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Ensure inverse of Symmetric{<:,Diagonal} returns same type #1439

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Ensure inverse of Symmetric{<:,Diagonal} returns same type #1439

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7300e8a
ensure inverse of Symmetric{<:,Diagonal} returns same type
vandenman Sep 10, 2025
af1fe00
remove hermitianpart(a::Number)
vandenman Sep 12, 2025
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4 changes: 4 additions & 0 deletions src/diagonal.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -970,6 +970,10 @@ function inv(D::Diagonal{T}) where T
Diagonal(Di)
end

# Ensure doubly wrapped matrices use efficient diagonal methods and return a Symmetric/Hermitian type
inv(A::Symmetric{<:Number,<:Diagonal}) = Symmetric(inv(A.data), sym_uplo(A.uplo))
inv(A::Hermitian{<:Number,<:Diagonal}) = Hermitian(inv(real(A.data)), sym_uplo(A.uplo))
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To avoid the issue of returning a real-eltype matrix for a complex-eltype argument, this should perhaps be

Suggested change
inv(A::Hermitian{<:Number,<:Diagonal}) = Hermitian(inv(real(A.data)), sym_uplo(A.uplo))
inv(A::Hermitian{T,S}) where {T<:Number, S<:Diagonal} = Hermitian{T,S}(inv(real(A.data)), A.uplo)

?

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I suppose that's possible, but a Hermitian Diagonal matrix is actually always a real Diagonal matrix, so we can deduce from the type alone that the inverse is always a real diagonal matrix. This also holds for quaternion and octonion valued matrices. If there is a number type where becomes a problem, then using real might also be a problem.


function pinv(D::Diagonal{T}) where T
Di = similar(D.diag, typeof(inv(oneunit(T))))
for i = 1:length(D.diag)
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15 changes: 15 additions & 0 deletions test/symmetric.jl
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Expand Up @@ -874,6 +874,21 @@ end
@test det(Hermitian(A))::Float64 == det(A) == 0.0
end

@testset "issue #1437: inverse of Symmetric|Hermitian{<:Any,<:Diagonal} returns of Symmetric|Hermitian{<:Any,<:Diagonal}" begin
Dreal = Diagonal(randn(3))
Dcomplex = Diagonal(randn(ComplexF64, 3))
# without wrapper
invDreal = inv(Dreal)
invDcomplex = inv(real(Dcomplex)) # because Hermitian implies a real diagonal
# with wrapper
SDreal = Symmetric(Dreal)
HDcomplex = Hermitian(Dcomplex)
@test inv(SDreal)::Symmetric{Float64,typeof(Dreal)} ≈ invDreal
@test inv(HDcomplex)::Hermitian{Float64,typeof(Dreal)} ≈ invDcomplex
Dcomplex[2,2] = 0
@test_throws SingularException inv(HDcomplex)
end

@testset "symmetric()/hermitian() for Numbers" begin
@test LinearAlgebra.symmetric(1) == LinearAlgebra.symmetric(1, :U) == 1
@test LinearAlgebra.symmetric_type(Int) == Int
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