This is the mail archive of the
gsl-discuss@sources.redhat.com
mailing list for the GSL project.
Re: multidimensional integration
- From: Manoj Warrier <mow at ipp dot mpg dot de>
- To: "Robert G. Brown" <rgb at phy dot duke dot edu>
- Cc: gsl-discuss at sources dot redhat dot com
- Date: Thu, 30 Jun 2005 06:45:12 +0200 (CEST)
- Subject: Re: multidimensional integration
Is not Monte-Carlo integration the recommended method for
multi-dimensional integration?
The GSL specific routines for this are described at:
http://www.gnu.org/software/gsl/manual/gsl-ref_23.html#SEC371
I think your point (b) below hits the nail on the head.
I have not used these techniques, and would like to hear other,
more expert opinion.
Best Regards.
Manoj
On Wed, 29 Jun 2005, Robert G. Brown wrote:
> Hi fellow GSL'ers.
>
> We have a postdoc in our department who is preparing to integrate
> something. In his previous position at another place, he used NAG to do
> this, and has the requisite code already in place. He requested that we
> buy and install a single copy of NAG just for him and a student to be
> able to use this one routine to do this one integral on just one
> computer, at a cost of many hundreds of dollars.
>
> I suggested that he look into using the GSL instead, since it is a very
> high-quality library to my own direct experience and of course is both
> free and universally installed in our department. GSL and NAG both use
> QUADPACK as the basis for their 1D integrals (and have nearly identical
> call structure) so I figured that the transition would actually be
> painless.
>
> However, the integrand he has to integrate is actually defined and
> integrated over somewhere between 5 to 7 dimensions (with rectangular
> limits). The routine he used from NAG was actually d01fcc, which is NOT
> from QUADPACK but rather implements the multidimensional adaptive
> routine HALF with a custom interval rule. When I looked at GSL's online
> manual (version 1.6 as of this last December) I didn't see a
> multidimensional integration routine equivalent to d01fcc.
>
> SO, questions:
>
> a) Is a multidimensional integration routine equivalent to d01fcc
> implemented or under development, and if so, where is it and/or how do I
> get a version that has it? I looked at the CVS tree and didn't
> immediately see one. In principle I could probably use e.g. a
> multidimentional ODE solver but I'd think that having a d01fcc
> equivalent would be much more efficient.
>
> b) If not, does anybody have any suggestions on the "best" way to
> attack this sort of integral using existing tools? At five dimensions I
> suspect that just calling 1 dim integrations five levels deep would
> result in an awful lot of wasted energy and time. Framing it as an ODE
> set also seems like it would work but likely not be terribly efficient
> or terribly easy to control error-wise.
>
> c) On a related note, has anybody done a head-to-head performance
> comparison of GSL with NAG -- either time/efficiency performance or
> numerical accuracy type performance? This isn't a significant issue on
> this particular project but is an issue that I expect to see come up in
> the future.
>
> rgb
>
--
Manoj Warrier (manoj.warrier@ipp.mpg.de)
Stellaratortheorie, Max-Planck Institut Fur Plasmaphysik
TeilInstitut Greifswald Wendelsteinstrasse 1
D-17491 Greifswald Germany Tel: +49-3834-882434
--------- History of Computing 10-11-3003 ---------------
Then there used to be this great user friendly OS which
overwrote your MBR whenever you installed it.
---------------------------------------------------------