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 GaussLegendre, GaussHermite,
GaussPatterson, or a nested variation of GaussHermite 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:

Volker Barthelmann, Erich Novak, Klaus Ritter,
High Dimensional Polynomial Interpolation on Sparse Grids,
Advances in Computational Mathematics,
Volume 12, Number 4, 2000, pages 273288.

Thomas Gerstner, Michael Griebel,
Numerical Integration Using Sparse Grids,
Numerical Algorithms,
Volume 18, Number 34, 1998, pages 209232.

Albert Nijenhuis, Herbert Wilf,
Combinatorial Algorithms for Computers and Calculators,
Second Edition,
Academic Press, 1978,
ISBN: 0125192606,
LC: QA164.N54.

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 23092345.

Sergey Smolyak,
Quadrature and Interpolation Formulas for Tensor Products of
Certain Classes of Functions,
Doklady Akademii Nauk SSSR,
Volume 4, 1963, pages 240243.

Dennis Stanton, Dennis White,
Constructive Combinatorics,
Springer, 1986,
ISBN: 0387963472,
LC: QA164.S79.
Source Code:
Examples and Tests:
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.
Last revised on 29 April 2014.