Editing Sobol sequence (section)

== Implementation and availability ==

Good initialisation numbers for different numbers of dimensions are provided by several authors. For example, Sobol’ provides initialisation numbers for dimensions up to 51.<ref name=SobLev76>Sobol’, I.M. and Levitan, Y.L. (1976). "The production of points uniformly distributed in a multidimensional cube" ''Tech. Rep. 40, Institute of Applied Mathematics, USSR Academy of Sciences'' (in Russian).</ref> The same set of initialisation numbers is used by Bratley and Fox.<ref name=BF88>Bratley, P. and Fox, B. L. (1988), "Algorithm 659: Implementing Sobol’ quasirandom sequence generator". ''ACM Trans. Math. Software'' '''14''': 88–100.</ref>

Initialisation numbers for high dimensions are available on Joe and Kuo.<ref name=JK>{{cite web|url=http://web.maths.unsw.edu.au/~fkuo/sobol/ |title=Sobol' sequence generator |publisher=[[University of New South Wales]] |date=2010-09-16 |accessdate=2013-12-20}}</ref> [[Peter Jaeckel|Peter Jäckel]] provides initialisation numbers up to dimension 32 in his book "[[Monte Carlo methods in finance]]".<ref name=Jackel>Jäckel, P. (2002) "Monte Carlo methods in finance". New York: [[John Wiley and Sons]]. ({{ISBN|0-471-49741-X}}.)</ref>

Other implementations are available as C, Fortran 77, or Fortran 90 routines in the [[Numerical Recipes]] collection of software.<ref name=NumRec>Press, W.H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992) "Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed." ''Cambridge University Press, Cambridge, U.K.''</ref> A [[Free and open-source software|free/open-source]] implementation in up to 1111 dimensions, based on the Joe and Kuo initialisation numbers, is available in C,<ref>[https://github.com/stevengj/nlopt/blob/master/src/util/sobolseq.c C implementation of the Sobol’ sequence] in the [http://ab-initio.mit.edu/nlopt NLopt library] (2007).</ref> and up to 21201 dimensions in Python<ref>{{Cite web|url=https://scipy.github.io/devdocs/reference/generated/scipy.stats.qmc.Sobol.html|title=SciPy API Reference: scipy.stats.qmc.Sobol}}</ref><ref>{{Cite web|url=https://pyscenarios.readthedocs.io|title=pyscenarios: Python Scenario Generator|last=Imperiale|first=G.}}</ref> and [[Julia (programming language)|Julia]].<ref>[https://github.com/stevengj/Sobol.jl Sobol.jl] package: Julia implementation of the Sobol’ sequence.</ref> A different free/open-source implementation in up to 1111 dimensions is available for [[C++]], [[Fortran 90]], [[Matlab]], and [[Python (programming language)|Python]].<ref>[http://people.sc.fsu.edu/~jburkardt/cpp_src/sobol/sobol.html The Sobol’ Quasirandom Sequence], code for C++/Fortran 90/Matlab/Python by J. Burkardt</ref>

Commercial Sobol’ sequence generators are available within, for example, the [[NAG Numerical Libraries|NAG Library]].<ref name=NAG>{{cite web|url=http://www.nag.co.uk/ |title=Numerical Algorithms Group |publisher=Nag.co.uk |date=2013-11-28 |accessdate=2013-12-20}}</ref> BRODA Ltd.<ref name=BRODA_info_article>{{cite journal |author=I. Sobol’, D. Asotsky, A. Kreinin, S. Kucherenko |title=Construction and Comparison of High-Dimensional Sobol' Generators |url=http://www.broda.co.uk/doc/HD_SobolGenerator.pdf |journal=Wilmott Journal |year=2011 |volume=Nov |issue=56 | pages=64–79|doi=10.1002/wilm.10056 }}</ref><ref name=BRODA>{{cite web|url=http://www.broda.co.uk |title=Broda |publisher=Broda |date=2024-01-23 |accessdate=2024-01-23}}</ref> provides Sobol' and scrambled Sobol' sequences generators with additional unifomity properties A and A' up to a maximum dimension 131072. These generators were co-developed with Prof. I. Sobol'. MATLAB <ref>[https://www.mathworks.com/help/stats/sobolset.html sobolset reference page]. Retrieved 2017-07-24.</ref> contains Sobol' sequences generators up to dimension 1111 as part of its Statistics Toolbox.