hammersley

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

A more sophisticated library is available in HAMMERSLEY_ADVANCED, but I find this simple version to be preferable for everyday use!

The standard M-dimensional Hammersley sequence based on N is simply composed of a first component of successive fractions 0/N, 1/N, ..., N/N, paired with M-1 1-dimensional van der Corput sequences, using as bases the first M-1 primes.

The HAMMERSLEY function will return the M-dimensional element of this sequence with index I.

The HAMMERSLEY_SEQUENCE function will return the M-dimensional elements of this sequence with indices I1 through I2.

The HAMMERSLEY_INVERSE function accepts an M-dimensional value, presumably computed by HAMMERSLEY, and returns its original index I.

Languages:

hammersley is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

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Reference:

1. John Hammersley, Monte Carlo methods for solving multivariable problems, Proceedings of the New York Academy of Science, Volume 86, 1960, pages 844-874.