Airy function cleanup #18050

simonbyrne · 2016-08-16T10:18:16Z

This rearranges the different airy functions, deprecating airy, airyx and airyprime in favour of the more specific variants (airyai, airyaiprime, etc.), and clarifies the docs of each remaining function. Fixes #17032.

tkelman · 2016-08-16T10:55:57Z

base/special/bessel.jl

 """
-    airy(k,x)
+    airyai(x::Complex128)


all docstring signature changes need to be made in the RST

good catch, thanks.

tkelman · 2016-08-16T13:02:13Z

doc/stdlib/math.rst

@@ -1396,47 +1396,53 @@ Mathematical Functions

   Compute the polygamma function of order ``m`` of argument ``x`` (the ``(m+1)th`` derivative of the logarithm of ``gamma(x)``\ )

-.. function:: airy(k,x)
+.. function:: airyai(x)


and they need to match ... the inline docstring has ::Complex128 here, this one doesn't

(probably better without if that's not the only input type that works)

They do: I added function airyai end between the docstring and the Complex128 method.

the contents don't match

julia/base/special/bessel.jl

Lines 43 to 46 in 54ec215

"""

airyai(x::Complex128)

Airy function of the first kind ``\\operatorname{Ai}(x)``.

Ah, I missed that one. Thanks

ararslan · 2016-08-16T17:08:42Z

This looks great to me! 👍

Once this is merged, any chance you'd want to apply these same changes in JuliaMath/SpecialFunctions.jl? If not I can do so later.

giordano · 2016-08-28T23:37:05Z

Reading the code I understand that all the Airy functions of real arguments are always real, is it correct? So airyaix(-3) != airyaix(complex(-3)). If so, would you mind documenting this?

simonbyrne · 2016-09-07T14:57:02Z

@giordano Thanks, I thought they were, but it turns out not: the Airy functions themselves are real for real values, but the scaled airyaix and airyaiprimex ones are not due to the sqrt(x) term.

The question here is should we return a complex value, or throw a domain error?

simonbyrne · 2016-09-07T14:59:23Z

@stevengj Your thoughts?

simonbyrne · 2016-09-07T15:01:10Z

Note this is also an issue in the existing code:

julia> airyx(-3)
0.35928383932620317

julia> airyx(complex(-3))
0.35928383932620317 - 0.1200641157612309im

stevengj · 2016-09-07T16:35:24Z

Either throw a domain error, or (similar to lgamma) define it to be the analytic complex version for complex x and to be scaled bysqrt(abs(x)) for real x.

simonbyrne · 2016-09-07T16:47:15Z

define it ... to be scaled by sqrt(abs(x)) for real x.

Won't that require changes to the AMOS code?

giordano · 2016-09-07T16:57:15Z

GSL uses as scaling factor the same as Julia for x>0, and 1 for x < 0 (https://www.gnu.org/software/gsl/manual/html_node/Derivatives-of-Airy-Functions.html). Is this an option for Julia? Of course it would be backward incompatible.

stevengj · 2016-09-07T20:38:08Z

Looking at this more closely, I would suggest throwing a DomainError for negative Real arguments.

For negative arguments, there is no exponential growth or decay that needs to be cancelled, so there is no real need for any scale factor. In that sense, GSL's choice of a scale factor of 1 for x < 0 makes a certain amount of sense.

However, if you switch scale factors to 1 for negative arguments, then any code calling the airyaix function would need to take this into account (if it cares about negative x). So, the caller's code will need an if x < 0 check. But if they are doing an if x < 0 check anyway, they can just call airyai(x) for x < 0 themselves — there is no need for us to provide it.

Furthermore, if we silently switch scale factors for x < 0, then user code that does not check for this case will be incorrect. It is better to throw a DomainError so that they know they need to call the unscaled function manually for the case of negative arguments.

simonbyrne · 2016-09-08T08:37:49Z

I agree with the logic. I've updated the PR and added some more tests for this case.

tkelman · 2016-12-22T18:14:56Z

@simonbyrne any update here?

simonbyrne · 2016-12-22T19:16:55Z

I think the only thing holding this back was the decision on what was happening with #4301/#8536, but we should probably still do it. I'll rebase.

tkelman · 2016-12-22T19:27:42Z

If #8536 happens soon it should probably incorporate this change anyway.

This rearranges the different airy functions, deprecating `airy`, `airyx` and `airyprime` in favour of the more specific variants (`airyai`, `airyaiprime`, etc.), and clarifies the docs of each remaining function. Fixes #17032.

simonbyrne · 2016-12-22T19:44:21Z

Updated.

tkelman · 2016-12-22T19:57:44Z

oops, ignore any travis failures about cmake here, need to restart after https://travis-ci.org/JuliaLang/julia/jobs/186158977 and https://travis-ci.org/JuliaLang/julia/jobs/186158972 have finished and uploaded a new cache

(old logs, for reference sake - not too important though https://gist.github.com/a46d92bdbdfdcd1670fc657f15bee43c and https://gist.github.com/dba158e84bee20504e87f0a77975cd28)

tkelman

(squash) merge when green?

stevengj

LGTM.

giordano · 2016-12-29T23:51:08Z

Just compiled Julia master, but compatibility function doesn't seem to work:

julia> airy(0, 4.0)
ERROR: UndefVarError: afn not defined
Stacktrace:
 [1] airy at ./deprecated.jl:1188 [inlined]
 [2] airy(::Int64, ::Float64) at ./deprecated.jl:1196

tkelman · 2016-12-30T00:33:53Z

oops, we should sanity check deprecations in a better way...

~~might be enough to add a dollar sign inside the QuoteNode calls?~~

giordano · 2016-12-30T00:36:06Z

Do you mean

$(QuoteNode($afn))

? I tried that but compilation of Julia fails with

deprecated.jl
error during bootstrap:
LoadError(at "sysimg.jl" line 369: LoadError(at "deprecated.jl" line 1183: ErrorException("error compiling anonymous: syntax: prefix "$" in non-quoted expression")))

In Julia 0.6 Airy functions have been reorganized, see JuliaLang/julia#18050. I will keep a method for `airy' until support for Julia 0.5 will be dropped.

cf #18050

nalimilan · 2016-12-31T09:47:25Z

This broke make docs:

Documenter: setting up build directory.
Documenter: expanding markdown templates.
 !! Undefined binding 'Base.Math.airyaix'. [src/stdlib/math.md]
 !! Undefined binding 'Base.Math.airyaiprimex'. [src/stdlib/math.md]
 !! Undefined binding 'Base.Math.airybix'. [src/stdlib/math.md]
 !! Undefined binding 'Base.Math.airybiprimex'. [src/stdlib/math.md]
Documenter: building cross-references.
 !! No doc found for reference '[`airyaix(z)`](@ref)'. [src/manual/mathematical-operations.md]
 !! No doc found for reference '[`airyaiprimex(z)`](@ref)'. [src/manual/mathematical-operations.md]
 !! No doc found for reference '[`airybix(z)`](@ref)'. [src/manual/mathematical-operations.md]
 !! No doc found for reference '[`airybiprimex(z)`](@ref)'. [src/manual/mathematical-operations.md]
Documenter: running document checks.
 !! Skipped doctesting.
 > checking footnote links.
Documenter: populating indices.
ERROR: LoadError: `makedocs` encountered errors. Terminating build
 in runner(::Type{Documenter.Builder.RenderDocument}, ::Documenter.Documents.Document) at /home/milan/Dev/julia-packaging/julia-master/doc/deps/v0.6/Documenter/src/Builder.jl:202

Maybe we should run it on CI to catch this kind of bug?

tkelman · 2016-12-31T09:49:49Z

It did run on CI though https://travis-ci.org/JuliaLang/julia/jobs/187530248#L745 just didn't flag an error?

nalimilan · 2016-12-31T09:57:58Z

Sorry, probably a bug on my end then. I guess I used the incorrect Julia executable to build the docs.

giordano · 2016-12-31T11:18:11Z

The fact that airyaix(x) for negative real x throws a DomainError should be documented? Sorry for being pedantic :-)

simonbyrne · 2016-12-31T11:27:36Z

Yes, it should. Would you mind making a pull request?

giordano · 2016-12-31T11:48:44Z

No, I can do it!

tkelman reviewed Aug 16, 2016
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simonbyrne added the maths Mathematical functions label Aug 16, 2016

tkelman reviewed Aug 16, 2016
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kshyatt added the docs This change adds or pertains to documentation label Aug 16, 2016

simonbyrne force-pushed the sb/airy branch from a5e7a63 to 7bc0975 Compare September 7, 2016 14:48

simonbyrne force-pushed the sb/airy branch from 7bc0975 to 9502ffb Compare September 7, 2016 22:29

simonbyrne added this to the 0.6.0 milestone Nov 18, 2016

Airy function cleanup

0d8d54f

This rearranges the different airy functions, deprecating `airy`, `airyx` and `airyprime` in favour of the more specific variants (`airyai`, `airyaiprime`, etc.), and clarifies the docs of each remaining function. Fixes #17032.

simonbyrne force-pushed the sb/airy branch from 9502ffb to 0d8d54f Compare December 22, 2016 19:44

Merge branch 'master' into sb/airy

3aa98a2

tkelman approved these changes Dec 29, 2016

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stevengj approved these changes Dec 29, 2016

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tkelman merged commit e73c556 into master Dec 29, 2016

tkelman deleted the sb/airy branch December 29, 2016 22:57

jrevels added a commit that referenced this pull request Dec 30, 2016

fix airy function deprecations (follow-up to #18050)

c8c4c38

jrevels added a commit that referenced this pull request Dec 30, 2016

fix airy function deprecations (follow-up to #18050)

199da05

simonbyrne added a commit that referenced this pull request Dec 30, 2016

Fix deprecation error for 2 arg airy

b36e4d9

cf #18050

simonbyrne mentioned this pull request Dec 30, 2016

Fix deprecation error for 2 arg airy #19775

Merged

jrevels mentioned this pull request Dec 30, 2016

fix airy function deprecations (follow-up to #18050) #19776

Closed

simonbyrne added a commit that referenced this pull request Dec 30, 2016

Fix deprecation error for 2 arg airy

f9122ac

cf #18050

simonbyrne added a commit that referenced this pull request Dec 30, 2016

Fix deprecation error for 2 arg airy

0566973

cf #18050

tkelman pushed a commit that referenced this pull request Dec 30, 2016

Fix deprecation error for 2 arg airy (#19775)

4280d3c

cf #18050

giordano mentioned this pull request Dec 31, 2016

Document DomainError in airyaix and airyaiprimex #19795

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Airy function cleanup #18050

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giordano commented Dec 31, 2016

	"""
	airyai(x::Complex128)

	Airy function of the first kind ``\\operatorname{Ai}(x)``.

Airy function cleanup #18050

Airy function cleanup #18050

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