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From Gilles <gil...@harfang.homelinux.org>
Subject Re: [math] new feature to allow infinite limits in numerical integration.
Date Sun, 23 Jun 2013 22:14:59 GMT
On Sat, 22 Jun 2013 22:36:04 -0700, Phil Steitz wrote:
> On 6/21/13 5:17 PM, Ajo Fod wrote:
>> I've submitted a patch for the issue (see MATH-994). This will allow 
>> users
>> to integrate functions with infinity as one of the bounds.
>>
>> Cheers,
>> Ajo Fod.
>>
> Thanks for bringing the discussion to the dev list, Ajo.  As Gilles
> said on the ticket, its a little easier to have a discussion here
> than on JIRA tickets, so  We usually start the discussion here about
> whether or not a new feature makes sense and, if so, how to
> implement it.
>
> I am +1 for adding support for improper integrals.  I am not a
> numerical integration expert, however, so can't definitively
> evaluate the merits / drawbacks of the change of variable approach
> in the patch.  My intuition tells me though that the other
> approaches mentioned in the javadoc reference in the patch [1] might
> be more robust.  Does anyone have experience or references that can
> help us here?

Which other approaches, exactly?

I want to mention that issue:
   https://issues.apache.org/jira/browse/MATH-797
I.e. S├ębastien Brisard provided the initial code which I adapted to
create the contents of the package
   o.a.c.m.analysis.integration.gauss
S├ębastien's implementation contains additional code (Gauss-Chebyshev,
Gauss-Hermite, Gauss-Kronrod) that is not (yet) part of Commons Math.
It would be wasteful to not use it (but it is also a fair amount of
work to adapt the code, as the design was substantially modified to
get to what is in CM now).

Just saying that if those other quadrature schemes are useful to
compute some improper integrals, they should probably be included first
(this requires implementing appropriate "Factory" classes, cf. the
mentioned package).

Even if we would be satisfied with the algorithm proposed in MATH-994,
I'd still wonder whether the code could not be designed similarly to
what was done in the above-mentioned package rather that an unrelated
class.

Gilles

>
> Phil
>
> [1] http://en.wikipedia.org/wiki/Numerical_integration


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