Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math challenge)

[brian whatcott <betwys1@sbcglobal.net>]

The MATLAB rand function supports a method of random number generation 
called the Mersenne Twister from version 7.1 on.  The algorithm used by 
this method, developed by Nishimura and Matsumoto,  generates double 
precision values in the closed interval [2^(-53), 1-2^(-53)], with a 
period of (2^19937-1)/2.

For a full description of the Mersenne twister algorithm, see
<http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html>.

A broad overview with sample metacode is available as a wiki at
<http://en.wikipedia.org/wiki/Mersenne_twister>
It begins in this way:
"The *Mersenne twister* is a pseudorandom number 
generator<http://en.wikipedia.org/wiki/Pseudorandom_number_generator> 
(PRNG). It is, by far, the most widely used 
PRNG.^<http://en.wikipedia.org/wiki/Mersenne_twister#cite_note-1> Its 
name derives from the fact that its period length is chosen to be a  
Mersenne prime. <http://en.wikipedia.org/wiki/Mersenne_prime>. "The 
Mersenne Twister was developed in 1997 by Makoto Matsumoto 
<http://en.wikipedia.org/w/index.php?title=Makoto_Matsumoto&action=edit&redlink=1> 
(?? ?^? 
<http://en.wikipedia.org/wiki/Help:Installing_Japanese_character_sets> ) 
and Takuji Nishimura 
<http://en.wikipedia.org/w/index.php?title=Takuji_Nishimura&action=edit&redlink=1> 
(?? ??^? 
<http://en.wikipedia.org/wiki/Help:Installing_Japanese_character_sets> 
).^[2] <http://en.wikipedia.org/wiki/Mersenne_twister#cite_note-2> It 
was designed specifically to rectify most of the flaws found in older 
PRNGs. It was the first PRNG to provide fast generation of high-quality 
pseudo random integers. "The most commonly-used version of the Mersenne 
Twister algorithm is based on the Mersenne prime 2^19937 -1. The 
standard implementation of that, MT19937, uses a 32-bit word length. 
There is another implementation that uses a 64-bit word length, 
MT19937-64; it generates a different sequence."

Brian Whatcott   Altus OK

On 2/27/2014 8:59 AM, Paul Nord wrote:
> /snip/
> We had this discussion on the TWIST experiment where it was believed that our pRNG had a period of 10^9.  Each simulation run used about this number of random numbers.  10^5 events were simulated with each requiring about 10^4 random numbers (if I’m remembering correctly). /snip/  For TWIST, it turned out that we misunderstood the documentation on the pRNG.  Someone had provided a list of “known good seeds” which were tested to 10^9 entries.  I think that the pRNG was Mersenne Twister with its astronomical period.  But it was a good point of discussion for this high statistics experiment.
>
> Paul
>
>
>
> On Feb 26, 2014, at 5:08 PM, Craig Wiegert <wiegert@physast.uga.edu> wrote:
>
> > This raises a question.  In a simulation code, I might need to generate
> > random numbers for energies, particle displacements, and branch
> > conditions, all intermingled.  Do I go to the same pRNG well for all of
> > my random number needs, or is it prudent to use different pRNGs (perhaps
> > the same algorithm but with different seeds) for each type of quantity?
> >
> >   - Craig