[SciPy-Dev] Fixing a bug with scipy's hypergeometric function hyp2f1

[Ted Pudlik]

Concerning the actual formulas: there's a compromise between leaving them
implicit and creating a separate LaTeX doc.  You could add the formulas to
the docstring
<https://github.com/scipy/scipy/blob/8a994cac55f6ec5d4279d9910ac3cee9f5c6a2be/scipy/special/add_newdocs.py#L3367>.
The LaTeX will render in the HTML version of the documentation (example
<https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.jv.html#scipy.special.jv>).
I'm not sure how the maintainers feel about this, though (this is just a
suggestion from a "private citizen").



On Thu, Oct 19, 2017 at 11:59 AM Adam <Former at physicist.net> wrote:

> Okay cool; thanks for the helpful reply!
>
> I'll look at Gosper's method and see how it compares with Buhring's method.
> For now I'll plan on doing a PR that implements one of these two methods.
> I
> was just worried that I might end up doing a lot of work on a PR that
> implements Buhring's series only to have a reviewer reject it saying "Well,
> you should have used such-and-such's algorithm which is must faster, much
> more accurate, etc."
>
> I'll also hold off on adding a latex doc to the repo of the actual formulas
> used for the b-a=integer special case (unless I hear otherwise).
>
> Thanks again!
>
> --Adam
>
> -----Original Message-----
> From: Joshua Wilson
> Sent: Thursday, October 19, 2017 9:35 AM
> To: SciPy Developers List
> Subject: Re: [SciPy-Dev] Fixing a bug with scipy's hypergeometric function
> hyp2f1
>
> Hey Adam,
>
> > Does this sound like a worthwhile PR?
>
> Yes, definitely
>
> > Does the implementation sound reasonable?
>
> It's been a while since I've thought about this, but if I recall
> correctly the problematic region you've found is one that comes up
> quite frequently--see e.g. page 14 in
>
> http://fredrikj.net/math/hypgeom.pdf
>
> Floating around in the ether is a method credited to Bill Gosper for
> handling that region which also uses a recurrence relation (maybe
> related to/the same as in the paper you cited)? I can never seem to
> find the original reference (dead link), but I've attached someone's
> writeup of it.
>
> So, your implementation sounds reasonable, but if you really want to
> dig into it you could check out the Gosper stuff and see how they
> compare.
>
> > Can the PR implement formulas/methods that don't appear in the
> literature?
> > Is it going to be a problem if I implement this limit case in the PR?
>
> It's implicit in the literature, so I think it's fine.
>
> > I don't what reference I would place hyp2f1's doc string
>
> The Buhring paper. The formula is something that an informed reader
> could figure out after reading it.
>
> > I would be wiling to maybe add a latex doc to the PR (placed somewhere in
> > the doc folder?)
>
> If I recall correctly people were opposed to adding LaTeX docs. (But
> maybe I recall incorrectly; if so please someone correct me.) I also
> have various special function write ups that might be handy for future
> devs... maybe in a separate repo?
>
> On Wed, Oct 18, 2017 at 6:47 PM, Adam <Former at physicist.net> wrote:
> > Hello guys,
> >
> > I've found a small region in the complex plane where scipy's
> > implementation
> > of the hypergeometric function hyp2f1 fails. I've documented this error
> in
> > issue 8054 on github.
> >
> > I am willing to submit a PR that fixes this issue. My PR would basically
> > implement the analytic continuation formula given in this paper:
> (Buhring,
> > An Analytic Continuation of the Hypergeometric Series). I've already
> > implemented this series in some prototype code written in Fortran and it
> > agrees well with the values returned by mpmath's implementation of
> hyp2f1.
> >
> > Before I attempt a PR, I just wanted to touch base and ask the group the
> > following:
> >
> > 1) Does this sound like a worthwhile PR? The failure region is somewhat
> > small and I don't know with what urgency people would want this fixed.
> >
> > 2) Does the implementation sound reasonable? My background is physics and
> > so
> > I haven't done a complete literature search looking for the *fastest*
> > algorithm. All I can say that the Buhring's formula works and my
> > implementation only seems to be about %50 slower than the current hyp2f1
> > (at
> > points in the complex plane where both methods converge). I would only
> > apply
> > Buhring's series in the region where hyp2f1 currently diverges.
> >
> > 3) Can the PR implement formulas/methods that don't appear in the
> > literature? Buhring's paper *only* gives the analytic continuation for
> the
> > case where the difference between the a/b parameters is NOT an integer.
> > When
> > a-b=m, the limit case of his series can be derived using a method
> > described
> > in "The Special Functions and Their Approximations" by Y. Luke (as
> Buhling
> > mentions in his paper). I've derived the formula for this limit case and
> > have an implementation of it that produces values in agreement with
> > mpmath.
> > Is it going to be a problem if I implement this limit case in the PR? I
> > ask
> > because I don't what reference I would place hyp2f1's doc string. I would
> > be
> > wiling to maybe add a latex doc to the PR (placed somewhere in the doc
> > folder?) that contains the formula so that future scipy devs have
> > something
> > to reference when reviewing hyp2f1's source code.
> >
> > Anyways, let me know if my idea for a PR sounds like a good idea! I
> > apologize for the longish email, but this is my first time trying to
> > contribute to scipy...
> >
> > --Adam
> >
> > _______________________________________________
> > SciPy-Dev mailing list
> > SciPy-Dev at python.org
> > https://mail.python.org/mailman/listinfo/scipy-dev
> >
>
>
>
>
>
>
> _______________________________________________
> SciPy-Dev mailing list
> SciPy-Dev at python.org
> https://mail.python.org/mailman/listinfo/scipy-dev
>
> _______________________________________________
> SciPy-Dev mailing list
> SciPy-Dev at python.org
> https://mail.python.org/mailman/listinfo/scipy-dev
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.python.org/pipermail/scipy-dev/attachments/20171020/38fa3948/attachment.html>