toms738, a FORTRAN90 code which implements ACM TOMS algorithm 738, to compute Niederreiter's low discrepancy sequence.
A low discrepancy or quasirandom sequence, such as the Faure, Halton, Hammersley, Niederreiter, or Sobol sequence, 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 version displayed here has been converted to FORTRAN90, and other internal changes have been made to suit me.
The text of many ACM TOMS algorithms is available online through ACM: https://calgo.acm.org/ or NETLIB: https://www.netlib.org/toms/index.html.
The computer code and data files made available on this web page are distributed under the MIT license
toms738 is available in a FORTRAN90 version.
CVT, a FORTRAN90 code which computes elements of a Centroidal Voronoi Tessellation.
FAURE, a FORTRAN90 code which computes elements of a Faure quasirandom sequence.
GRID, a FORTRAN90 code which computes elements of a grid dataset.
HALTON, a FORTRAN90 code which computes elements of a Halton quasirandom sequence.
HAMMERSLEY, a FORTRAN90 code which computes elements of a Hammersley quasirandom sequence.
HEX_GRID, a FORTRAN90 code which computes elements of a hexagonal grid dataset.
HEX_GRID_ANGLE, a FORTRAN90 code which computes elements of an angled hexagonal grid dataset.
IHS, a FORTRAN90 code which computes elements of an improved distributed Latin hypercube dataset.
LATIN_CENTER, a FORTRAN90 code which computes elements of a Latin Hypercube dataset, choosing center points.
LATIN_EDGE, a FORTRAN90 code which computes elements of a Latin Hypercube dataset, choosing edge points.
LATIN_RANDOM, a FORTRAN90 code which computes elements of a Latin Hypercube dataset, choosing points at random.
LCVT, a FORTRAN90 code which computes a latinized Centroidal Voronoi Tessellation.
NIEDERREITER, a FORTRAN90 code which is a modification of ACM TOMS algorithm 738, which, among other things, allows the user to start the sequence at any point. This is for the arbitrary base calculations.
NIEDERREITER2, a FORTRAN90 code which is a modification of ACM TOMS algorithm 738, which, among other things, allows the user to start the sequence at any point. This is for the base 2 calculations.
SOBOL, a FORTRAN90 code which computes elements of a Sobol quasirandom sequence.
UNIFORM, a FORTRAN90 code which computes elements of a uniform pseudorandom sequence.
VAN_DER_CORPUT, a FORTRAN90 code which computes elements of a van der Corput pseudorandom sequence.