SOBOL_DATASET
Generate Sobol Datasets

SOBOL_DATASET is a MATLAB program which creates a Sobol dataset.

Usage:

r = sobol_dataset ( m, n, skip )

• m is the spatial dimension.
• n is the number of points to generate;
• skip is the initial number of points to skip over. The value of skip is used to allow the sequence to "warm up". One common strategy is to set skip to the smallest power of 2 which is equal to or greater than n.
• r is the computed m by n sequence.

Licensing:

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

Languages:

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

Related Data and Programs:

FAURE_DATASET, a MATLAB program which creates a Faure quasirandom dataset;

GRID_DATASET, a MATLAB program which creates a grid sequence and writes it to a file.

LATIN_CENTER_DATASET, a MATLAB program which creates a Latin Center Hypercube dataset;

LATIN_EDGE_DATASET, a MATLAB program which creates a Latin Edge Hypercube dataset;

LATIN_RANDOM_DATASET, a MATLAB program which creates a Latin Random Hypercube dataset;

NIEDERREITER2_DATASET, a MATLAB program which creates a Niederreiter quasirandom dataset with base 2;

NORMAL_DATASET, a MATLAB program which generates a dataset of multivariate normal pseudorandom values and writes them to a file.

SOBOL, a dataset directory which contains sample Sobol datasets created by SOBOL_DATASET.

SOBOL, a MATLAB library which computes elements of a Sobol quasirandom sequence.

UNIFORM_DATASET, a MATLAB program which generates a dataset of multivariate uniform pseudorandom values and writes them to a file.

VAN_DER_CORPUT_DATASET, a MATLAB program which creates a van der Corput quasirandom sequence and writes it to a file.

Reference:

1. IA Antonov, VM Saleev,
   An Economic Method of Computing LP Tau-Sequences,
   USSR Computational Mathematics and Mathematical Physics,
   Volume 19, 1980, pages 252 - 256.
2. Paul Bratley, Bennett Fox,
   Algorithm 659: Implementing Sobol's Quasirandom Sequence Generator,
   ACM Transactions on Mathematical Software,
   Volume 14, Number 1, pages 88-100, 1988.
3. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Springer Verlag, pages 201-202, 1983.
4. Paul Bratley, Bennett Fox, Harald Niederreiter,
   Implementation and Tests of Low Discrepancy Sequences,
   ACM Transactions on Modeling and Computer Simulation,
   Volume 2, Number 3, pages 195-213, 1992.
5. Bennett Fox,
   Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
   ACM Transactions on Mathematical Software,
   Volume 12, Number 4, pages 362-376, 1986.
6. Harald Niederreiter,
   Random Number Generation and quasi-Monte Carlo Methods,
   SIAM, 1992.
7. William Press, Brian Flannery, Saul Teukolsky, William Vetterling,
   Numerical Recipes: The Art of Scientific Computing,
   Cambridge University Press.
8. Ilya Sobol,
   USSR Computational Mathematics and Mathematical Physics,
   Volume 16, pages 236-242, 1977.
9. Ilya Sobol, Levitan,
   The Production of Points Uniformly Distributed in a Multidimensional Cube (in Russian),
   Preprint IPM Akad. Nauk SSSR,
   Number 40, Moscow 1976.

Source Code:

• sobol_dataset.m, the source code.

Examples and Tests:

• sobol_02_00100.txt, the Sobol dataset of dimension 2, computing 100 points, after skipping 128 points.

You can go up one level to the MATLAB source codes.