From ed3fd1eeaa7d7db5ca6a0eac037c994cd79712a3 Mon Sep 17 00:00:00 2001
From: Aravindh Krishnamoorthy <aravindh.krishnamoorthy@fau.de>
Date: Tue, 5 Dec 2023 20:21:08 +0100
Subject: [PATCH] Update the bunchkaufman.jl/getproperties! function to align
 to the anti-aliasing implementation in #51763 + include comments in
 symmetriceigen.jl

---
 stdlib/LinearAlgebra/src/bunchkaufman.jl   | 6 +++---
 stdlib/LinearAlgebra/src/symmetriceigen.jl | 3 +++
 2 files changed, 6 insertions(+), 3 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/bunchkaufman.jl b/stdlib/LinearAlgebra/src/bunchkaufman.jl
index fa464815ac5c4..f995b3b8444c4 100644
--- a/stdlib/LinearAlgebra/src/bunchkaufman.jl
+++ b/stdlib/LinearAlgebra/src/bunchkaufman.jl
@@ -279,7 +279,7 @@ Base.propertynames(B::BunchKaufman, private::Bool=false) =
     (:p, :P, :L, :U, :D, (private ? fieldnames(typeof(B)) : ())...)
 
 function getproperties!(B::BunchKaufman{T,<:StridedMatrix}) where {T<:BlasFloat}
-    # NOTE: Copy of BunchKaufman's getproperty(B, :D) and getproperty(B, :L/U) since 'getproperty' is not in place.
+    # NOTE: Unlike in the 'getproperty' function, in this function L/U and D are computed in place.
     if B.rook
         LUD, od = LAPACK.syconvf_rook!(B.uplo, 'C', B.LD, B.ipiv)
     else
@@ -289,12 +289,12 @@ function getproperties!(B::BunchKaufman{T,<:StridedMatrix}) where {T<:BlasFloat}
         M = UnitUpperTriangular(LUD)
         du = od[2:end]
         # Avoid aliasing dl and du.
-        dl = B.symmetric ? copy(du) : conj.(du)
+        dl = B.symmetric ? du : conj.(du)
     else
         M = UnitLowerTriangular(LUD)
         dl = od[1:end-1]
         # Avoid aliasing dl and du.
-        du = B.symmetric ? copy(dl) : conj.(dl)
+        du = B.symmetric ? dl : conj.(dl)
     end
     return (M, Tridiagonal(dl, diag(LUD), du), B.p)
 end
diff --git a/stdlib/LinearAlgebra/src/symmetriceigen.jl b/stdlib/LinearAlgebra/src/symmetriceigen.jl
index f78092a2780ad..4e35616f62181 100644
--- a/stdlib/LinearAlgebra/src/symmetriceigen.jl
+++ b/stdlib/LinearAlgebra/src/symmetriceigen.jl
@@ -286,6 +286,9 @@ end
 function eigvals!(A::StridedMatrix{T}, F::LU{T,<:StridedMatrix}; sortby::Union{Function,Nothing}=nothing) where {T}
     L = UnitLowerTriangular(F.L)
     U = UpperTriangular(F.U)
+    # Compute generalized eigenvalues of equivalent matrix:
+    #    A' = inv(L)*(P*A)*inv(U)
+    # See: https://github.com/JuliaLang/julia/pull/50471#issuecomment-1627836781
     permuterows!(A, F.p)
     ldiv!(L, A)
     rdiv!(A, U)