lu(Symmetric(Diagonal(...))) fails

[tpapp]

julia> VERSION
v"1.8.0-beta3"

julia> using LinearAlgebra

julia> M = Symmetric(Diagonal(ones(3)))
3×3 Symmetric{Float64, Diagonal{Float64, Vector{Float64}}}:
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> lu(M)
ERROR: MethodError: no method matching lu!(::Diagonal{Float64, Vector{Float64}}, ::RowMaximum; check=true)

[tpapp]

Suggestion:

Symmetric(D::Diagonal, uplo=:U) = D

and the same for Hermitian. Possibly checking uplo.

The downside is violating T(...) isa T.

[dkarrasch]

One would need to respect the array of arrays case:

Symmetric(D::Diagonal, uplo=:U) = Diagonal(symmetric.(D.diag), uplo)

Or pick up some of #41288.

[tpapp]

I don't understand why #41288 was closed in the first place.

The issue is not explicitly why LU is useful for Diagonal in the first place (it isn't), or why Symmetric(Diagonal(...)) makes sense (it doesn't, really). But code that wants to handle a generic AbstractMatrix can end up with constructs like this so there should be code path that just works.

@andreasnoack, I would appreciate your thoughts on this.

[dkarrasch]

This has been fixed, perhaps in #47107. The question is whether the resulting LU object is useful. Getting properties à la F.L creates dense factors, while F.factors is a memory-efficient Diagonal. Some further optimizations are proposed in #48189.