FAURE
The Faure Quasirandom Sequence

FAURE is a FORTRAN90 library, using double precision arithmetic, which computes elements of the Faure 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. Faure sequences, in particular, seem to have become popular in mathematical finance simulations.

FAURE is adapted from code in ACM TOMS Algorithm 647. The original, true, correct version of ACM TOMS Algorithm 647 is available in the TOMS subdirectory of the NETLIB web site.

Related Data and Programs:

CVT is a FORTRAN90 library which computes elements of a Centroidal Voronoi Tessellation.

FAURE is also available in a C++ version and a MATLAB version.

FAURE is a dataset directory which contains files of sample Faure datasets.

FAURE_DATASET is a FORTRAN90 program which can create a Faure dataset.

GRID is a FORTRAN90 library which computes elements of a grid dataset.

HALTON is a FORTRAN90 library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY is a FORTRAN90 library which computes elements of a Hammersley quasirandom sequence.

HEX_GRID is a FORTRAN90 library which computes elements of a hexagonal grid dataset.

HEX_GRID_ANGLE is a FORTRAN90 library which computes elements of an angled hexagonal grid dataset.

IHS is a FORTRAN90 library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing points at random.

LCVT is a FORTRAN90 library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 is a FORTRAN90 library which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL is a FORTRAN90 library which computes elements of a sequence of pseudorandom normally distributed values.

SOBOL is a FORTRAN90 library which computes elements of a Sobol quasirandom sequence.

TOMS647 is a FORTRAN90 version of ACM TOMS algorithm 647, for evaluating Faure, Halton and Sobol sequences.

UNIFORM is a FORTRAN90 library which computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT is a FORTRAN90 library which computes elements of a van der Corput quasirandom sequence.

Reference:

1. 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 195-213.
2. Henri Faure,
   Discrepance de suites associees a un systeme de numeration (en dimension s),
   Acta Arithmetica,
   Volume 41, 1982, pages 337-351.
3. Henri Faure,
   Good permutations for extreme discrepancy,
   Journal of Number Theory,
   Volume 42, 1992, pages 47-56.
4. Bennett Fox,
   Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
   ACM Transactions on Mathematical Software,
   Volume 12, Number 4, December 1986, pages 362-376.

Source Code:

• faure.f90, the source code;
• faure.csh, commands to compile the source code;

Examples and Tests:

• faure_prb.f90, the sample test code;
• faure_prb.csh, commands to compile the test code;
• faure_prb_output.txt, output from a run of the test code;

List of Routines:

• BINOMIAL_TABLE computes a table of bionomial coefficients MOD QS.
• FAURE generates a new quasirandom Faure vector with each call.
• FAURE_GENERATE generates a Faure dataset.
• FAURE_WRITE writes a Faure dataset to a file.
• GET_UNIT returns a free FORTRAN unit number.
• PRIME_GE returns the smallest prime greater than or equal to N.
• PRIME returns any of the first PRIME_MAX prime numbers.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.

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