- To: bjg at network-theory dot co dot uk
- Subject: Re: quasi-random numbers in high dimensions
- From: "Dherminder Kainth" <dherminder_kainth at hotmail dot com>
- Date: Thu, 11 Oct 2001 13:11:13 +0000
Dear Brian,
It is relatively straightforward to extend the Sobol generator (for example)
to higher dimensions by altering the dimension etc to beyond 40 and putting
in more irreducible polynomials (see Numerical Recipes for further
discussion). The polynomials can - if you are keen - be computed using eg
Mathematica; alternatively go to the NR web page and look for contributed
code - in particular a file by Peter Jaeckel. Here there is a list of all
the polynomials - one simply has to transcribe them to the code.
Alternatively there is the SPRNG web side and a number of fortran
implementations (use f2c to get a quick and dirty c translation).
A point of warning - quasi randoms are NOT good for integrating to dimension
400 (basically to do with the Kloskwa Hlawka) bound.
Instead you must
a. Hope the "effective dimension" of the problem is < 400 ~20 is good (!).
By that I mean most of the weight of the integral is in 20 generalised
dimensions.
b. Then use Brownian bridging/ pseudospectral methods. This will generally
work for most problems. For a further discussion of these points see R E
Caflisch (on the web).
>From: Brian Gough <bjg@network-theory.co.uk>
>To: <vcrespi@ists.dartmouth.edu>
>CC: gsl-discuss@sources.redhat.com
>Subject: Re: quasi-random numbers in high dimensions
>Date: Thu, 11 Oct 2001 12:28:07 +0100 (BST)
>
>crespi@ists.dartmouth.edu writes:
> > Dear Sir,
> >
> > I am a user of the gsl library and in particular I'm trying to
> > use the quasi-random numbers generators. Unfortunately the highest
> > dimension is 40 whereas I would need dimensions of about 400.
> >
> > Please, could you tell me whether you know of some specific free C code
> > that I can use?
> >
> > Thank you in advance for your suggestions.
> >
> > Best Regards,
> > Valentino Crespi
>
>I'm not familiar with that subject myself so I'm forwarding your
>message to the gsl-discuss list to see if the original author or
>anyone else has any suggestions.
>
>Brian Gough
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