[Numpy-discussion] skip samples in random number generator

Sturla Molden sturla.molden at gmail.com
Thu Oct 2 16:52:59 EDT 2014


Robert Kern <robert.kern at gmail.com> wrote:

> No one needs small jumps of arbitrary size. The real use case for
> jumping is to make N parallel streams that won't overlap. You pick a
> number, let's call it `jump_steps`, much larger than any single run of
> your system could possibly consume (i.e. the number of core PRNG
> variates pulled is << `jump_steps`). Then you can initializing N
> parallel streams by initializing RandomState once with a seed, storing
> that RandomState, then jumping ahead by `jump_steps`, storing *that*
> RandomState, by `2*jump_steps`, etc. to get N RandomState streams that
> will not overlap. Give those to your separate processes and let them
> run.
> 
> So the alternative may actually be to just generate and distribute
> *one* set of these jump coefficients for a really big jump size but
> still leaves you enough space for a really large number of streams
> (fortunately, 2**19937-1 is a really big number).


DCMT might be preferred in this case. It works the same, except you have N
"random state" streams with characteristic polynomials that are distinct
and relatively prime to each other. Thus each of the N processes will get
an independent stream of random numbers, without any chance of overlap.

http://www.math.sci.hiroshima-u.ac.jp/∼m-mat/MT/DC/dc.html

Jump-ahead is easier to accomplish with MRG-32k3a than MT19937. Another
generator with an efficient jump-ahead is XORWOW.



Sturla




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