Updated Lambert W function implementation #371

alyst · 2021-12-31T10:50:35Z

This is a fork of #84. I did:

rebased PR implement Lambert W function #84 against the current master
synced with the current master of LambertW.jl
implemented suggestions from implement Lambert W function #84
made some code simplifications that utilize compile-time dispatch
updated tests to check for compile-time type inference and improved approximation testing
~~moved Omega and 1/e constants to IrrationalConstants.jl (PR Lambert's Omega constant IrrationalConstants.jl#12), so this PR requires that Omega constant PR is merged~~uses inve = 1/e constant from Add 1/e constant IrrationalConstants.jl#13
Omega constant is exported as LambertW.Omega or LambertW.Ω

codecov · 2021-12-31T10:52:34Z

Codecov Report

Patch coverage: 96.74% and project coverage change: -0.07 ⚠️

Comparison is base (07a890c) 94.25% compared to head (ed3c825) 94.19%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #371      +/-   ##
==========================================
- Coverage   94.25%   94.19%   -0.07%     
==========================================
  Files          14       15       +1     
  Lines        2908     3031     +123     
==========================================
+ Hits         2741     2855     +114     
- Misses        167      176       +9

Flag	Coverage Δ
unittests	`94.19% <96.74%> (-0.07%)`	⬇️

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Impacted Files	Coverage Δ
src/SpecialFunctions.jl	`100.00% <ø> (ø)`
src/lambertw.jl	`96.74% <96.74%> (ø)`
src/beta_inc.jl	`91.46% <0.00%> (-0.75%)`	⬇️

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ViralBShah · 2022-01-01T09:47:52Z

cc @jlapeyre

CarloLucibello · 2022-02-28T08:07:49Z

Can this be merged? Seems well tested and well documented

devmotion · 2022-02-28T08:31:01Z

No, I don't think it should be merged. My impression from the discussion in #84 was that there was a tendency/agreement to keep the function in a separate package.

alyst · 2022-02-28T08:36:05Z

At this point I wonder if you are interested to improve the implementation of this function at all.

devmotion · 2022-02-28T08:45:21Z

There's a package with this function, and the general opinion (not just my personal one) was to keep the function there. So if it can be improved, I guess you should open a PR in that repo.

alyst · 2022-02-28T09:03:29Z

The "general opinion" is a bit of a stretch. But thank you for your efforts to guard the quality of Julia ecosystem.

As for me, I think trying to put this code elsewhere would be a waste of my resources, given that nobody have reviewed it here (I have noted "if it can be improved").

ViralBShah · 2022-02-28T13:36:19Z

@alyst thanks for putting it together. It is generally true that it has been hard to get reviews here.

devmotion · 2022-02-28T14:47:36Z

I'm sorry for you that the PR is not reviewed, but I guess many people, including myself, are not eager to review a PR in detail if there's already a longer discussion that indicates that there is no general agreement that the Lambert W function should be added to SpecialFunctions but instead shows that people seem to be in favour of keeping it in LambertW.jl. Therefore my suggestion was to make a PR to LambertW.jl instead if you would like to improve its implementation. I think you will receive more reviews and comments there.

ViralBShah · 2022-02-28T14:54:13Z

It did seem that the original author @jlapeyre (IIRC, and if I have my facts straight) expressed interest in keeping it separate - and thus I feel that we should respect that opinion.

ViralBShah · 2022-03-01T01:10:22Z

Since I was the one who triggered the original thought of getting this in - I would like to apologize for causing wasted effort here. :-(

jlapeyre · 2022-03-01T17:55:51Z

I'm also sorry if I caused wasted effort. Like many people, I'm over-extended and this is not the highest priority. I was also reluctant to put effort into a PR because I made one (for the same question) a few years ago, and it sat around till it bitrotted. I'm not blaming anyone: Most of us are not paid for this and have other obligations. But, my best estimation was that the best first step is to put LambertW under the JuliaMath org. I asked how to do that in the appropriate (I think) channel in slack a few weeks ago. But, I never got a response.

ViralBShah · 2022-03-01T22:33:07Z

@jlapeyre I can help with moving LambertW.jl to the JuliaMath org. I'm inviting you as an owner of JuliaMath, and you should be able to then transfer the package.

This copies the implementation of the Lambert W function and related functions and data from jlapeyre/LambertW.jl to SpecialFunctions.jl

- use Base.evalpoly() instead of horner macro reimplementation - use Val()-based dispatch instead of function generation

using the code from JuliaMath/IrrationalConstants.jl/issues/12 No __init__() section is required

ararslan · 2023-03-07T01:58:08Z

src/lambertw.jl

+
+### root finding, iterative solution
+
+# Use Halley's root-finding method to find


Worth noting that there's a paper from Lóczi published last year in Applied Mathematics and Computation called "Guaranteed- and high-precision evaluation of the Lambert W function" that describes algorithms that improve significantly on e.g. Halley's method. I used it to implement W_-1 for real arguments in (-1/e, 0) in https://github.com/JuliaStats/Distributions.jl/blob/master/src/univariate/continuous/lindley.jl#L137-L156.

I've actually tried the iteration scheme evaluated in the paper, but it looks like it's on par with Halley or the latter requires 1-2 iterations less from the same starting point (but I have not tested very extensively).
IIUC the paper doesn't claim that the Iacono-Boyd method provides faster convergence than Halley method, it just proves the bounds for the Iacono-Boyd one (because it's a simpler formula).

Ah good to know, it's been a bit since I read it so the details have been largely GC'd. Probably should have reread the paper before attempting to summarize it. 😅 One thing I recall was that when I was testing things out for the -1 branch in (-1/e, 0), I was comparing LambertW.jl vs. Iacono-Boyd vs. Mathematica as "ground truth" and found that Iacono-Boyd produced more accurate results near -1/e and 0 but was otherwise the same. Your comment makes me realize that I had actually neglected to check the number of iterations that LambertW.jl required for convergence. LambertW.jl explicitly keeps track of the change between iterations and will stop early based on that, whereas my naive implementation of Iacono-Boyd just iterates a set number of times. In developing it, I was playing around with the number of iterations and found that most inputs required only 2 or so iterations to converge, so I'd be interested to see how that compares with LambertW.jl.

I've tried to implement Iacono-Boyd scheme here: https://github.com/alyst/SpecialFunctions.jl/tree/lambertw_iacono_iters.
Actually, the iteration scheme is just an input parameter to the root finding function, so that code could be easily adopted for more comprehensive evaluation of efficiency of both schemes over the whole LambertW(x) domain and for different numeric types.

jlapeyre · 2023-04-17T13:28:19Z

The separate package has been moved here https://github.com/JuliaMath/LambertW.jl

This was referenced Jan 2, 2022

Lambert's Omega constant JuliaMath/IrrationalConstants.jl#12

Closed

Add 1/e constant JuliaMath/IrrationalConstants.jl#13

Open

alyst force-pushed the newest_lambertw branch 4 times, most recently from 03062c9 to 8f2cfd4 Compare January 3, 2022 14:13

alyst mentioned this pull request Jan 4, 2022

implement Lambert W function #84

Closed

alyst force-pushed the newest_lambertw branch from 8f2cfd4 to 0ce1415 Compare May 23, 2022 22:28

alyst force-pushed the newest_lambertw branch from 0ce1415 to cbbafb5 Compare June 24, 2022 00:44

alyst force-pushed the newest_lambertw branch from cbbafb5 to 05da0e5 Compare August 2, 2022 22:47

alyst and others added 7 commits March 6, 2023 17:00

implement Lambert W function

44deb6e

This copies the implementation of the Lambert W function and related functions and data from jlapeyre/LambertW.jl to SpecialFunctions.jl

made changes request in PR review

87b5509

sync with latest LambertW.jl master

8bc1814

lambertw tests: check correct type inference

0f6bce3

lambertw tests: correct approx equality tests

46f5b54

lambertwbp: simplify series coeffs code

0894aad

lambertw_root_find: fix diff type

59f1f84

alyst added 17 commits March 6, 2023 17:00

lambertw: simplify handling non-finite vals

edf1820

lambertw: use inv(e)

83d79ca

lambertw: annotate function args with types

87f9749

lambertw: use dispatch to compute diff. branches

d39470c

lambertwbp_series(): simplify

8f0e616

- use Base.evalpoly() instead of horner macro reimplementation - use Val()-based dispatch instead of function generation

lambertw(): make maxiter a keyword

6fc569f

lambertw: small fixes

739a17c

lambertwbp(): cleanup tests

e34e8d9

lambertw(): use inve constant in tests

4f8b18b

rename omega => LambertW.Omega and update its def

c90b502

using the code from JuliaMath/IrrationalConstants.jl/issues/12 No __init__() section is required

lambertw(): more inference tests

87d0828

lambertw: improve test precision

adf29b4

lambertw(): use inve constant

d277be3

use Compat to support evalpoly() on Julia 1.3

5b38fec

DONTMERGE temporarily define inve here

afa1d0e

lambertw: test maxiter= and convergence warning

b0c63e5

lambertw: fix jldoctests

ed3c825

alyst force-pushed the newest_lambertw branch from 05da0e5 to ed3c825 Compare March 7, 2023 01:04

ararslan reviewed Mar 7, 2023

View reviewed changes

jlapeyre mentioned this pull request Apr 17, 2023

Add (and unify) Julia Lambert W function? #27

Open

tomchor mentioned this pull request Jan 26, 2024

Cannot use lambertw on the GPU JuliaMath/LambertW.jl#30

Closed

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Updated Lambert W function implementation #371

Updated Lambert W function implementation #371

alyst commented Dec 31, 2021 •

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ararslan Mar 7, 2023

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jlapeyre commented Apr 17, 2023


		### root finding, iterative solution

		# Use Halley's root-finding method to find

Updated Lambert W function implementation #371

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Updated Lambert W function implementation #371

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