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:

The values of M and N are specified in the dataset file names.

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:

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

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

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

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

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

You can go up one level to the DATASETS directory.


Last revised on 31 August 2005.