[SciPy-Dev] Discussion on a new interface for multidimensional quadrature

[Nathan Woods]

On Aug 14, 2013, at 5:54 AM, Evgeni Burovski <evgeny.burovskiy at gmail.com> wrote:

> 
> On Aug 13, 2013 9:08 PM, "Ralf Gommers" <ralf.gommers at gmail.com> wrote:
> >
> >
> >
> >
> > On Tue, Aug 13, 2013 at 9:49 PM, Nathan Woods <charlesnwoods at gmail.com> wrote:
> >>
> >> Right, that's what I thought, too. The thing is that dbl- and tplquad DON'T do that. If you carefully at the calling sequence for tplquad, 
> >> -----------
> >>  
> >>
> >> scipy.integrate.tplquad(func, a, b, gfun, hfun, qfun, rfun, args=(), epsabs=1.49e-08, epsrel=1.49e-08)[source]¶
> >>
> >> Return the triple integral of func(z, y, x) from x=a..b, y=gfun(x)..hfun(x), and z=qfun(x,y)..rfun(x,y)
> >> ------------
> >>
> >> The only way that the underlying quad routine can accept qfun(x,y) and rfun(x,y) as limits is if they are evaluated to be constants. That is, integration over z must be the innermost loop of integration, with fund(z,y,z), qfun(x,y), and rfun(x,y) receiving (x,y) passed in as arguments from the outer loops. 
> >>
> >> I agree that the changes I just put in are kind of ridiculous, but (as far as I can tell) they exactly duplicate what is done in dbl- and tplquad.
> >>
> >>
> >> If we really want to put in some kind of integration order, then that's also not too hard, though a bit more than just reversing the lists. It's just something that I don't see a real, compelling reason to do. 
> >
> >
> > Agreed, no very compelling reason. What's required would be not that much more, basically ``lambda x, y, z: func(z, y, x)``, plus *args. I have written little function wrappers like that before for use with dblquad/tplquad.
> >
> > Maybe better to leave it out and merge as it was.
> >
> > Ralf
> >
> 
> Well, my first thought was to allow a user to change, say,
> tplquad(...whatever...)
> to
> nquad(...whatever..., reversed=True),
> and that would just work.
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Unfortunately, the interfaces are different enough that a simple flag wouldn't be enough. nquad wraps all of the range arguments into nested lists, where tplquad keeps them all out in the argument list. You would have to write either some kind of wrapper, or else allow for different calling sequences with some creative use of *args and **kwargs. Not to mention, keeping all of the ordering for everything straight would be a nightmare. Take a look at the function "nquad", if you want to see what I mean. https://github.com/thezealite/scipy/blob/master/scipy/integrate/quadpack.py

Mostly, I think that's a bad idea, since it pretty much explodes the number of ways things can go wrong. I think it's much better to keep things simple, and just have users learn the new interface if they want the new functionality (more dimensions, more option control).

N
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