springer, 1986,\ ISBN: 0387963472,\ LC: QA164.S79.

Source Code: {#source-code align=”center”}

Examples and Tests: {#examples-and-tests align=”center”}

Here are the files created by the command

sparse_grid_cc_dataset 2 3

List of Routines: {#list-of-routines align=”center”}

You can go up one level to the C++ source codes.


Last revised on 12 January 2010