SOBOL_DATASET
Generate Sobol Datasets

SOBOL_DATASET is a FORTRAN90 program which creates a Sobol dataset.

The program is interactive, and allows the user to choose

• M, the spatial dimension;
• N, the number of points to generate;
• SKIP, 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.

Licensing:

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

Related Data and Programs:

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

SOBOL_DATASET is essentially a special calling program for the SOBOL library, and a compiled copy of that library must be available to build the executable program.

The TABLE format is used for the output files of SOBOL_DATASET.

TABLE_DISCREPANCY is an executable C++ program which can read a TABLE file of points (presumed to lie in the unit hypercube) and compute bounds on the star discrepancy, a measure of dispersion.

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.f90, the source code.
• sobol_dataset.csh, commands to compile and load the source code.

Examples and Tests:

• sobol_dataset_input.txt, a short set of input to define a dataset.
• sobol_dataset_output.txt, printed output from a run of the program with the sample input.
• sobol_02_00100.txt, the Sobol dataset of 100 points of dimension 2.

List of Routines:

• MAIN is the main program for SOBOL_DATASET.

You can go up one level to the FORTRAN90 source codes.