niederreiter2

niederreiter2, a C++ code which implements the Niederreiter quasirandom sequence, using a base of 2.

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 code is an adapation of the INLO2 and GOLO2 routines in ACM TOMS Algorithm 738. The original code can only compute the "next" element of the sequence. The revised code allows the user to specify the index of the desired element.

The original, true, correct version of ACM TOMS Algorithm 738 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:

niederreiter2 is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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 points in a Centroidal Voronoi Tessellation.

FAURE, a C++ code which computes Faure sequences.

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 improved Latin Hypercube datasets.

LATIN_CENTER, a C++ code which computes Latin square data choosing the center value.

LATIN_EDGE, a C++ code which computes Latin square data choosing the edge value.

LATIN_RANDOM, a C++ code which computes Latin square data choosing a random value in the square.

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

niederreiter2_test

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

UNIFORM, a C++ code which computes uniform random values.

VAN_DER_CORPUT, a C++ code which computes van der Corput sequences.

Reference:

1. 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.
2. 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.
3. 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.
4. 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.
5. R Lidl, Harald Niederreiter,
   Finite Fields,
   Cambridge University Press, 1984, page 553.
6. Harald Niederreiter,
   Low-discrepancy and low-dispersion sequences,
   Journal of Number Theory,
   Volume 30, 1988, pages 51-70.
7. Harald Niederreiter,
   Random Number Generation and quasi-Monte Carlo Methods,
   SIAM, 1992.

Source Code:

• niederreiter2.cpp, the source code;
• niederreiter2.sh, compiles the source code;
• niederreiter2.hpp, the include file;