toms647
toms647,
a FORTRAN90 code which
implements the Faure, Halton, and
Sobol quasirandom sequences.
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.
The version displayed here has been converted to FORTRAN90,
and other internal changes have been made to suit me.
The text of many ACM TOMS algorithms is available online
through ACM:
https://calgo.acm.org/
or NETLIB:
https://www.netlib.org/toms/index.html.
Licensing:
The computer code and data files made available on this
web page are distributed under
the MIT license
Languages:
toms647 is available in
a FORTRAN90 version.
Related Data and Programs:
FAURE,
a FORTRAN90 code which
computes elements of a Faure sequence.
HALTON,
a FORTRAN90 code which
computes elements of a Halton sequence.
HAMMERSLEY,
a FORTRAN90 code which
computes elements of a Hammersley sequence.
SOBOL,
a FORTRAN90 code which
computes elements of a Sobol sequence.
toms647_test
Reference:

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

Paul Bratley, 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, Harald Niederreiter,
Algorithm 738:
Programs to Generate Niederreiter's LowDiscrepancy Sequences,
ACM Transactions on Mathematical Software,
Volume 20, Number 4, pages 494495, 1994.

Paul Bratley, Bennett Fox, Linus 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.

Henri Faure,
Discrepance de suites associees a un systeme de numeration
(en dimension s),
Acta Arithmetica,
Volume XLI, 1982, pages 337351, especially page 342.

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

John Halton, G B Smith,
Algorithm 247: RadicalInverse QuasiRandom Point Sequence,
Communications of the ACM,
Volume 7, 1964, pages 701702.

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

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.
Source Code:
Last revised on 14 March 2021.