[Rd] portable parallel seeds project: request for critiques

[Martin Maechler]

>>>>> Karl Forner <karl.forner at gmail.com>
>>>>>     on Fri, 2 Mar 2012 10:36:14 +0100 writes:

    >> Some of the random number generators allow as a seed a
    >> vector, not only a single number. This can simplify
    >> generating the seeds.  There can be one seed for each of
    >> the 1000 runs and then, the rows of the seed matrix can
    >> be
    >> 
    >> c(seed1, 1), c(seed1, 2), ...  c(seed2, 1), c(seed2, 2),
    >> ...  c(seed3, 1), c(seed3, 2), ...  ...
    >> 
    >> There could be even only one seed and the matrix can be
    >> generated as
    >> 
    >> c(seed, 1, 1), c(seed, 1, 2), ...  c(seed, 2, 1), c(seed,
    >> 2, 2), ...  c(seed, 3, 1), c(seed, 3, 2), ...
    >> 
    >> If the initialization using the vector c(seed, i, j) is
    >> done with a good quality hash function, the runs will be
    >> independent.
    >> 
    >> What is your opinion on this?
    >> 
    >> An advantage of seeding with a vector is also that there
    >> can be significantly more initial states of the generator
    >> among which we select by the seed than 2^32, which is the
    >> maximum for a single integer seed.
    >> 
    >> 

    > Hello, I would be also in favor for using multiple seeds
    > based on (seed, task_number) for convenience
    > (i.e. avoiding storing the seeds) and with the possibility
    > of having a dynamic number of tasks, but I am mot sure it
    > is theoretically correct.  But I can refer you to this
    > article: http://www.agner.org/random/ran-instructions.pdf
    > , section 6.1 where the author states:

    > For example, if we make 100 streams of 10^10 random
    > numbers each from an
    >> SFMT generator with cycle length ρ = 2^11213, we have a
    >> probability of overlap p ≈ 10^3362.
    >> 

    > What do you think ? 

well, if that article really gets a probability of 10^3362
(= Inf in R's double precision) 
I'd doubt the validity of every thing else there,
but maybe you've got a transcription error there?

;-)

Martin

    > I am very concerned by the correctness
    > of this approach so would appreciate any advice on that
    > matter.

    > Thanks Karl

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