MIXMAX generator
| Class | pseudorandom number generator |
|---|---|
| Data structure | Array |
| Worst-case performance | O(n) |
| Best-case performance | O(n) |
| Average performance | O(n) |
| Worst-case space complexity | O(n) |
| Optimal | Yes |
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]
The first realization of MIXMAX generator as a Fortran code, as well the first statistical tests were performed by Norayr Akopov. [2] The abbreviation MIXMAX for the created generator was first introduced in this article.
A fast implementation in C/C++ of the generator was developed by Konstantin Savvidy.[3] It is genuine 64-bit generator. The period of the generator is and the Kolmogorov entropy is for the matrix size .[4] 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,[5] has been chosen as the default generator in CLHEP[6] for use in Geant4[7] and there exists a ROOT interface [8] and a PYTHIA interface. [9] It has been recently tested extensively on very wide variety of platforms, as part of the CLHEP/Geant4 release. EU-funded MIXMAX project [10]
An analysis by L’Ecuyer, Wambergue and Bourceret,[11] see also,[12] 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
- ^ Savvidy, G.K; Ter-Arutyunyan-Savvidy, N.G (1991). "On the Monte Carlo simulation of physical systems". Journal of Computational Physics. 97 (2): 566–572. Bibcode:1991JCoPh..97..566S. doi:10.1016/0021-9991(91)90015-D.
- ^ Akopov, N.Z.; Savvidy, G.K; Ter-Arutyunyan-Savvidy, N.G (1991). "MATRIX GENERATOR OF PSEUDORANDOM NUMBERS". Journal of Computational Physics. 97 (2): 573–579. Bibcode:1991JCoPh..97..566S. doi:10.1016/0021-9991(91)90016-E.
- ^ Savvidy, K. (2015). "The MIXMAX Random Number Generator". Computer Physics Communications. 196: 161–165. arXiv:1403.5355. Bibcode:2015CoPhC.196..161S. doi:10.1016/j.cpc.2015.06.003. S2CID 16908633.
- ^ Savvidy, K.; Savvidy, G. (2015). "Spectrum and Entropy of C-systems MIXMAX Random Number Generator". Chaos, Solitons and Fractals. 91: 33–38. arXiv:1510.06274. Bibcode:2016CSF....91...33S. doi:10.1016/j.chaos.2016.05.003. S2CID 119291387.
- ^ "boost". proj-www.boost.org.
- ^ "CLHEP". proj-clhep.web.cern.ch.
- ^ "Geant4". proj-clhep.web.cern.ch. 15 December 2022.
- ^ "ROOT - ROOT::Math::MixMaxEngine Class". root.cern.ch. Retrieved 2016-04-09.
- ^ "PYTHIA - PYTHIA::Random::MixMaxRndm class". thep.lu.se. Retrieved 2022-01-01.
- ^ "Fastest random number generator could cut energy bills". commission.europa.eu/index_en.
- ^ L’Ecuyer, Pierre; Wambergue, Paul; Bourceret, Erwan (September 22, 2017). "Spectral Analysis of the MIXMAX Random Number Generators" (PDF).
- ^ Martirosyan, N.; Savvidy, K.; Savvidy, G. (Nov 19, 2018). "Spectral Test of the MIXMAX Random Number Generator". Chaos, Solitons and Fractals. 118: 242–248. arXiv:1806.05243. doi:10.1016/j.chaos.2018.11.024. S2CID 51687163.
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, ISBN 978-0-12-819739-4.
- K. Anagnostopoulos, (2014). Computational Physics, Lulu.com, ISBN 978-1312464414.