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

Nathan Woods charlesnwoods@gmail....
Sun Aug 11 22:00:05 CDT 2013


I like the optional argument idea. I think it gives a good balance between a clean interface and legacy support. It's also not too difficult to implement. 

Nate

On Aug 10, 2013, at 8:48 AM, Ralf Gommers <ralf.gommers@gmail.com> wrote:

> 
> 
> 
> On Fri, Aug 9, 2013 at 5:55 AM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
> How about adding an optional argument to nquad, specifying the order of integration limits? Defaulting to the 'forward' order. Something like
> 
> nquad(f(x,y), [a, b], [g(x), h(x)])
> being the default, and
> 
> nquad(f(x,y), [a, b], [g(y), h(y)], integration_order='reversed')
> interpreting the limits the way dblquad/tplquad do.
> 
> 
> That makes sense to me, both to make it easier to map to dblquad/tplquad and to avoid writing an argument-reversing wrapper when you want to integrate an existing function.
>  
> Evgeni
> 
> On Aug 9, 2013 11:35 AM, "Nathan Woods" <charlesnwoods@gmail.com> wrote:
> Clear documentation is always important, so I don't think there will be any problems there. Does anyone else have thoughts they'd like to share?
> 
> Nate
> 
> On Aug 5, 2013, at 11:35 PM, josef.pktd@gmail.com wrote:
> 
> > On Mon, Aug 5, 2013 at 4:24 PM, Ralf Gommers <ralf.gommers@gmail.com> wrote:
> >>
> >>
> >>
> >> On Fri, Aug 2, 2013 at 7:19 PM, Nathan Woods <charlesnwoods@gmail.com>
> >> wrote:
> >>>
> >>> I'm copying the most relevant parts over from a discussion on GitHub,
> >>> having to do with a new n-dimensional integration tool. The discussion is
> >>> whether or not to make nquad's new interface consistent with dbl-and
> >>> tplquad, even though their precedent is arguably more confusing to users.
> >>>
> >>> nquad is a recursively defined wrapper to scipy.integrate.quad that allows
> >>> for n-dimensional integration with almost the entire list of arguments
> >>> allowed by quad. It is therefore more general than either dbl- or tplquad,
> >>> and encompasses their use cases, while allowing the user greater control
> >>> over the integration. The interface is given: nquad( f(x0,x1,…xn,t0,…tm)
> >>> ,[[x0_lo,x0_hi],…[xn_lo,xn_hi]],[t0,…tm],[opts0,…optsn]).
> >>> The ranges of integration are given in the same order as the arguments in
> >>> the function to be integrated. This ordering is consistent with both Matlab
> >>> and Octave, and it is similar to what is encountered in other SciPy packages
> >>> such as fft. It is also what makes sense to new users.
> >>>
> >>> dbl- and tplquad, however, reverse the order of arguments in f. From the
> >>> documentation for tplquad:
> >>>
> >>> 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)
> >>>
> >>> This is confusing, and contrary to common practice.
> >>>
> >>> It is proposed that nquad's calling sequence be left as is, and that the
> >>> use of dbl- and tplquad be deprecated in some future version of SciPy, and
> >>> that nquad be recommended for multidimensional integration in new code. dbl-
> >>> and tplquad would of course be retained, though not recommended, in order to
> >>> avoid breaking existing code.
> >>>
> >>> Wow, that came out all legalistic. Anyway, what do you all think about
> >>> this change? I have a horse in the race (I wrote most of nquad), but I
> >>> really think that maintaining the backwards style from dbl- and tplquad and
> >>> enshrining it in new code is a bad idea. This is a perfect time to get away
> >>> from it, if that's what we want to do.
> >>
> >>
> >> My first instinct was that nquad should match what's already there in
> >> scipy.integrate, but I've changed my mind. I always have to look at the
> >> dblquad/tplquad documentation to get it right, so those functions don't have
> >> a good API imho. Therefore just making nquad do the logical thing (i.e.
> >> ``f(x, y ,z)``) makes sense to me.
> >>
> >> Let's not use the word "deprecate" for dblquad/tplquad, since they shouldn't
> >> be removed. Instead just recommend `nquad` as the function to use in the
> >> docs.
> >>
> >> Any other opinions?
> >
> > How do you know the integration order in the new interface?
> >
> > The current dblquad, tplquad looks to me like writing an integral
> >
> > integral_x integral_y integral_z  func3d(z, y,x)  dz dy dz
> > where integration limits are x=a..b, y=gfun(x)..hfun(x), and
> > z=qfun(x,y)..rfun(x,y)
> >
> > based on reading of the docstrings for tplquad. So this doesn't look
> > very strange to me.
> 
> I guess that was the reason why dblquad/tplquad are implemented the way they are. The problem with that is that no one writes functions like f(z, y, x), everyone writes f(x, y, z). So it's plain unnatural.
>  
> >
> > The suggested description
> > ``
> > The interface is given: nquad( f(x0,x1,…xn,t0,…tm)
> > ,[[x0_lo,x0_hi],…[xn_lo,xn_hi]],[t0,…tm],[opts0,…optsn]).
> > The ranges of integration are given in the same order as the arguments
> > in the function to be integrated. 
> > ```
> >
> > Does this mean we integrate over x0 first (innermost integral) or last
> > (outermost integral) ?
> 
> x0 first, that should be made clearer in the docstring.
> 
> Ralf
> 
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