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

From: Karl Forner <karl.forner_at_gmail.com>
Date: Fri, 02 Mar 2012 10:36:14 +0100

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

Thanks
Karl

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