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## Re: [Help-gsl] Adaptive double integration

 From: Maximilian Treiber Subject: Re: [Help-gsl] Adaptive double integration Date: Wed, 25 Apr 2012 16:26:49 +0200 User-agent: Mozilla/5.0 (X11; U; Linux x86_64; en-US; rv:1.9.2.28) Gecko/20120313 Thunderbird/3.1.20

```Hi Jonny,

there is Monte-Carlo integration in GSL, but for 2D this is most
probably not an improvement.

Furthermore, there is this adaptive multidimensional integration code:
http://ab-initio.mit.edu/wiki/index.php/Cubature
which is very similar to the gsl routines, but allows for arbitrary
dimensions. They claim that it is best suited for a moderate number
of dimensions, which should fit your needs.

I had to do a 4D integral recently for a physics project and after
playing around with MC and Cubature for a long time, I found that
simply nesting the integrals was be best method, because one has
a much greater flexibility to exploit the symmetries of the problem.
In particular when you know a lot about your function: Choosing a
suitable coordinate transformation and integration limits can be
much more important ...

Best regards,

Max

On 04/25/2012 02:26 PM, Jonathan Taylor wrote:
> Hi all,
>
> I fear this must have come up on the list before, but I haven't been able to
> find much in the way of GSL-specific discussion on the question of adaptive
> double integration. I have a 2D surface integral that I would like to
> integrate adaptively (converging to a specified relative/absolute precision).
> My understanding is that the GSL integration functions are limited to one
> dimension. Clearly one possibility is to perform two nested adaptive single
> integrations, but I suspect that is probably not optimal (but I would be
> delighted to hear encouraging words on its effectiveness!).
>
> The integral in question is a surface integral, and the function in question
> is reasonably well behaved. It is based around spherical harmonics so will
> involve sinusoidal type variations with potentially quite rapid oscillations,
> but no singularities etc. I would be grateful for any advice on what the best
> way of approaching this is. It looks like it will be the bottleneck in my
> problem, so I would like to speed it up as much as possible - at least for a
> reasonable amount of effort invested!
>
> Thanks in advance
> Jonny

```

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