Re: multidimensional integration

[Manoj Warrier <mow at ipp dot mpg dot de>]

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

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