Re: Best random number generator algorithms to use with `gsl_ran_gaussian`

[Jean-François Caron]

Based on the descriptions in the docs, and since you don't care about speed of 
generation, I would recommend ranlxs2 for single-precision and ranlxd2 for 
double-precision floats.  

Mersenne Twister is a good balance of speed and quality of the randomness (and 
large period), while ranlxd2 makes no compromises for speed.

Jean-François

> On Dec 10, 2021, at 13:16, Vicent Giner Bosch <vigibos@eio.upv.es> wrote:
> 
> [CAUTION: Non-UBC Email]
> 
> I am using GSL's `gsl_ran_gaussian` (actually, the version with unit
> variance `gsl_ran_ugaussian`) to generate pseudorandom values of a
> normal random variable.
> 
> According to the documentation, one of the arguments of the function
> `gsl_ran_gaussian` is a pseudorandom number generator `r` (an instance
> of the `gsl_rng` struct) that will be intialised before calling
> `gsl_ran_gaussian` for the first time.
> 
> I was planning to use MT19937 (`gsl_rng_mt19937`) or one of the
> RANLUX-like ones (`ranlxs0`, for instance) as the algorithm to be used
> by `r`, but I am not sure. There are plenty of possible algorithms to
> choose from (see
> https://www.gnu.org/software/gsl/doc/html/rng.html#random-number-generator-algorithms).
> 
> I am not looking for how fast the algorithm may be. I am rather much
> more interested in generating pseudorandom values from a Gaussian
> distribution with the best quality from a mathematical standpoint,
> meaning that they seem as 'random' as possible.
> 
> So, according to your experience, which is a good pseudorandom number
> algorithm to be used when sampling from a Gaussian distribution.
> 
> NOTE: In case it matters, those Gaussian observations will not be
> combined in any way after being generated ---I mean, I am neither
> thinking about adding or subtracting them nor creating n-tuples of
> them, etc.
> 
> I look forward to your answers,
> 
> 
> --
> vicent
> 
> @vginer_upv
> vigibos.webs.upv.es
>