On 6/23/13 3:14 PM, Gilles wrote:
> 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?

The ones referred to in the Wikipedia article cited in the javadoc
patch:

http://en.wikipedia.org/wiki/Gauss-Hermite_quadrature
http://en.wikipedia.org/wiki/Gauss-Laguerre_quadrature

>
> I want to mention that issue:
>   https://issues.apache.org/jira/browse/MATH-797
> I.e. Sébastien Brisard provided the initial code which I adapted to
> create the contents of the package
>   o.a.c.m.analysis.integration.gauss
> Sébastien'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.

+1 to all points above.

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