SOBOL
Sobol Quasirandom Datasets
SOBOL
is a dataset directory which
contains points generated
by the Mdimensional 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 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:

Antonov and Saleev,
USSR Computational Mathematics and Mathematical Physics,
Volume 19, 1980, pages 252  256.

Paul Bratley and Bennett Fox,
Algorithm 659:
Implementing Sobol's Quasirandom Sequence Generator,
ACM Transactions on Mathematical Software,
Volume 14, Number 1, pages 88100, 1988.

Paul Bratley, Bennett Fox, L E Schrage,
A Guide to Simulation,
Springer Verlag, pages 201202, 1983.

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 195213, 1992.

Bennett Fox,
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,
ACM Transactions on Mathematical Software,
Volume 12, Number 4, pages 362376, 1986.

Harald Niederreiter,
Random Number Generation and quasiMonte Carlo Methods,
SIAM, 1992.

William Press, Brian Flannery, Saul Teukolsky,
William Vetterling,
Numerical Recipes: The Art of Scientific Computing,
Cambridge University Press.

I Sobol,
USSR Computational Mathematics and Mathematical Physics,
Volume 16, pages 236242, 1977.

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.
Last revised on 31 August 2005.