“MIXMAX generator”的意思、由来-开放百科全书

The MIXMAX generator is a family of pseudorandom number generators (PRNG) and is based on Anosov C-systems (Anosov diffeomorphism) 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.^[1]

A fast implementation in C/C++ of the generator was developed by Konstantin Savvidy.^[2] The period of the generator is

and the Kolmogorov entropy is

for the matrix size

^[3].

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 for use in Geant4^[4] and there exists a ROOT interface ^[5]. 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^[6], see also ^[7], showed that MIXMAX generators, just as all other Multiple Recursive Generators and linear congruential generators, has a lattice structure and that the produced random numbers, when considered as coordinate in a n > N - dimentional space, lie on a set of parallel hyperplanes and determined the maximum distance between the covering hyperplanes.

References

1. ^{{cite journal |doi=10.1016/0021-9991(91)90015-D|title=On the Monte Carlo simulation of physical systems|journal=Journal of Computational Physics|volume=97|issue=2|pages=566|year=1991|last1=Savvidy|first1=G.K|last2=Ter-Arutyunyan-Savvidy|first2=N.G|bibcode=1991JCoPh..97..566S}}
2. ^{{cite journal |author=K. Savvidy |date=2015 |arxiv=1403.5355|title=The MIXMAX Random Number Generator |journal=Computer Physics Communications |volume=196 |pages=161–165 |doi= 10.1016/j.cpc.2015.06.003 |bibcode=2015CoPhC.196..161S }}
3. ^{{cite journal |author=K. Savvidy and G.Savvidy |date=2015 |arxiv=1510.06274|title=Spectrum and Entropy of C-systems MIXMAX Random Number Generator |journal=Chaos, Solitons and Fractals |volume=91 |pages=33–38 |doi= 10.1016/j.chaos.2016.05.003 |bibcode=2016CSF....91...33S }}
4. ^{{cite web|url=https://gitlab.cern.ch/CLHEP/CLHEP/blob/develop/Random/src/MixMaxRng.cc|title=Geant4/CLHEP - A Class Library for High Energy Physics|publisher=proj-clhep.web.cern.ch|accessdate=2016-04-09}}
5. ^{{cite web|url=https://root.cern.ch/doc/master/classTRandom.html|title=ROOT - ROOT::Math::MixMaxEngine Class|publisher=root.cern.ch|accessdate=2016-04-09}}
6. ^{{Cite journal|last=Pierre L’Ecuyer, Paul Wambergue, and Erwan Bourceret|first=|date=September 22, 2017|title=Spectral Analysis of the MIXMAX Random Number Generators|url=http://www.iro.umontreal.ca/~lecuyer/myftp/papers/mixmax-lattice.pdf|journal=|volume=|pages=|via=}}
7. ^{{Cite journal|last=N.Martirosyan, K.Savvidy, and G.Savvidy|first=|date=Nov 19, 2018|title= Spectral Test of the MIXMAX Random Number Generator|journal=Chaos, Solitons and Fractals |volume=118 |pages=242–248 |doi= 10.1016/j.chaos.2018.11.024| arxiv=1806.05243}}

References

External links