The MIXMAX generator is a family of
pseudorandom number generators (PRNG) and is based on Anosov C-systems (
Anosov diffeomorphism
In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold ''M'' is a certain type of mapping, from ''M'' to itself, with rather clearly marked local directions of "expansion" and "cont ...
) and Kolmogorov K-systems (
Kolmogorov automorphism). It was introduced in a 1986 preprint by G. Savvidy and N. Ter-Arutyunyan-Savvidy and published in 1991.
A fast implementation in
C/
C++ of the generator was developed by Konstantin Savvidy.
The period of the generator is
and the Kolmogorov entropy is
for the matrix size
.
That generator occupies less than 2 kb, and if a smaller generator state is required, a ''N'' = 17 version with less than 200 bytes memory requirement also exists.
The generator works on most 64-bit systems, including 64-bit Linux flavors and Intel Mac. It has also been tested on
PPC and
ARM architectures. The latest version also runs on 32-bit systems and on Windows. The generator is equally usable with
C++ programs,
has been chosen as the default generator in
CLHEP
CLHEP (short for ''A Class Library for High Energy Physics'') is a C++ library that provides utility classes for general numerical programming, vector arithmetic, geometry, pseudorandom number generation, and linear algebra, specifically targe ...
for use in
Geant4 and there exists a
ROOT interface
and a
PYTHIA interface.
It has been recently tested extensively on very wide variety of platforms, as part of the CLHEP/Geant4 release.
An analysis by L’Ecuyer, Wambergue and Bourceret, see also,
showed that MIXMAX generators has a lattice structure when the produced random numbers are considered in ''n'' - dimensional space larger than the dimension ''N'' of the matrix generator, and only in that high dimensions ''n'' > ''N'' they lie on a set of parallel hyperplanes and determined the maximum distance between the covering hyperplanes.
References
External links
The open source MIXMAX C/C++ source code on hepforge.org* William L. Dunn, J. Kenneth Shultis, (2022). ''Exploring Monte Carlo Methods'', 2nd edition, Elsevier Science, .
* K. Anagnostopoulos, (2014). ''Computational Physics'', Lulu.com, {{ISBN, 978-1312464414.
Random number generation
Pseudorandom number generators