Multivariate Numerical Integration

Multivariate Numerical Integration

[John.Cagnol]

Dear All,

If I understand correctly, multivariate integration routines have yet
to be be implemented in gsl.  Is there a project in progress?  

May be functions of two variables and a simple domains would be a good
start.  I believe we would need two new types, one for the domains and
one for functions of several variables.

I am looking forward to hearing your reactions.

John.

Re: Multivariate Numerical Integration

[Brian Gough]

John.Cagnol@devinci.fr writes:
 > I'm following up on my earlier post.  Here is a simple 2-variable
 > integration routine based what already exists for 1-variable
 > integration.  At this time the integration is performed by the
 > means of iterated integrals, which is not the most efficient
 > algorithm.  The routine is also limited triangle-domains.  The
 > point is to test the types and discuss what should be improved in
 > the format before embarking in programming more complex algorithms.
 > It is also to see if there would be an interest in such routines in
 > gsl.

It would be reasonable to have something like this in the library.  I
think it would take quite a bit of work though.  Some things to
consider are how to create the domains, perhaps to avoid having to
free points individually, and having a 3d version.  Maybe it is
possible to make the code object oriented so that the user can easily
provide new types of regions extensibly, with pointers to method
functions, rather than using switch statements.

I noticed some non-standard things in the code (such as nested
functions).  If you are interested in working on it I'd recommend
reading the GSL Design document in the gsl-1.5 distribution.

-- 
Brian Gough

Network Theory Ltd,
Publishing Free Software Manuals --- http://www.network-theory.co.uk/

Re: Multivariate Numerical Integration

[John.Cagnol]

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Hi,

I'm following up on my earlier post.

Here is a simple 2-variable integration routine based what already
exists for 1-variable integration.

At this time the integration is performed by the means of iterated
integrals, which is not the most efficient algorithm.  The routine is
also limited triangle-domains.

The point is to test the types and discuss what should be improved in
the format before embarking in programming more complex algorithms.
It is also to see if there would be an interest in such routines in
gsl.

Best regards,
John.

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