SPARSE_COUNT
Sparse Grids Using a Single Factor

SPARSE_COUNT is a FORTRAN90 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 SPARSE_GRID_MIXED allows different rules to be used in different dimensions.

Licensing:

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

Languages:

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

Related Data and Programs:

SPARSE_GRID_HW, a FORTRAN90 library which creates sparse grids based on Gauss-Legendre, Gauss-Hermite, Gauss-Patterson, or a nested variation of Gauss-Hermite rules, by Florian Heiss and Viktor Winschel.

SPARSE_GRID_MIXED, a FORTRAN90 library which creates a sparse grid dataset based on a mixed set of 1D factor rules.

Reference:

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:

• sparse_count.f90, the source code.

Examples and Tests:

• sparse_count_test.f90, a sample calling program.
• sparse_count_test.txt, the output file.

List of Routines:

• CC_SE_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_SE_SIZE: Fejer Type 2 Slow Exponential Growth.
• GP_ME_SIZE: Gauss Patterson, Moderate Exponential Growth.
• GP_SE_SIZE: Gauss Patterson, Slow Exponential 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 FORTRAN90 source codes.