Inconsistency in copyto! for structured matrices

[jishnub]

MWE

julia> D1 = Diagonal(ones(4))
4×4 Diagonal{Float64, Vector{Float64}}:
 1.0   ⋅    ⋅    ⋅ 
  ⋅   1.0   ⋅    ⋅ 
  ⋅    ⋅   1.0   ⋅ 
  ⋅    ⋅    ⋅   1.0

julia> D2 = Diagonal(2ones(3))
3×3 Diagonal{Float64, Vector{Float64}}:
 2.0   ⋅    ⋅ 
  ⋅   2.0   ⋅ 
  ⋅    ⋅   2.0

julia> copyto!(Matrix(D1), Matrix(D2))
4×4 Matrix{Float64}:
 2.0  2.0  2.0  0.0
 0.0  0.0  0.0  0.0
 0.0  0.0  1.0  0.0
 0.0  0.0  0.0  1.0

julia> copyto!(D1, D2)
4×4 Diagonal{Float64, Vector{Float64}}:
 2.0   ⋅    ⋅    ⋅ 
  ⋅   2.0   ⋅    ⋅ 
  ⋅    ⋅   2.0   ⋅ 
  ⋅    ⋅    ⋅   1.0

The docstring of copyto! states

  copyto!(dest::AbstractArray, src) -> dest

  Copy all elements from collection src to array dest, whose length must be greater than or equal to the length n of src. The first n elements of dest are overwritten, the other
  elements are left untouched.

This linear copying doesn't seem to be followed by structured matrices.

Version info:

julia> versioninfo()
Julia Version 1.7.3
Commit 742b9abb4d (2022-05-06 12:58 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: 11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-12.0.1 (ORCJIT, tigerlake)
Environment:
  JULIA_EDITOR = vim

but the same behavior is there on

Julia Version 1.9.0-DEV.888
Commit eb72c2aaf2 (2022-07-05 12:07 UTC)

[N5N3]

It seems that we should perform an axes check before trying the structural copyto!

List to be fixed:

copyto!(A::T, B::T) where T<:Union{UnitUpperTriangular, UpperTriangular}  # miss unaliasing
copyto!(A::T, B::T) where T<:Union{LowerTriangular, UnitLowerTriangular}  # miss unaliasing
copyto!(D1::Diagonal, D2::Diagonal)
copyto!(dest::Tridiagonal, src::Tridiagonal)
copyto!(dest::SymTridiagonal, src::SymTridiagonal)
copyto!(dest::Symmetric, src::Symmetric)   # miss unaliasing in `transpose!` branch
copyto!(dest::Hermitian, src::Hermitian)   # miss unaliasing in `adjoint!` branch