The Hammersley Quasi Monte Carlo (QMC) Sequence

HAMMERSLEY is a Python library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence using a simple interface.

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.


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


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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  1. John Hammersley, Monte Carlo methods for solving multivariable problems, Proceedings of the New York Academy of Science, Volume 86, 1960, pages 844-874.
  2. Ladislav Kocis, William Whiten,
    Computational Investigations of Low-Discrepancy Sequences,
    ACM Transactions on Mathematical Software,
    Volume 23, Number 2, 1997, pages 266-294.

Source Code:

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Last revised on 02 October 2016.