quadrature routines

[fjhickernell]

It would be nice for Julia to have the quadrature routines such as MATLAB's quad or quadgk

[JeffBezanson]

Do you have any opinions on the methods here:

https://github.com/JeffBezanson/numal/blob/master/CHAPTER4/qadrat.c
https://github.com/JeffBezanson/numal/blob/master/CHAPTER4/integral.c

?

I could port them to julia easily.

[fjhickernell]

Hi Jeff,

Sorry, I cannot tell enough about these routines just by looking at the code. Could you tell me what they are? E.g., I do like MATLAB's

quad (adaptive Simpson by

@Article{GanGau00a,
Author = {W. Gander and W. Gautschi},
Journal = {BIT},
Pages = {84--101},
Title = {Adaptive Quadrature --- Revisited},
Volume = {40},
Year = {2000}}

and

quadgk (adaptive Gauss-Konrod by

@Article{Sha08a,
Author = {L. F. Shampine},
Date-Added = {2012-06-23 20:46:34 +0000},
Date-Modified = {2012-06-23 20:47:41 +0000},
Journal = jcam,
Pages = {131--140},
Title = {Vectorized Adaptive Quadrature in Matlab},
Volume = {211},
Year = {2008}}

Fred

On Aug 30, 2012, at 3:20 AM, Jeff Bezanson notifications@github.com wrote:

Do you have any opinions on the methods here:

https://github.com/JeffBezanson/numal/blob/master/CHAPTER4/qadrat.c
https://github.com/JeffBezanson/numal/blob/master/CHAPTER4/integral.c

?

I could port them to julia easily.

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[stevengj]

The Cubature package (see preceding PR) should help fill this gap, although it probably can't go into Julia's standard library due to its GPL provenance. Also, it would be nice to have a pure-Julia quadrature routine, at least in 1d, for a variety of other reasons, e.g. to handle arbitrary real types and vector fields.

It would be pretty easy for me to implement an adaptive Gauss-Kronrod 1d quadrature scheme in pure Julia (especially given a priority-queue data structure, #2438), if there is interest.

[cmcbride]

+1 on this request. quad / romb / trap can be very useful for 1d use. I also agree with @stevengj: having an adaptive GK scheme in pure Julia would be great. Ideally, I'd love to step up to help -- but I have a solid negative balance in free time, so that's unlikely to happen soon. But I would use them if they existed!