Revert "Materialize complex Symmetric matrices in eigen (#55348)"

This reverts commit c28dc85.

Author: KristofferC

stdlib/LinearAlgebra/src/bunchkaufman.jl

@@ -127,9 +127,6 @@ function bunchkaufman!(A::StridedMatrix{<:BlasFloat}, rook::Bool = false; check:
     end
 end
 
-bkcopy_oftype(A, S) = eigencopy_oftype(A, S)
-bkcopy_oftype(A::Symmetric{<:Complex}, S) = Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo(A.uplo))
-
 """
     bunchkaufman(A, rook::Bool=false; check = true) -> S::BunchKaufman
 
@@ -209,7 +206,7 @@ julia> S.L*S.D*S.L' - A[S.p, S.p]
 ```
 """
 bunchkaufman(A::AbstractMatrix{T}, rook::Bool=false; check::Bool = true) where {T} =
-    bunchkaufman!(bkcopy_oftype(A, typeof(sqrt(oneunit(T)))), rook; check = check)
+    bunchkaufman!(eigencopy_oftype(A, typeof(sqrt(oneunit(T)))), rook; check = check)
 
 BunchKaufman{T}(B::BunchKaufman) where {T} =
     BunchKaufman(convert(Matrix{T}, B.LD), B.ipiv, B.uplo, B.symmetric, B.rook, B.info)
@@ -1532,7 +1529,7 @@ function bunchkaufman(A::AbstractMatrix{TS},
     rook::Bool = false;
     check::Bool = true
     ) where TS <: ClosedScalar{TR} where TR <: ClosedReal
-    return bunchkaufman!(bkcopy_oftype(A, TS), rook; check)
+    return bunchkaufman!(eigencopy_oftype(A, TS), rook; check)
 end
 
 function bunchkaufman(A::AbstractMatrix{TS},
@@ -1554,15 +1551,15 @@ function bunchkaufman(A::AbstractMatrix{TS},
     # We promote input to BigInt to avoid overflow problems
     if TA == Nothing
         if TS <: Integer
-            M = Rational{BigInt}.(bkcopy_oftype(A, TS))
+            M = Rational{BigInt}.(eigencopy_oftype(A, TS))
         else
-            M = Complex{Rational{BigInt}}.(bkcopy_oftype(A, TS))
+            M = Complex{Rational{BigInt}}.(eigencopy_oftype(A, TS))
         end
     else
         if TS <: Integer
-            M = TA(Rational{BigInt}.(bkcopy_oftype(A, TS)), Symbol(A.uplo))
+            M = TA(Rational{BigInt}.(eigencopy_oftype(A, TS)), Symbol(A.uplo))
         else
-            M = TA(Complex{Rational{BigInt}}.(bkcopy_oftype(A, TS)),
+            M = TA(Complex{Rational{BigInt}}.(eigencopy_oftype(A, TS)),
                 Symbol(A.uplo))
         end
     end

stdlib/LinearAlgebra/src/symmetriceigen.jl

@@ -3,7 +3,6 @@
 # preserve HermOrSym wrapper
 eigencopy_oftype(A::Hermitian, S) = Hermitian(copy_similar(A, S), sym_uplo(A.uplo))
 eigencopy_oftype(A::Symmetric, S) = Symmetric(copy_similar(A, S), sym_uplo(A.uplo))
-eigencopy_oftype(A::Symmetric{<:Complex}, S) = copyto!(similar(parent(A), S), A)
 
 # Eigensolvers for symmetric and Hermitian matrices
 eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}; sortby::Union{Function,Nothing}=nothing) =

stdlib/LinearAlgebra/test/hessenberg.jl

@@ -250,11 +250,4 @@ end
     @test axes(S) === (r,r)
 end
 
-@testset "complex Symmetric" begin
-    D = diagm(0=>ComplexF64[1,2])
-    S = Symmetric(D)
-    H = hessenberg(S)
-    @test H.H == D
-end
-
 end # module TestHessenberg

stdlib/LinearAlgebra/test/symmetriceigen.jl

@@ -151,10 +151,4 @@ end
     @test HT * V ≈ V * Diagonal(λ)
 end
 
-@testset "complex Symmetric" begin
-    S = Symmetric(rand(ComplexF64,2,2))
-    λ, v = eigen(S)
-    @test S * v ≈ v * Diagonal(λ)
-end
-
 end # module TestSymmetricEigen