faure


faure, a C++ code 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.

The code 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.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

faure is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

faure_test

box_behnken, a C++ code which computes a Box-Behnken design, that is, a set of arguments to sample the behavior of a function of multiple parameters;

cvt, a C++ code which computes elements of a Centroidal Voronoi Tessellation.

faure, a dataset directory which contains files of sample Faure datasets.

halton, a C++ code which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.

hammersley, a C++ code which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.

ihs, a C++ code which computes elements of an improved distributed Latin hypercube dataset.

latin_center, a C++ code which computes elements of a Latin Hypercube dataset, choosing center points.

latin_edge, a C++ code which computes elements of a Latin Hypercube dataset, choosing edge points.

latin_random, a C++ code which computes elements of a Latin Hypercube dataset, choosing points at random.

lcvt, a C++ code which computes a latinized Centroidal Voronoi Tessellation.

niederreiter2, a C++ code which computes elements of a Niederreiter quasirandom sequence using base 2.

normal, a C++ code which computes elements of a sequence of pseudorandom normally distributed values.

sobol, a C++ code which computes Sobol sequences.

uniform, a C++ code which computes elements of a uniform pseudorandom sequence.

van_der_corput, a C++ code which computes elements of a 1D van der Corput 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:


Last revised on 26 February 2020.