Resolve all method ambiguities in LinearAlgebra

[tkf]

This PR has three commits to:

1. Add a test using detect_ambiguities to avoid further introduction of method ambiguities within LinearAlgebra. I'm suggesting a similar test across all standard libraries in Check ambiguous methods in stdlib #28665. But I think in general it's nice to have it per-package basis especially if it were to split into a separate repository at some point.

2. Simply apply @andreasnoack's suggestion Resolve mul!(::Matrix, ::Diagonal, ::Adjoint) ambiguity #27405 (comment) and define mul!(::AbstractMatrix, ::Diagonal, ::StridedMatrix) instead of mul!(::AbstractMatrix, ::Diagonal, ::AbstractMatrix). Similar change for Adjoint{<:Any,<:Diagonal} and Transpose{<:Any,<:Diagonal} too.

3. Tweak promote_leaf_eltypes signature to make the test suite happy. I don't think it will introduce any change for working code. I'll inline-comment on this.

[tkf]

[Copied from my commit message] This change is only for supressing Test.detect_ambiguities and shouldn't introduce any change in working code (unless it depends on MethodError).

Before this change, we have:

julia> LinearAlgebra.promote_leaf_eltypes(())
ERROR: MethodError: LinearAlgebra.promote_leaf_eltypes(::Tuple{}) is ambiguous. Candidates:
...

With this change, we have:

julia> LinearAlgebra.promote_leaf_eltypes(())
Bool

[tkf]

Actually, considering that we have mapreduce(promote_leaf_eltypes, promote_type, x; init=Bool) below, I suppose it was intended to return Bool?

[StefanKarpinski]

Nice! That is a surprisingly and happily small number of tweaks required.

[Sacha0]

Thanks @tkf! :)

[tkf]

@Sacha0 Don't you think it's a good timing to merge #28665? 😉

[tkf]

Oh no. I think the test I added broke the CI.

Some tests did not pass: 597 passed, 1 failed, 0 errored, 0 broken.LinearAlgebra/matmul: Test Failed at /tmp/julia/share/julia/stdlib/v1.1/LinearAlgebra/test/matmul.jl:449
  Expression: detect_ambiguities(LinearAlgebra, Base; imported=true, recursive=true) == []
   Evaluated: Tuple{Method,Method}[(isequal(x, ::Main.Test80Main_arrayops.totally_not_five26034) in Main.Test80Main_arrayops at /tmp/julia/share/julia/test/arrayops.jl:2459, isequal(::Missing, ::Any) in Base at missing.jl:60), (==(x, ::Main.Test80Main_arrayops.totally_not_five26034) in Main.Test80Main_arrayops at /tmp/julia/share/julia/test/arrayops.jl:2464, ==(w::WeakRef, v) in Base at gcutils.jl:4), (==(::Main.Test80Main_arrayops.totally_not_five26034, x) in Main.Test80Main_arrayops at /tmp/julia/share/julia/test/arrayops.jl:2463, ==(::Any, ::Missing) in Base at missing.jl:55), (==(x, ::Main.Test80Main_arrayops.totally_not_five26034) in Main.Test80Main_arrayops at /tmp/julia/share/julia/test/arrayops.jl:2464, ==(::Missing, ::Any) in Base at missing.jl:54), (==(::Main.Test80Main_arrayops.totally_not_five26034, x) in Main.Test80Main_arrayops at /tmp/julia/share/julia/test/arrayops.jl:2463, ==(w, v::WeakRef) in Base at gcutils.jl:5), (isequal(::Main.Test80Main_arrayops.totally_not_five26034, x) in Main.Test80Main_arrayops at /tmp/julia/share/julia/test/arrayops.jl:2458, isequal(::Any, ::Missing) in Base at missing.jl:61)] == Any[]

--- https://travis-ci.org/JuliaLang/julia/jobs/418693949#L2141-L2142

Does recursive=true mean to check Main as well?

[tkf]

I noticed that the issue was already filed #28804