SOBOL
Sobol Quasirandom Datasets

SOBOL is a dataset directory which contains points generated by the M-dimensional Sobol sequence.

The datasets are distinguished by the values of the following parameters:

• M, the spatial dimension;
• N, the number of points to generate;
• SKIP, the initial number of points to skip over (default = 0);

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:

PLOT_POINTS, a FORTRAN90 program which can plot two dimensional datasets, making Encapsulated PostScript images.

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

SOBOL_DATASET, a FORTRAN90 program which allows the user to define and compute a Sobol dataset.

TABLE, a file format which is used to store the datasets.

TABLE_TOP, a FORTRAN90 program which can be used to analyze datasets of any dimension, by creating images of pairwise coordinates.

Example dataset:

A typical (but small) dataset looks like this:

#  sobol_02_00010.txt
#  created by SOBOL_DATASET.
#
#  File generated on March 20 2003  10:15:23.258 AM
#
#  Spatial dimension M =      2
#  Number of points N =     10
#  Initial values skipped =      0
#
  0.000000  0.000000
  0.500000  0.500000
  0.750000  0.250000
  0.250000  0.750000
  0.375000  0.375000
  0.875000  0.875000
  0.625000  0.125000
  0.125000  0.625000
  0.187500  0.312500
  0.687500  0.812500
      

Reference:

1. Antonov and Saleev,
   USSR Computational Mathematics and Mathematical Physics,
   Volume 19, 1980, pages 252 - 256.
2. Paul Bratley and 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, L E 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. I Sobol,
   USSR Computational Mathematics and Mathematical Physics,
   Volume 16, pages 236-242, 1977.
9. I Sobol, Levitan,
   The Production of Points Uniformly Distributed in a Multidimensional Cube (in Russian),
   Preprint IPM Akad. Nauk SSSR,
   Number 40, Moscow 1976.

Datasets:

Datasets in M = 2 dimensions, with 0 skipping, include:

• sobol_02_00010.txt, M = 2, N = 10, SKIP = 0;
• sobol_02_00010.png, a PNG image of the dataset;
• sobol_02_00100.txt, M = 2, N = 100, SKIP = 0;
• sobol_02_00100.png, a PNG image of the dataset;
• sobol_02_01000.txt, M = 2, N = 1000, SKIP = 0;
• sobol_02_01000.png, a PNG image of the dataset;
• sobol_02_10000.txt, M = 2, N = 10000, SKIP = 0;

Datasets in M = 2 dimensions, with power of 2 skipping, include:

• sobol_02_00010_a.txt, M = 2, N = 10, SKIP = 16;
• sobol_02_00100_a.txt, M = 2, N = 100, SKIP = 128;
• sobol_02_01000_a.txt, M = 2, N = 1000, SKIP = 1024;
• sobol_02_10000_a.txt, M = 2, N = 10000, SKIP = 16384;

Datasets in M = 7 dimensions, with 0 skipping, include:

• sobol_07_00010.txt, M = 7, N = 10, SKIP = 0;
• sobol_07_00100.txt, M = 7, N = 100, SKIP = 0;
• sobol_07_01000.txt, M = 7, N = 1000, SKIP = 0;
• sobol_07_10000.txt, M = 7, N = 10000, SKIP = 0;

Datasets in M = 7 dimensions, with power of 2 skipping, include:

• sobol_07_00010_a.txt, M = 7, N = 10, SKIP = 16;
• sobol_07_00100_a.txt, M = 7, N = 100, SKIP = 128;
• sobol_07_01000_a.txt, M = 7, N = 1000, SKIP = 1024;
• sobol_07_10000_a.txt, M = 7, N = 10000, SKIP = 16384;

Datasets in M = 16 dimensions, with 0 skipping, include:

• sobol_16_00010.txt, M = 16, N = 10, SKIP = 0;
• sobol_16_00100.txt, M = 16, N = 100, SKIP = 0;
• sobol_16_01000.txt, M = 16, N = 1000, SKIP = 0;
• sobol_16_10000.txt, M = 16, N = 10000, SKIP = 0;

Datasets in M = 16 dimensions, with power of 2 skipping, include:

• sobol_16_00010_a.txt, M = 16, N = 10, SKIP = 16;
• sobol_16_00100_a.txt, M = 16, N = 100, SKIP = 128;
• sobol_16_01000_a.txt, M = 16, N = 1000, SKIP = 1024;
• sobol_16_10000_a.txt, M = 16, N = 10000, SKIP = 16384;

You can go up one level to the DATASETS directory.