Remove some pirated methods for the symmetric eigenvalue problem.

They don't seem to be needed anymore and avoid an ambiguity introduced
by Julia 1.11. Also, sort the eigenvalues of the symmetric problem
when nothing is passed.

src/eigenSelfAdjoint.jl

@@ -216,7 +216,10 @@ function eigvalsPWK!(S::SymTridiagonal{T}; tol = eps(T), sortby::Union{Function,
             end
         end
     end
-    LinearAlgebra.sorteig!(d, sortby)
+
+    # LinearAlgebra.eigvals will pass sortby=nothing but LAPACK always sort the symmetric
+    # eigenvalue problem so we'll will do the same here
+    LinearAlgebra.sorteig!(d, sortby === nothing ? LinearAlgebra.eigsortby : sortby)
 end
 
 function eigQL!(
@@ -639,30 +642,30 @@ else
     LinearAlgebra.copy_oftype
 end
 
-function LinearAlgebra.eigvals(A::Hermitian{<:Real})
-    T = typeof(sqrt(zero(eltype(A))))
-    return eigvals!(_eigencopy_oftype(A, T))
-end
-function LinearAlgebra.eigvals(A::Hermitian{<:Complex})
-    T = typeof(sqrt(zero(eltype(A))))
-    return eigvals!(_eigencopy_oftype(A, T))
-end
-function LinearAlgebra.eigvals(A::Hermitian)
-    T = typeof(sqrt(zero(eltype(A))))
-    return eigvals!(_eigencopy_oftype(A, T))
-end
-function LinearAlgebra.eigen(A::Hermitian{<:Real})
-    T = typeof(sqrt(zero(eltype(A))))
-    return eigen!(_eigencopy_oftype(A, T))
-end
-function LinearAlgebra.eigen(A::Hermitian{<:Complex})
-    T = typeof(sqrt(zero(eltype(A))))
-    return eigen!(_eigencopy_oftype(A, T))
-end
-function LinearAlgebra.eigen(A::Hermitian)
-    T = typeof(sqrt(zero(eltype(A))))
-    return eigen!(_eigencopy_oftype(A, T))
-end
+# function LinearAlgebra.eigvals(A::Hermitian{<:Real})
+#     T = typeof(sqrt(zero(eltype(A))))
+#     return eigvals!(_eigencopy_oftype(A, T))
+# end
+# function LinearAlgebra.eigvals(A::Hermitian{<:Complex})
+#     T = typeof(sqrt(zero(eltype(A))))
+#     return eigvals!(_eigencopy_oftype(A, T))
+# end
+# function LinearAlgebra.eigvals(A::Hermitian)
+#     T = typeof(sqrt(zero(eltype(A))))
+#     return eigvals!(_eigencopy_oftype(A, T))
+# end
+# function LinearAlgebra.eigen(A::Hermitian{<:Real})
+#     T = typeof(sqrt(zero(eltype(A))))
+#     return eigen!(_eigencopy_oftype(A, T))
+# end
+# function LinearAlgebra.eigen(A::Hermitian{<:Complex})
+#     T = typeof(sqrt(zero(eltype(A))))
+#     return eigen!(_eigencopy_oftype(A, T))
+# end
+# function LinearAlgebra.eigen(A::Hermitian)
+#     T = typeof(sqrt(zero(eltype(A))))
+#     return eigen!(_eigencopy_oftype(A, T))
+# end
 
 # Aux (should go somewhere else at some point)
 function LinearAlgebra.givensAlgorithm(f::Real, g::Real)

test/eigenselfadjoint.jl

@@ -164,4 +164,11 @@ using Test, GenericLinearAlgebra, LinearAlgebra, Quaternions
             @test eigen(A).values == diag(A)
         end
     end
+
+    if VERSION >= v"1.11"
+        @testset "Method ambiguity in eigen with Julia 1.11 #141" begin
+            M = Hermitian(Tridiagonal(ones(ComplexF64, 2), ones(ComplexF64, 3), ones(ComplexF64, 2)))
+            @test eigen(M).values ≈ Float64.(eigen(big.(M)).values)
+        end
+    end
 end