[Rd] portable parallel seeds project: request for critiques
Martin Maechler
maechler at stat.math.ethz.ch
Fri Mar 2 14:32:58 CET 2012
>>>>> 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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