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.
sparse_grid_cc_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.
Each sparse grid is stored using the "quadrature rule" format, that is, as three files:
- an "R" or "region" file, which lists two points that bound the region;
- a "W" or "weight" file, which lists the weight for each abscissa;
- an "X" or "abscissa" file, which lists the abscissas of the rule.
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.
The code described and made available on this web page is distributed under the GNU LGPL license.
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.
- 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_cc_dataset.cpp, the source code.
Here are the files created by the command
sparse_grid_cc_dataset 2 3
- sparse_grid_cc_dataset_output.txt, the output file.
- cc_d2_level3_r.txt, the "R" or "region" file.
- cc_d2_level3_w.txt, the "W" or "weight" file.
- cc_d2_level3_x.txt, the "X" or "abscissa" file.
- MAIN is the main program for SPARSE_GRID_CC_DATASET.
- ABSCISSA_LEVEL_CLOSED_ND: first level at which an abscissa is generated.
- CC_ABSCISSA returns the I-th abscissa of the Clenshaw Curtis rule.
- CC_WEIGHTS computes Clenshaw Curtis weights.
- CHOOSE computes the binomial coefficient C(N,K).
- COMP_NEXT computes the compositions of the integer N into K parts.
- 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 integer 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 integer vector.
- INDEX_TO_LEVEL_CLOSED determines the level of a point given its index.
- LEVEL_TO_ORDER_CLOSED converts a level to an order for closed rules.
- MULTIGRID_INDEX0 returns an indexed multidimensional grid.
- MULTIGRID_SCALE_CLOSED renumbers a grid as a subgrid on a higher level.
- PRODUCT_WEIGHTS_CC computes weights for a Clenshaw Curtis product 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 with no header.
- 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_CC computes a sparse grid of Clenshaw Curtis points.
- SPARSE_GRID_CC_INDEX indexes the points forming a sparse grid.
- SPARSE_GRID_CFN_SIZE sizes a sparse grid of Closed Fully Nested points.
- SPARSE_GRID_CC_WEIGHTS gathers the weights.
- 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 12 January 2010