<HTML><HEAD></HEAD>
<BODY dir=ltr>
<DIV dir=ltr>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: 'Calibri'; COLOR: #000000">
<DIV>okay; tomorrow I’ll make a small PR that just fixes the reference type and
the code comments referring to ‘_generate_ufuncs.py’. I’ll grep the
‘./special/’ folder to see if I can find any other places that refer to
‘_generate_ufuncs.py’</DIV>
<DIV> </DIV>
<DIV>--Adam</DIV>
<DIV
style='FONT-SIZE: small; TEXT-DECORATION: none; FONT-FAMILY: "Calibri"; FONT-WEIGHT: normal; COLOR: #000000; FONT-STYLE: normal; DISPLAY: inline'>
<DIV style="FONT: 10pt tahoma">
<DIV> </DIV>
<DIV style="BACKGROUND: #f5f5f5">
<DIV style="font-color: black"><B>From:</B> <A
title=josh.craig.wilson@gmail.com>Joshua Wilson</A> </DIV>
<DIV><B>Sent:</B> Friday, October 27, 2017 5:26 PM</DIV>
<DIV><B>To:</B> <A title=scipy-dev@python.org>SciPy Developers List</A> </DIV>
<DIV><B>Subject:</B> Re: [SciPy-Dev] Fixing a bug with scipy's hypergeometric
function hyp2f1</DIV></DIV></DIV>
<DIV> </DIV></DIV>
<DIV
style='FONT-SIZE: small; TEXT-DECORATION: none; FONT-FAMILY: "Calibri"; FONT-WEIGHT: normal; COLOR: #000000; FONT-STYLE: normal; DISPLAY: inline'>
<DIV dir=ltr>
<DIV>It might make sense to submit some of these smaller fixes as quick PRs.
They will require little review and can get merged quickly, while the process
for algorithm changes will likely take more time.<BR><BR></DIV>- Josh<BR></DIV>
<DIV class=gmail_extra>
<DIV> </DIV>
<DIV class=gmail_quote>On Fri, Oct 27, 2017 at 6:50 PM, Adam <SPAN
dir=ltr><<A target=_blank>Former@physicist.net</A>></SPAN> wrote:<BR>
<BLOCKQUOTE class=gmail_quote
style="PADDING-LEFT: 1ex; BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex">
<DIV style="WORD-WRAP: break-word">
<DIV>Okay *that* worked! Thank you very much!</DIV><SPAN>
<DIV> </DIV>
<DIV>
<BLOCKQUOTE type="cite">
<DIV dir=ltr>
<DIV>> If _generate_ufuncs.py is in your repo then you aren't working
with the master branch of SciPy. It was changed to _generate_pyx.py recently
and is now run automatically as part of the build process. Make sure you
update (or there will be a ton of merge conflicts when you submit the
PR).</DIV></DIV></BLOCKQUOTE><BR></DIV></SPAN>
<DIV>My repo actually does have _generate_pyx.py which is what I meant; I
copied _generate_ufuncs.py from the comment header of add_newdocs.py. In
my PR, I'll change these comments so they refer to the new
_generate_pyx.py...</DIV>
<DIV> </DIV>
<DIV>I'll also fix the reference to "Computation of Special Functions" in my
PR unless someone objects...</DIV>
<DIV>
<DIV class=h5>
<DIV> </DIV>
<DIV>On Fri, 2017-10-27 at 16:46 -0500, Joshua Wilson wrote:</DIV>
<BLOCKQUOTE type="cite">
<DIV dir=ltr>
<DIV>
<DIV>
<DIV>> it appears I wasn't running _generate_ufuncs.py
beforehand<BR><BR></DIV>If _generate_ufuncs.py is in your repo then you
aren't working with the master branch of SciPy. It was changed to
_generate_pyx.py recently and is now run automatically as part of the build
process. Make sure you update (or there will be a ton of merge conflicts
when you submit the PR).<BR><BR>> Is there a way of generating HTML that
renders the latex equations?<BR><BR></DIV>Maybe try make html-scipyorg. The
first time you try it will probably complain that you are missing a git
submodule, but it should also give instructions on how to fix
that.<BR><BR>> Is the 2nd author of the first reference
misspelled<BR><BR></DIV>Looks like it.<BR></DIV>
<DIV class=gmail_extra>
<DIV> </DIV>
<DIV class=gmail_quote>On Fri, Oct 27, 2017 at 3:56 PM, Adam <SPAN
dir=ltr><<A target=_blank>Former@physicist.net</A>></SPAN> wrote:<BR>
<BLOCKQUOTE type="cite">
<DIV>
<DIV>I figured it out and it appears I wasn't running _generate_ufuncs.py
beforehand...</DIV>
<DIV> </DIV>
<DIV>That said, the generated HTML still doesn't render my equations as a
latex equation. That is to say, my output looks like:</DIV>
<DIV><IMG
src="cid:F8941ACB37B9491B96E121314FEF511E@DESKTOPPNU8RST"><BR></DIV>
<DIV> </DIV>
<DIV><B>Is there a way of generating HTML that renders the latex
equations?</B> Like it appears on the <A
href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.hyp2f1.html"
target=_blank>https://docs.scipy.org/doc<WBR>/scipy/reference/generated/sci<WBR>py.special.hyp2f1.html</A></DIV>
<DIV> </DIV>
<DIV><B>Bonus question: </B>Is the 2nd author of the first reference
misspelled, i.e., Jjie [sic]? Shouldn't the entire reference
be:<BR></DIV>
<DIV>S. Zhang, J. Jin "Computation of Special Functions", Wiley, 1996? See
<A
href="https://books.google.com/books/about/Computation_of_special_functions.html?id=ASfvAAAAMAAJ"
target=_blank>https://books.google.com/b<WBR>ooks/about/Computation_of_spec<WBR>ial_functions.html?id=ASfvAAAA<WBR>MAAJ</A></DIV>
<DIV><B><BR></B></DIV>
<DIV></DIV>
<DIV>I can fix the first reference in my PR as well...</DIV><SPAN
class=m_8372675968087872395HOEnZb><FONT color=#888888>
<DIV><B><BR></B></DIV>
<DIV></DIV>
<DIV>--Adam</DIV></FONT></SPAN>
<DIV>
<DIV class=m_8372675968087872395h5>
<DIV> </DIV>
<DIV>On Thu, 2017-10-26 at 20:52 -0500, Joshua Wilson wrote:</DIV>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<DIV> </DIV>
<DIV>I do in fact get a bunch of html in the folders build/html, but
the html for hyp2f1 doesn't contain my edits</DIV></BLOCKQUOTE>
<DIV>If I recall correctly, Sphinx doesn't detect changes in the
`_ufuncs`</DIV>
<DIV>extension module. Maybe try forcing a complete rebuild with
`make</DIV>
<DIV>SPHINXOPTS=-Ea html`.</DIV>
<DIV> </DIV>
<DIV>On Thu, Oct 26, 2017 at 8:26 PM, Adam <<A
target=_blank>Former@physicist.net</A>> wrote:</DIV>
<BLOCKQUOTE type="cite">
<DIV> </DIV>
<DIV>Hey guys,</DIV>
<DIV> </DIV>
<DIV>How do I view the html version of a functions docstring?
I've added my</DIV>
<DIV>Buhring reference to the docstring and I want to see how it
renders in HTML.</DIV>
<DIV> </DIV>
<DIV>I've tried both methods described in</DIV>
<DIV><A
href="https://github.com/scipy/scipy/blob/master/doc/README.txt"
target=_blank>https://github.com/scipy/scipy<WBR>/blob/master/doc/README.txt</A>
but neither of</DIV>
<DIV>them worked.</DIV>
<DIV> </DIV>
<DIV>When I try:</DIV>
<DIV>(scipy-dev) <A
target=_blank>adam@adam-P7xxDM-G</A>:~/scipy-dev<WBR>/scipy$ python
setup.py</DIV>
<DIV>build_sphinx</DIV>
<DIV>I get:</DIV>
<DIV>(...blah...blah...)</DIV>
<DIV>usage: setup.py [global_opts] cmd1 [cmd1_opts] [cmd2 [cmd2_opts]
...]</DIV>
<DIV>or: setup.py --help [cmd1 cmd2 ...]</DIV>
<DIV>or: setup.py --help-commands</DIV>
<DIV>or: setup.py cmd --help</DIV>
<DIV>error: invalid command 'build_sphinx'</DIV>
<DIV> </DIV>
<DIV>When I try :</DIV>
<DIV>(scipy-dev) <A
target=_blank>adam@adam-P7xxDM-G</A>:~/scipy-dev<WBR>/scipy/doc$ make
html</DIV>
<DIV> </DIV>
<DIV>I do in fact get a bunch of html in the folders build/html, but
the html for</DIV>
<DIV>hyp2f1 doesn't contain my edits. I've tried building html
after</DIV>
<DIV>reinstalling my dev version of scipy, but that didn't change
anything.</DIV>
<DIV> </DIV>
<DIV>Thanks for any help!</DIV>
<DIV> </DIV>
<DIV>--Adam</DIV>
<DIV> </DIV>
<DIV>On Fri, 2017-10-20 at 18:23 -0700, Adam wrote:</DIV>
<DIV> </DIV>
<DIV>I can certainly add the formulas to the doc string if that's what
people</DIV>
<DIV>want. My only concern is that the a-b=m case involves about
a page of</DIV>
<DIV>formula's and would take a lot of space in the doc string (I've
attached the</DIV>
<DIV>pdf from my latex file of the formulas). Originally I was
thinking that the</DIV>
<DIV>docstring would just contain some reference to the pdf document,
e.g., "See</DIV>
<DIV>the pdf at location X for the method used when a-b is an
integer."</DIV>
<DIV> </DIV>
<DIV>But like I said, I can put them wherever they need to go; I
justed wanted to</DIV>
<DIV>make sure that future maintainers have some reference as to what
the code is</DIV>
<DIV>trying to do...</DIV>
<DIV> </DIV>
<DIV>--Adam</DIV>
<DIV> </DIV>
<DIV>On Fri, 2017-10-20 at 08:54 -0400, <A
target=_blank>josef.pktd@gmail.com</A> wrote:</DIV>
<DIV> </DIV>
<DIV>One possibility:</DIV>
<DIV>Currently the only more extensive Latex based documentation is in
the</DIV>
<DIV>tutorial.</DIV>
<DIV>I think it would be possible to add a technical appendix or
something like</DIV>
<DIV>that</DIV>
<DIV>to the scipy.special tutorial, a bit similar to the distributions
formulas</DIV>
<DIV>attached to the</DIV>
<DIV>stats tutorial.</DIV>
<DIV> </DIV>
<DIV>For example Boost, last time I checked, had long documentation
for the</DIV>
<DIV>special</DIV>
<DIV>functions, which might be too long to fit in docstrings.</DIV>
<DIV> </DIV>
<DIV>I don't know how much there would be for special functions and
whether it is</DIV>
<DIV>difficult to maintain those notes. However, I think it would be
good to have</DIV>
<DIV>notes that developers have already written available for
future</DIV>
<DIV>developers and users that are interested in technical
details.</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>Josef</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>On Fri, Oct 20, 2017 at 2:01 AM, Ralf Gommers <<A
target=_blank>ralf.gommers@gmail.com</A>></DIV>
<DIV>wrote:</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>On Thu, Oct 19, 2017 at 8:04 PM, Ted Pudlik <<A
target=_blank>tpudlik@gmail.com</A>> wrote:</DIV>
<DIV> </DIV>
<DIV>Concerning the actual formulas: there's a compromise between
leaving them</DIV>
<DIV>implicit and creating a separate LaTeX doc. You could add
the formulas to</DIV>
<DIV>the docstring. The LaTeX will render in the HTML version of
the</DIV>
<DIV>documentation (example). I'm not sure how the maintainers
feel about this,</DIV>
<DIV>though (this is just a suggestion from a "private
citizen").</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>In general: using LaTeX can be a good idea, the one thing that
has to be</DIV>
<DIV>kept in mind is readability as plain text (important both for
reading</DIV>
<DIV>docstrings in IPython terminal and when working on the code in an
editor).</DIV>
<DIV>Best to add LaTeX formulas to the Notes section rather than in
the first</DIV>
<DIV>sentences. And avoid usage of things like \left[ that make the
rendered html</DIV>
<DIV>slightly prettier but the actual math much harder to read as
plain text.</DIV>
<DIV> </DIV>
<DIV>Here's a recent PR with discussion about various LaTeX
styles:</DIV>
<DIV><A href="https://github.com/scipy/scipy/pull/7756"
target=_blank>https://github.com/scipy/scipy<WBR>/pull/7756</A>. The
style that got merged is about</DIV>
<DIV>right.</DIV>
<DIV> </DIV>
<DIV>Cheers,</DIV>
<DIV>Ralf</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>On Thu, Oct 19, 2017 at 11:59 AM Adam <<A
target=_blank>Former@physicist.net</A>> wrote:</DIV>
<DIV> </DIV>
<DIV>Okay cool; thanks for the helpful reply!</DIV>
<DIV> </DIV>
<DIV>I'll look at Gosper's method and see how it compares with
Buhring's method.</DIV>
<DIV>For now I'll plan on doing a PR that implements one of these two
methods. I</DIV>
<DIV>was just worried that I might end up doing a lot of work on a PR
that</DIV>
<DIV>implements Buhring's series only to have a reviewer reject it
saying "Well,</DIV>
<DIV>you should have used such-and-such's algorithm which is must
faster, much</DIV>
<DIV>more accurate, etc."</DIV>
<DIV> </DIV>
<DIV>I'll also hold off on adding a latex doc to the repo of the
actual formulas</DIV>
<DIV>used for the b-a=integer special case (unless I hear
otherwise).</DIV>
<DIV> </DIV>
<DIV>Thanks again!</DIV>
<DIV> </DIV>
<DIV>--Adam</DIV>
<DIV> </DIV>
<DIV>-----Original Message-----</DIV>
<DIV>From: Joshua Wilson</DIV>
<DIV>Sent: Thursday, October 19, 2017 9:35 AM</DIV>
<DIV>To: SciPy Developers List</DIV>
<DIV>Subject: Re: [SciPy-Dev] Fixing a bug with scipy's hypergeometric
function</DIV>
<DIV>hyp2f1</DIV>
<DIV> </DIV>
<DIV>Hey Adam,</DIV>
<DIV> </DIV>
<BLOCKQUOTE type="cite">
<DIV> </DIV>
<DIV>Does this sound like a worthwhile PR?</DIV></BLOCKQUOTE>
<DIV>Yes, definitely</DIV>
<DIV> </DIV>
<BLOCKQUOTE type="cite">
<DIV> </DIV>
<DIV>Does the implementation sound reasonable?</DIV></BLOCKQUOTE>
<DIV>It's been a while since I've thought about this, but if I
recall</DIV>
<DIV>correctly the problematic region you've found is one that comes
up</DIV>
<DIV>quite frequently--see e.g. page 14 in</DIV>
<DIV> </DIV>
<DIV><A href="http://fredrikj.net/math/hypgeom.pdf"
target=_blank>http://fredrikj.net/math/hypge<WBR>om.pdf</A></DIV>
<DIV> </DIV>
<DIV>Floating around in the ether is a method credited to Bill Gosper
for</DIV>
<DIV>handling that region which also uses a recurrence relation
(maybe</DIV>
<DIV>related to/the same as in the paper you cited)? I can never seem
to</DIV>
<DIV>find the original reference (dead link), but I've attached
someone's</DIV>
<DIV>writeup of it.</DIV>
<DIV> </DIV>
<DIV>So, your implementation sounds reasonable, but if you really want
to</DIV>
<DIV>dig into it you could check out the Gosper stuff and see how
they</DIV>
<DIV>compare.</DIV>
<DIV> </DIV>
<BLOCKQUOTE type="cite">
<DIV> </DIV>
<DIV>Can the PR implement formulas/methods that don't appear in the
literature?</DIV>
<DIV>Is it going to be a problem if I implement this limit case in
the PR?</DIV></BLOCKQUOTE>
<DIV>It's implicit in the literature, so I think it's fine.</DIV>
<DIV> </DIV>
<BLOCKQUOTE type="cite">
<DIV> </DIV>
<DIV>I don't what reference I would place hyp2f1's doc
string</DIV></BLOCKQUOTE>
<DIV>The Buhring paper. The formula is something that an informed
reader</DIV>
<DIV>could figure out after reading it.</DIV>
<DIV> </DIV>
<BLOCKQUOTE type="cite">
<DIV> </DIV>
<DIV>I would be wiling to maybe add a latex doc to the PR (placed
somewhere in</DIV>
<DIV>the doc folder?)</DIV></BLOCKQUOTE>
<DIV>If I recall correctly people were opposed to adding LaTeX docs.
(But</DIV>
<DIV>maybe I recall incorrectly; if so please someone correct me.) I
also</DIV>
<DIV>have various special function write ups that might be handy for
future</DIV>
<DIV>devs... maybe in a separate repo?</DIV>
<DIV> </DIV>
<DIV>On Wed, Oct 18, 2017 at 6:47 PM, Adam <<A
target=_blank>Former@physicist.net</A>> wrote:</DIV>
<BLOCKQUOTE type="cite">
<DIV> </DIV>
<DIV>Hello guys,</DIV>
<DIV> </DIV>
<DIV>I've found a small region in the complex plane where
scipy's</DIV>
<DIV>implementation</DIV>
<DIV>of the hypergeometric function hyp2f1 fails. I've documented
this error in</DIV>
<DIV>issue 8054 on github.</DIV>
<DIV> </DIV>
<DIV>I am willing to submit a PR that fixes this issue. My PR would
basically</DIV>
<DIV>implement the analytic continuation formula given in this
paper: (Buhring,</DIV>
<DIV>An Analytic Continuation of the Hypergeometric Series). I've
already</DIV>
<DIV>implemented this series in some prototype code written in
Fortran and it</DIV>
<DIV>agrees well with the values returned by mpmath's implementation
of hyp2f1.</DIV>
<DIV> </DIV>
<DIV>Before I attempt a PR, I just wanted to touch base and ask the
group the</DIV>
<DIV>following:</DIV>
<DIV> </DIV>
<DIV>1) Does this sound like a worthwhile PR? The failure region is
somewhat</DIV>
<DIV>small and I don't know with what urgency people would want this
fixed.</DIV>
<DIV> </DIV>
<DIV>2) Does the implementation sound reasonable? My background is
physics and</DIV>
<DIV>so</DIV>
<DIV>I haven't done a complete literature search looking for the
*fastest*</DIV>
<DIV>algorithm. All I can say that the Buhring's formula works and
my</DIV>
<DIV>implementation only seems to be about %50 slower than the
current hyp2f1</DIV>
<DIV>(at</DIV>
<DIV>points in the complex plane where both methods converge). I
would only</DIV>
<DIV>apply</DIV>
<DIV>Buhring's series in the region where hyp2f1 currently
diverges.</DIV>
<DIV> </DIV>
<DIV>3) Can the PR implement formulas/methods that don't appear in
the</DIV>
<DIV>literature? Buhring's paper *only* gives the analytic
continuation for the</DIV>
<DIV>case where the difference between the a/b parameters is NOT an
integer.</DIV>
<DIV>When</DIV>
<DIV>a-b=m, the limit case of his series can be derived using a
method</DIV>
<DIV>described</DIV>
<DIV>in "The Special Functions and Their Approximations" by Y. Luke
(as Buhling</DIV>
<DIV>mentions in his paper). I've derived the formula for this limit
case and</DIV>
<DIV>have an implementation of it that produces values in agreement
with</DIV>
<DIV>mpmath.</DIV>
<DIV>Is it going to be a problem if I implement this limit case in
the PR? I</DIV>
<DIV>ask</DIV>
<DIV>because I don't what reference I would place hyp2f1's doc
string. I would</DIV>
<DIV>be</DIV>
<DIV>wiling to maybe add a latex doc to the PR (placed somewhere in
the doc</DIV>
<DIV>folder?) that contains the formula so that future scipy devs
have</DIV>
<DIV>something</DIV>
<DIV>to reference when reviewing hyp2f1's source code.</DIV>
<DIV> </DIV>
<DIV>Anyways, let me know if my idea for a PR sounds like a good
idea! I</DIV>
<DIV>apologize for the longish email, but this is my first time
trying to</DIV>
<DIV>contribute to scipy...</DIV>
<DIV> </DIV>
<DIV>--Adam</DIV>
<DIV> </DIV>
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