# HALTON The Halton Quasi Monte Carlo (QMC) Sequence

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

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

The standard M-dimensional Halton sequence is simply composed of M 1-dimensional van der Corput sequences, using as bases the first M primes.

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

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

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

The HALTON_BASE function allows the user to replace the standard basis of primes with some other choice.

### Languages:

HALTON 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 Halton,
On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals,
Numerische Mathematik,
Volume 2, 1960, pages 84-90.
2. John Halton, GB Smith,
Algorithm 247: Radical-Inverse Quasi-Random Point Sequence,
Communications of the ACM,
Volume 7, 1964, pages 701-702.