Symmetric(::Symmetric) and Hermitian(::Hermitian) with bug

[KlausC]

I think it is common understanding, that for X::AbstractMatrix.

1. Symmetric(X, uplo) == Symmetric(Matrix(X), uplo)
2. Symmetric(X) == Symmetric(X, :U)

Actually we observe

julia> VERSION
v"1.2.0-DEV.212"

julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
 1  2
 3  4
julia> X = Symmetric(A, :L)
2×2 Symmetric{Int64,Array{Int64,2}}:
 1  3
 3  4
julia> Symmetric(X) == Symmetric(X, :U) # result contradicts 2.
ERROR: ArgumentError: Cannot construct Symmetric; uplo doesn't match
Stacktrace:
 [1] Symmetric(::Symmetric{Int64,Array{Int64,2}}, ::Symbol) at
      /home/julia/julia/usr/share/julia/stdlib/v1.2/LinearAlgebra/src/symmetric.jl:162
 [2] top-level scope at REPL[87]:1

julia> Symmetric(X) == Symmetric(Matrix(X))
true
julia> Symmetric(Matrix(X), :U) # result contradicts 1.
2×2 Symmetric{Int64,Array{Int64,2}}:
 1  3
 3  4
julia> Symmetric(Matrix(X), :L)
2×2 Symmetric{Int64,Array{Int64,2}}:
 1  3
 3  4

I think, we should have
Symmetric(X::Symmetric, uplo::Symbol=:U) = X
independent of uplo and X.uplo.

The same is true for Hermitian

[andreasnoack]

Would you just ignore the uplo argument?

[fredrikekre]

Ref #423, JuliaLang/julia#21622 and JuliaLang/julia#22264

[KlausC]

Yes, I would ignore the uplo argument.

The argument of "correct aliasing" given in #423 (comment) is just another word for sticking to the uplo value of the outer constructor.
IMHO that is a much less valuable property than the given rules 1. and 2.

Rule 1 is well-definedness of the functions Symmetrix(., uplo) (if x == y => f(x) == f(y))
Rule 2 is the meaning of the default value

[KlausC]

@fredrikekre I read Ref #423 (comment) carefully, but I still don't understand, why
Symmetric(A, :U).uplo == 'U'
is more important than
Symmetric(A) == Symmetric(Matrix(A))
for all abstract matrices A. The second one is a general principle, while the first one looks more like a random technical restriction.

Look also at this text, which tries to present a fresh view to the meaning of wrappers: universal matrix wrappers.