SPARSE_GRID_LAGUERRE_DATASET
Create Gauss-Laguerre Sparse Grid Dataset {#sparse_grid_laguerre_dataset-create-gauss-laguerre-sparse-grid-dataset align="center"}
SPARSE_GRID_LAGUERRE_DATASET is a C++ program which creates a Gauss-Laguerre sparse grid dataset.
sparse_grid_laguerre_dataset dim_num level_max
where
- dim_num is the spatial dimension, typically between 2 and 10;
- level_max is the sparse grid level, typically between 0 and 6, which controls the number of points in the grid. The 1D rules used will have order 2^(level_max)+1.
The code described and made available on this web page is distributed under the GNU LGPL license.
SPARSE_GRID_LAGUERRE_DATASET is available in a C++ version and a FORTRAN90 version and a MATLAB version.
CC_DISPLAY, a MATLAB library which computes and displays Clenshaw Curtis grids in two dimensions, as well as sparse grids formed from sums of Clenshaw Curtis grids.
QUADRATURE_RULES, a dataset directory which defines quadrature rules; a number of examples of sparse grid quadrature rules are included.
QUADRULE, a C++ library which defines quadrature rules for various intervals and weight functions.
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 dataset directory which contains the abscissas of sparse grids based on a Clenshaw Curtis rule.
SPARSE_GRID_CC_DATASET, a C++ program which creates a sparse grid dataset based on Clenshaw-Curtis rules.
SPARSE_GRID_F2, a dataset directory which contains the abscissas of sparse grids based on a Fejer Type 2 rule.
SPARSE_GRID_GL, a C++ library which can create a Gauss-Legendre sparse grid.
SPARSE_GRID_GP, a dataset directory which contains the abscissas of sparse grids based on a Gauss Patterson rule.
SPARSE_GRID_HERMITE, a C++ library which creates a Gauss-Hermite sparse grid.
SPARSE_GRID_LAGUERRE, a C++ library which can create a Gauss-Laguerre sparse grid.
SPARSE_GRID_LAGUERRE, a dataset directory which contains Gauss-Laguerre sparse grids.
SPARSE_GRID_MIXED, a C++ library which constructs a sparse grid using different rules in each spatial dimension.
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.
- 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. - Thomas Gerstner, Michael Griebel,
Numerical Integration Using Sparse Grids,
Numerical Algorithms,
Volume 18, Number 3-4, 1998, pages 209-232. - Albert Nijenhuis, Herbert Wilf,
Combinatorial Algorithms for Computers and Calculators,
Second Edition,
Academic Press, 1978,
ISBN: 0-12-519260-6,
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 2309-2345. - Sergey Smolyak,
Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions,
Doklady Akademii Nauk SSSR,
Volume 4, 1963, pages 240-243. - Dennis Stanton, Dennis White,
Constructive Combinatorics,
Springer, 1986,
ISBN: 0387963472,
LC: QA164.S79.
- sparse_grid_laguerre_dataset.cpp, the source code.
Here are the three quadrature files created by the command
sparse_grid_laguerre_dataset 2 3
- sparse_grid_laguerre_dataset_output.txt, the printed output from the command.
- lag_d2_level3_r.txt, the "R" or "region" file.
- lag_d2_level3_w.txt, the "W" or "weight" file.
- lag_d2_level3_x.txt, the "X" or "abscissa" file.
- MAIN is the main program for SPARSE_GRID_LAGUERRE_DATASET.
- CHOOSE computes the binomial coefficient C(N,K).
- COMP_NEXT computes the compositions of the integer N into K parts.
- I4_LOG_2 returns the integer part of the logarithm base 2 of an I4.
- I4_MAX returns the maximum of two I4's.
- I4_MIN returns the smaller of two I4's.
- I4_MODP returns the nonnegative remainder of I4 division.
- I4_POWER returns the value of I^J.
- I4_TO_STRING converts an I4 to a C++ string.
- I4VEC_PRODUCT multiplies the entries of an I4VEC.
- LAGUERRE_ABSCISSA sets abscissas for multidimensional Gauss-Laguerre quadrature.
- LAGUERRE_WEIGHTS returns weights for certain Gauss-Laguerre quadrature rules.
- LEVEL_TO_ORDER_OPEN converts a level to an order for open rules.
- MULTIGRID_INDEX_ONE returns an indexed multidimensional grid.
- PRODUCT_WEIGHT_LAGUERRE: weights for a product Gauss-Laguerre rule.
- R8_EPSILON returns the R8 roundoff unit.
- R8_HUGE returns a "huge" R8.
- R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
- R8MAT_WRITE writes an R8MAT file.
- R8VEC_DIRECT_PRODUCT2 creates a direct product of R8VEC's.
- R8VEC_PRINT_SOME prints "some" of an R8VEC.
- S_LEN_TRIM returns the length of a string to the last nonblank.
- SPARSE_GRID_LAGUERRE computes a sparse grid of Gauss-Laguerre points.
- SPARSE_GRID_LAGUERRE_INDEX indexes points in a Gauss-Laguerre sparse grid.
- SPARSE_GRID_LAGUERRE_SIZE sizes a sparse grid of Gauss-Laguerre points.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
- VEC_COLEX_NEXT2 generates vectors in colex order.
You can go up one level to the C++ source codes.
Last revised on 08 November 2009.