Cholesky fails for Hermitian{.., Diagonal}

[baggepinnen]

There appears to be some missing method that handles Hermitian/Symmetric wrappers around special matrices.

julia> cholesky((1.0I(3)))
Cholesky{Float64, Diagonal{Float64, Vector{Float64}}}
U factor:
3×3 Diagonal{Float64, Vector{Float64}}:
 1.0   ⋅    ⋅ 
  ⋅   1.0   ⋅ 
  ⋅    ⋅   1.0

julia> cholesky(Hermitian(1.0I(3)))
ERROR: MethodError: no method matching cholesky(::Hermitian{Float64, Diagonal{Float64, Vector{Float64}}})

julia> cholesky(Symmetric(1.0I(3)))
ERROR: MethodError: no method matching cholesky(::Symmetric{Float64, Diagonal{Float64, Vector{Float64}}})

I assume the pattern cholesky(Hermitian(Σ)), i.e., automatically wrapping symmetric matrices in a Hermitian wrapper is quite common, so it would be great if it worked for all AbstractMatrix.

Tested on Julia v1.7.1

[dkarrasch]

The simplest solution is perhaps to remove the restriction to StridedMatrixs in out-of-place cholesky methods that form a cholcopy anyway, and make that cholcopy form a mutable copy via 3-arg similar, and specialize some structured matrix types to improve memory consumption.