faure

faure, a MATLAB 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.

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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

faure is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

cvt, a MATLAB code which computes elements of a centroidal voronoi tessellation.

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

faure_test

grid, a MATLAB code which computes elements of a grid dataset.

halton, a MATLAB code which computes elements of a halton quasirandom sequence.

hammersley, a MATLAB code which computes elements of a hammersley quasi monte carlo (qmc) sequence, using a simple interface.

latin_center, a MATLAB code which computes elements of a latin hypercube dataset, choosing center points.

latin_edge, a MATLAB code which computes elements of a latin hypercube dataset, choosing edge points.

latin_random, a MATLAB code which computes elements of a latin hypercube dataset, choosing points at random.

lattice_rule, a MATLAB code which approximates multidimensional integrals using lattice rules.

niederreiter2, a MATLAB code which computes elements of a niederreiter quasirandom sequence with base 2.

sobol, a MATLAB code which computes elements of a sobol quasirandom sequence.

uniform, a MATLAB code which computes elements of a uniform pseudorandom sequence.

van_der_corput, a MATLAB code 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:

• binomial_table.m, returns a table of binomial coefficients mod QS.
• i4_log_i4.m, returns the logarithm of an I4 to an I4 base.
• faure.m, computes the SEED-th element of the Faure sequence with the given BASE vector.
• faure_generate.m generates a Faure dataset.
• prime_ge.m, returns the smallest prime number greater than or equal to the input argument.
• r8mat_write.m, writes an R8MAT file.