SOBOL
The Sobol Quasirandom Sequence
SOBOL
is a Python library which
computes elements of the Sobol quasirandom sequence.
A quasirandom or low discrepancy sequence, such as the Faure,
Halton, Hammersley, Niederreiter or Sobol sequences, is
"less random" than a pseudorandom number sequence, but
more useful for such tasks as approximation of integrals in
higher dimensions, and in global optimization.
This is because low discrepancy sequences tend to sample
space "more uniformly" than random numbers. Algorithms
that use such sequences may have superior convergence.
SOBOL is an adaptation of the INSOBL and GOSOBL routines
in ACM TOMS Algorithm 647 and ACM TOMS Algorithm 659. The original
code can only compute the "next" element of the sequence. The
revised code allows the user to specify the index of any desired element.
A remark by Joe and Kuo shows how to extend the algorithm from
the original maximum spatial dimension of 40 up to a maximum
spatial dimension of 1111. These changes have been implemented
in the FORTRAN90 and C++ versions of the program.
The original, true, correct versions of ACM TOMS Algorithm 647
and ACM TOMS Algorithm 659
are available in the TOMS subdirectory of
the NETLIB web site.
The version displayed here has been converted to Python,
and other internal changes have been made.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license.
Languages:
SOBOL is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version
Related Data and Programs:
NORMAL,
a Python library which
contains random number generators (RNG's) for normally distributed values.
Author:
This Python implementation was written by Corrado Chisari.
Reference:

IA Antonov, VM Saleev,
An Economic Method of Computing LP TauSequences,
USSR Computational Mathematics and Mathematical Physics,
Volume 19, 1980, pages 252256.

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

Paul Bratley, Bennett Fox, Harald Niederreiter,
Implementation and Tests of Low Discrepancy Sequences,
ACM Transactions on Modeling and Computer Simulation,
Volume 2, Number 3, July 1992, pages 195213.

Paul Bratley, Bennett Fox, Linus Schrage,
A Guide to Simulation,
Second Edition,
Springer, 1987,
ISBN: 0387964673,
LC: QA76.9.C65.B73.

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

Stephen Joe, Frances Kuo,
Remark on Algorithm 659:
Implementing Sobol's Quasirandom Sequence Generator,
ACM Transactions on Mathematical Software,
Volume 29, Number 1, March 2003, pages 4957.

Harald Niederreiter,
Random Number Generation and quasiMonte Carlo Methods,
SIAM, 1992,
ISBN13: 9780898712957,
LC: QA298.N54.

William Press, Brian Flannery, Saul Teukolsky, William Vetterling,
Numerical Recipes in FORTRAN: The Art of Scientific Computing,
Second Edition,
Cambridge University Press, 1992,
ISBN: 052143064X,
LC: QA297.N866.

Ilya Sobol,
Uniformly Distributed Sequences with an Additional Uniform
Property,
USSR Computational Mathematics and Mathematical Physics,
Volume 16, 1977, pages 236242.

Ilya Sobol, YL Levitan,
The Production of Points Uniformly Distributed in a Multidimensional
Cube (in Russian),
Preprint IPM Akademii Nauk SSSR,
Number 40, Moscow 1976.
Source Code:
Examples and Tests:
You can go up one level to
the Python source codes.
Last revised on 14 December 2014.