[SciPy-Dev] More robust scalar root finding

[Evgeni Burovski]

FWIW I'd always recommend brentq for scalar root-finding.

Trying to make newton-based methods more robust seems to be more or less
reinventing that wheel, which has already been implemented (don't know who
implemented it; hope you read this thread so that you see my thank you!)
and is as robust  as it gets.

чт, 27 авг. 2020 г., 12:57 Juan Luis Cano <juanlu001 at gmail.com>:

> Hi all,
>
> A month ago I was trying to migrate some MATLAB code to Python and found a
> couple of annoyances in the scalar root finding functions of SciPy. I
> opened these issues:
>
> "Make root_scalar work when only x0 is given, similar to newton"
> https://github.com/scipy/scipy/issues/12620
> "newton chokes when iteration steps outside function domain"
> https://github.com/scipy/scipy/issues/12625
>
> and a pull request to address #12625:
>
> "Make scalar, iterative root finding methods robust against steps outside
> domain" https://github.com/scipy/scipy/pull/12626
>
> It seems that the conversation has stalled, so I wanted to bring them to
> the mailing list.
>
> As I said in #12625, common wisdom dictates that if one chooses a starting
> guess closer to the real solution, convergence is achieved. However,
> leaving this well known numerical fact aside for a moment, I wonder if some
> work could be done on the *usability* side of things to
>
> (a) make root_scalar a drop-in replacement to newton (#12620)
> (b) have some opt-out way to increase the robustness of the solution in a
> way that "just works", which is that MATLAB and Octave achieve (#12625)
>
> A personal side note: The original authors of the code I'm migrating tried
> Python half a decade ago but noticed that "SciPy was not converging, while
> MATLAB had no problems", so they ended up using the latter. While we all
> scoffed when the infamous "top reasons to choose MATLAB" comparison was
> published [1][2][3][4], I do think there's still a lot to understand from a
> UX point of view of why people choose one or another. After 7 years of
> teaching Python to engineers, they either become data scientists or they go
> back to MATLAB, and as a result I have decided to get my hands dirty and
> find out the reasons, to the best of my possibilities.
>
> Best,
>
> Juan Luis
>
> [1]
> https://web.archive.org/web/20190806100605/https://www.mathworks.com/products/matlab/matlab-vs-python.html
> [2] https://twitter.com/moorepants/status/1158248132355874817
> [3] https://twitter.com/randal_olson/status/1158402855818018816
> [4] https://twitter.com/neuromusic/status/1158556716096618497
> [5] https://twitter.com/vboykis/status/1158559458173313024
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