Define promote_rule for Diagonal matrices

[jishnub]

This PR adds a promote_rule definition for Diagonal matrices using the promotion rule for the parent diagonal vectors. I've also added a method Diagonal{T, V}(::Diagonal) to carry out necessary conversions. This differs from the constructor Diagonal{T,V}(::AbstractVector), and I hope that the usage is clear from the context. Currently the conversion throws an error, so this is not a breaking change.

This has two positives:

bugfix

Master

julia> D = Diagonal(1:3)
3×3 Diagonal{Int64, UnitRange{Int64}}:
 1  ⋅  ⋅
 ⋅  2  ⋅
 ⋅  ⋅  3

julia> D^0
ERROR: MethodError: no method matching Vector{Int64}(::Diagonal{Int64, UnitRange{Int64}})
Closest candidates are:
  Array{T, N}(::AbstractArray{S, N}) where {T, N, S} at array.jl:540
  Vector{T}() where T at boot.jl:467
  Array{T, N}(::StaticArrays.SizedArray{S, T, N, M, TData} where {M, TData<:AbstractArray{T, M}}) where {T, S, N} at /home/jb6888/.julia/packages/StaticArrays/vxjOO/src/SizedArray.jl:98
  ...
Stacktrace:
 [1] convert(#unused#::Type{Vector{Int64}}, a::Diagonal{Int64, UnitRange{Int64}})
   @ Base ./array.jl:532
 [2] Diagonal{Int64, Vector{Int64}}(diag::Diagonal{Int64, UnitRange{Int64}})
   @ LinearAlgebra /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/diagonal.jl:10
 [3] convert(T::Type{Diagonal{Int64, Vector{Int64}}}, m::Diagonal{Int64, UnitRange{Int64}})
   @ LinearAlgebra /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/special.jl:53
 [4] to_power_type(x::Diagonal{Int64, UnitRange{Int64}})
   @ Base ./intfuncs.jl:241
 [5] power_by_squaring(x_::Diagonal{Int64, UnitRange{Int64}}, p::Int64)
   @ Base ./intfuncs.jl:256
 [6] ^(A::Diagonal{Int64, UnitRange{Int64}}, p::Int64)
   @ LinearAlgebra /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/dense.jl:447
 [7] macro expansion
   @ ./none:0 [inlined]
 [8] literal_pow(f::typeof(^), x::Diagonal{Int64, UnitRange{Int64}}, #unused#::Val{0})
   @ Base ./none:0
 [9] top-level scope
   @ REPL[298]:1

This PR

julia> D^0
3×3 Diagonal{Int64, Vector{Int64}}:
 1  ⋅  ⋅
 ⋅  1  ⋅
 ⋅  ⋅  1

type-stability

Currently on master

julia> [Diagonal([1]), Diagonal([1.0])]
2-element Vector{Diagonal}:
 [1;;]
 [1.0;;]

julia> [Diagonal([ones(Int,1,1)]), Diagonal([ones(1,1)])]
2-element Vector{Diagonal}:
 [[1;;];;]
 [[1.0;;];;]

The element types are not concrete, as promotion falls back to typejoin here.

After this PR

ulia> [Diagonal([1]), Diagonal([1.0])]
2-element Vector{Diagonal{Float64, Vector{Float64}}}:
 [1.0;;]
 [1.0;;]

julia> [Diagonal([ones(Int,1,1)]), Diagonal([ones(1,1)])]
2-element Vector{Diagonal{Matrix{Float64}, Vector{Matrix{Float64}}}}:
 [[1.0;;];;]
 [[1.0;;];;]

[jishnub]

@dkarrasch would like your opinion on this

[dkarrasch]

@timholy Would you be able to take another quick look? @jishnub I haven't touched the tests, so this should still do what you wanted it to do?