jburkardt

SPARSE_COUNT\ Sparse Grids Using a Single Factor {#sparse_count-sparse-grids-using-a-single-factor align=”center”} ==================================

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SPARSE_COUNT is a C++ library which contains routines for the analysis and construction of sparse grids in which a fixed family of 1D quadrature rules is used for all spatial dimensions.

By contrast, library MIXED allows different rules to be used in different dimensions.

Licensing: {#licensing align=”center”}

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages: {#languages align=”center”}

SPARSE_COUNT is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs: {#related-data-and-programs align=”center”}

MIXED, a library which creates a sparse grid dataset based on a mixed set of 1D factor rules.

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”}

• sparse_count.cpp, the source code.
• sparse_count.hpp, the include file.

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

• sparse_count_prb.cpp, a sample calling program.
• sparse_count_prb_output.txt, the output file.

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

• CC_S_SIZE: Clenshaw Curtis Slow Exponential Growth.
• CFN_E_SIZE; Closed Fully Nested, Exponential Growth.
• COMP_NEXT computes the compositions of the integer N into K parts.
• F2_S_SIZE: Fejer Type 2 Slow Growth.
• GP_S_SIZE: Gauss Patterson, Slow Growth.
• I4_CHOOSE computes the binomial coefficient C(N,K).
• OFN_E_SIZE: Open Fully Nested, Exponential Growth.
• ONN_E_SIZE: Open Non Nested, Exponential Growth.
• ONN_L_SIZE: Open Non Nested, Linear Growth.
• OWN_E_SIZE: Open Weakly Nested, Exponential Growth.
• OWN_L2_SIZE: Open Weakly Nested, Linear 2 Growth.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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

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Last revised on 25 April 2014.