inv of Symmetric and Hermitian matrices, with more eltypes than BlasF…

…loats (JuliaLang#22882)

base/linalg/symmetric.jl

@@ -364,8 +364,8 @@ function _inv(A::HermOrSym)
  end
  B
 end
-inv(A::Hermitian{T,S}) where {T<:BlasFloat,S<:StridedMatrix} = Hermitian{T,S}(_inv(A), A.uplo)
-inv(A::Symmetric{T,S}) where {T<:BlasFloat,S<:StridedMatrix} = Symmetric{T,S}(_inv(A), A.uplo)
+inv(A::Hermitian{<:Any,<:StridedMatrix}) = Hermitian(_inv(A), Symbol(A.uplo))
+inv(A::Symmetric{<:Any,<:StridedMatrix}) = Symmetric(_inv(A), Symbol(A.uplo))
 
 eigfact!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}) = Eigen(LAPACK.syevr!('V', 'A', A.uplo, A.data, 0.0, 0.0, 0, 0, -1.0)...)
 

test/linalg/symmetric.jl

@@ -176,6 +176,17 @@ end
  end
  end
 
+ @testset "inversion" begin
+ for uplo in (:U, :L)
+ @test inv(Symmetric(asym, uplo))::Symmetric ≈ inv(asym)
+ @test inv(Hermitian(aherm, uplo))::Hermitian ≈ inv(aherm)
+ @test inv(Symmetric(a, uplo))::Symmetric ≈ inv(Matrix(Symmetric(a, uplo)))
+ if eltya <: Real
+ @test inv(Hermitian(a, uplo))::Hermitian ≈ inv(Matrix(Hermitian(a, uplo)))
+ end
+ end
+ end
+
  # Revisit when implemented in julia
  if eltya != BigFloat
  @testset "cond" begin
@@ -185,19 +196,6 @@ end
  @test cond(Hermitian(aherm)) ≈ cond(aherm)
  end
 
- @testset "inversion" begin
- @test inv(Symmetric(asym)) ≈ inv(asym)
- @test inv(Hermitian(aherm)) ≈ inv(aherm)
- for uplo in (:U, :L)
- @test inv(Symmetric(asym, uplo)) ≈ inv(full(Symmetric(asym, uplo)))
- @test inv(Hermitian(aherm, uplo)) ≈ inv(full(Hermitian(aherm, uplo)))
- @test inv(Symmetric(a, uplo)) ≈ inv(full(Symmetric(a, uplo)))
- if eltya <: Real
- @test inv(Hermitian(a, uplo)) ≈ inv(full(Hermitian(a, uplo)))
- end
- end
- end
-
  @testset "symmetric eigendecomposition" begin
  if eltya <: Real # the eigenvalues are only real and ordered for Hermitian matrices
  d, v = eig(asym)