TOMS647
Faure, Halton and Sobol Quasirandom Sequences

TOMS647 is a FORTRAN90 library 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 original, true, correct version of ACM TOMS Algorithm 647 is available through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html".

The version displayed here has been converted to FORTRAN90, and other internal changes have been made to suit me.

Languages:

TOMS647 is available in a FORTRAN90 version.

Related Data and Programs:

FAURE, a FORTRAN90 library which computes elements of a Faure sequence.

HALTON, a FORTRAN90 library which computes elements of a Halton sequence.

HAMMERSLEY, a FORTRAN90 library which computes elements of a Hammersley sequence.

SOBOL, a FORTRAN90 library which computes elements of a Sobol sequence.

Reference:

1. Antonov, Saleev,
   USSR Computational Mathematics and Mathematical Physics,
   Volume 19, 1980, pages 252 - 256.
2. Paul Bratley, 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, Harald Niederreiter,
   Algorithm 738: Programs to Generate Niederreiter's Low-Discrepancy Sequences,
   ACM Transactions on Mathematical Software,
   Volume 20, Number 4, pages 494-495, 1994.
4. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Springer Verlag, pages 201-202, 1983.
5. 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.
6. Henri Faure,
   Discrepance de suites associees a un systeme de numeration (en dimension s),
   Acta Arithmetica,
   Volume XLI, 1982, pages 337-351, especially page 342.
7. 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.
8. John Halton, G B Smith,
   Algorithm 247: Radical-Inverse Quasi-Random Point Sequence,
   Communications of the ACM,
   Volume 7, 1964, pages 701-702.
9. Harald Niederreiter,
   Random Number Generation and quasi-Monte Carlo Methods,
   SIAM, 1992.
10. I Sobol,
    USSR Computational Mathematics and Mathematical Physics,
    Volume 16, pages 236-242, 1977.
11. 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:

• toms647.f90, the source code;

Examples and Tests:

• toms647_test.f90, the sample test code;
• toms647_test.txt, output from a run of the test code;

List of Routines:

• INFAUR initializes the Faure quasirandom number generator.
• GOFAUR generates a new quasirandom Faure vector with each call.
• INHALT initializes the Halton quasirandom number generator.
• GOHALT generates a new quasirandom Halton vector with each call.
• INSOBL initializes the Sobol quasirandom number generator.
• GOSOBL generates a new quasirandom Sobol vector with each call.
• EXOR calculates the exclusive OR of two integers.
• UNIF is a portable pseudorandom number generator.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.