Re: [Rd] portable parallel seeds project: request for critiques

From: Martin Maechler <maechler_at_stat.math.ethz.ch>
Date: Fri, 02 Mar 2012 14:32:58 +0100

>>>>> 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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