Re: Looking for good codes for 2D numerical integrals...

["Robert G. Brown" <rgb at phy dot duke dot edu>]

On Wed, 27 Jun 2007, Michael wrote:

> Hi all,
>
> I am looking for good (accurate, reliable and fast) programs for 2D
> numerical integrals, one of the integral is of Fourier type. Both integral
> are on infinite intervals. Could you please give a list of pointers of 2D
> numerical integration programs that worth trying out? I am planning to do a
> literature survey and I want to try out a few programs on my current
> problem. I've heard about the sparse grid based method for 2D integration,
> does anybody have the code?

I don't know if it will do what you want on an infinite interval, but
there is this:

  http://www.phy.duke.edu/~rgb/libcubature-0.1.0.tgz

which is my library port/hack of Stephen Johnson's demo port/hack of
HintLib's Genz-Malik adaptive cubature.  It's moderately successful on
up to something like 5-6 dimensions, although it can definitely be
fooled by problems with just the wrong integrand.  There's a discussion
in the list archives about it.

Then google turns up a bunch of multidimensional integration routines
these days.  Mind you, for 2D the problem of multidimensional
integration hasn't really "matured" yet, and simply nesting calls of 1D
adaptive integration is usually possible.  Genz-Malik is smarter than
that and gets similar accuracy with far fewer calls.  BUT, it isn't
really designed for infinite intervals IIRC although one can always
rescale and so on.  I googled up a quick link to Stephen's original
example here:

  http://www.cygwin.com/ml/gsl-discuss/2005-q2/msg00020.html

HTH,

   rgb

> Thanks a lot!

--
Robert G. Brown	                       http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567  Fax: 919-660-2525     email:rgb@phy.duke.edu