MIXMAX Generator
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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 10^ and the Kolmogorov entropy is 8679.2 for the matrix size N = 240. 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