| Re: How good is Randomu? [message #57931] |
Mon, 07 January 2008 02:32 |
wita
Messages: 43
Registered: January 2005
|
Member |
|
|
On Jan 4, 5:17 pm, john.cop...@nist.gov wrote:
> Many thanks to those of you who responded to my posting entitled "
> Bizarre (?) behavior of randomu". Your comments have been very useful.
>
> I now have a different question. How good is Randomu? I am developing
> some code to calculate multiple neutron scattering intensities and
> typically in any given run I would expect to invoke randomu (or some
> other IDL procedure that generates uniformly distributed pseudo-random
> numbers between 0 and 1) several hundred to several thousand times,
> each time obtaining of order 1 million numbers, in other words
> generating 10^9 or more random numbers in any given run. Is randomu up
> to the task, or do I need something better?
>
> If I need something better what should I use? I have come across
> exotica such as the "MT19937 generator of Makoto Matsumoto and Takuji
> Nishimura [which] is a variant of the twisted generalized feedback
> shift-register algorithm" and "has a Mersenne prime period of 2^19937
> - 1 (about 10^6000) and is equi-distributed in 623 dimensions" but
> that sounds like overkill. On the other hand the so-called Wichmann-
> Hill algorithm looks interesting and it is supposedly very easy to
> code.
>
> Thoughts, anyone?
> Many thanks
> John
Dear John,
I am also not a statistician and have no experience with periodicity
for that large amount of random numbers. What may be of interest to
you is that a fairly sophisticated random number generators was built
in Numeric Python (www.numpy.org), I quote from the manual: "The
fundamental random number generator is the Mersenne Twister based on
code written by Makoto Matsumoto and Takuji Nishimura (and modified
for Python by Raymond Hettinger)". Since NumPy is open source and
written in C or Fortran, you might be able to take that code and
modify it to suit your needs. That has the advantage that the code has
already been fairly well tested by the python community.
with best regards,
Allard
|
|
|
|
| Re: How good is Randomu? [message #57962 is a reply to message #57931] |
Fri, 04 January 2008 10:24  |
Rick Towler
Messages: 821
Registered: August 1998
|
Senior Member |
|
|
I'm not a statistician, but as far as I can tell ran1 from NRC and thus
randomu have a period of ~10^9. This is very short and surprises me...
I guess that is why you can buy the IDL Analyst add on. More info on
ran1 (and thus randomu) is here:
http://www.nrbook.com/a/bookcpdf/c7-1.pdf
MATLAB's default generator is based on "Marsaglia's ziggurat algorithm"
with a period of 2^64. The paper and example C code are here:
http://www.jstatsoft.org/v05/i08
Whatever generator you choose, you'll going to want to code it up as a
DLM or be *very* patient. I think you'll run into a real bottleneck
generating all those random numbers in IDL. Looking at the ziggurat
code, it would be pretty easy to code it up as a DLM. I recommend Ronn
Kling's "Calling C/C++ from IDL" www.kilvarock.com.
-Rick
john.copley@nist.gov wrote:
> Many thanks to those of you who responded to my posting entitled "
> Bizarre (?) behavior of randomu". Your comments have been very useful.
>
> I now have a different question. How good is Randomu? I am developing
> some code to calculate multiple neutron scattering intensities and
> typically in any given run I would expect to invoke randomu (or some
> other IDL procedure that generates uniformly distributed pseudo-random
> numbers between 0 and 1) several hundred to several thousand times,
> each time obtaining of order 1 million numbers, in other words
> generating 10^9 or more random numbers in any given run. Is randomu up
> to the task, or do I need something better?
>
> If I need something better what should I use? I have come across
> exotica such as the "MT19937 generator of Makoto Matsumoto and Takuji
> Nishimura [which] is a variant of the twisted generalized feedback
> shift-register algorithm" and "has a Mersenne prime period of 2^19937
> - 1 (about 10^6000) and is equi-distributed in 623 dimensions" but
> that sounds like overkill. On the other hand the so-called Wichmann-
> Hill algorithm looks interesting and it is supposedly very easy to
> code.
>
> Thoughts, anyone?
> Many thanks
> John
|
|
|
|
| Re: How good is Randomu? [message #57967 is a reply to message #57962] |
Fri, 04 January 2008 09:55 |
Brian Larsen
Messages: 270
Registered: June 2006
|
Senior Member |
|
|
From the IDL help on randomu
""The random number generator is taken from: "Random Number
Generators: Good Ones are Hard to Find", Park and Miller,
Communications of the ACM, Oct 1988, Vol 31, No. 10, p. 1192. To
remove low-order serial correlations, a Bays-Durham shuffle is added,
resulting in a random number generator similar to ran1() in Section
7.1 of Numerical Recipes in C: The Art of Scientific Computing (Second
Edition), published by Cambridge University Press.""
I don't have my copy of Numerical Recipes handy but it is also online
so you can read how good ran1() is. My gut feeling is that if you
want 10^9 random numbers randmonu() is probably not good (or fast)
enough. My gut says to use ran3() from Numerical Recipes build in C
can called via dlm for the large period and speed.
Cheers,
Brian
------------------------------------------------------------ --------------
Brian Larsen
Boston University
Center for Space Physics
|
|
|
|
comp.lang.idl-pvwave archive
Members
Search
Help
Login
Home
