Re: [Help-gsl] Adaptive double integration

[Maximilian Treiber]

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