Structured matrices don't extend missing dimensions correctly in broadcasting

[jishnub]

julia> D1 = Diagonal([1]); D2 = Diagonal([1,2]);

julia> D1 .+ D2
2×2 Diagonal{Int64, Vector{Int64}}:
 2  ⋅
 ⋅  3

julia> Matrix(D1) .+ D2
2×2 Matrix{Int64}:
 2  1
 1  3

Ideally, these should produce identical results.
In the structured case, the 1x1 matrix D1 isn't expanded to ones(size(D2)), but instead it's expanded to Diagonal(ones(Int, size(D2,1))). I'm unsure if there's a way to resolve this while preserving type-stability.

[mbauman]

Oh, yikes. The problem is in similar, but I'm not sure what to do about it:

julia/stdlib/LinearAlgebra/src/structuredbroadcast.jl

Lines 155 to 166 in e5821b3

	function Base.similar(bc::Broadcasted{StructuredMatrixStyle{T}}, ::Type{ElType}) where {T,ElType}
	inds = axes(bc)
	fzerobc = fzeropreserving(bc)
	if isstructurepreserving(bc) || (fzerobc && !(T <: Union{SymTridiagonal,UnitLowerTriangular,UnitUpperTriangular}))
	return structured_broadcast_alloc(bc, T, ElType, length(inds[1]))
	elseif fzerobc && T <: UnitLowerTriangular
	return similar(convert(Broadcasted{StructuredMatrixStyle{LowerTriangular}}, bc), ElType)
	elseif fzerobc && T <: UnitUpperTriangular
	return similar(convert(Broadcasted{StructuredMatrixStyle{UpperTriangular}}, bc), ElType)
	end
	return similar(convert(Broadcasted{DefaultArrayStyle{ndims(bc)}}, bc), ElType)
	end

julia> bc = Broadcast.instantiate(Broadcast.broadcasted(+, D1, D2))
Base.Broadcast.Broadcasted{LinearAlgebra.StructuredMatrixStyle{Diagonal}}(+, ([1;;], [1 0; 0 2]))

julia> similar(bc, Int)
2×2 Diagonal{Int64, Vector{Int64}}:
 4333067184           ⋅
          ⋅  4333069200

I think you're right that this will need to break type stability. It could alternatively be an error, but that also seems quite broken. This probably happens with all the structured matrices.