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Add issymmetrictype and ishermitiantype #1436

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6051a03
Add `issymmetrictype` and `ishermitiantype`
jishnub Sep 6, 2025
f9417e0
Fix leftover `_issymmetric` usage
jishnub Sep 7, 2025
efc43b4
Remove explicit test for helper function
jishnub Sep 8, 2025
a5975d8
Grammar
jishnub Sep 10, 2025
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31 changes: 28 additions & 3 deletions src/symmetric.jl
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Expand Up @@ -461,9 +461,34 @@ issymmetric(A::Hermitian{<:Real}) = true
issymmetric(A::Hermitian{<:Complex}) = isreal(A)
issymmetric(A::Symmetric) = true

# check if the symmetry is known from the type
_issymmetric(::Union{SymSymTri, Hermitian{<:Real}}) = true
_issymmetric(::Any) = false
"""
issymmetrictype(T::Type)

Return whether every instance `x` of the type `T` satisfies `issymmetric(x) == tue`,
that is, the fact that the instance is symmetric is known from its type.

!!! note
An instance `x::T` may still be symmetric when `issymmetrictype(T)` returns `false`.
"""
issymmetrictype(::Type) = false
issymmetrictype(::Type{<:Union{Symmetric,Hermitian{<:Real}}}) = true
issymmetrictype(::Type{<:Real}) = true
issymmetrictype(::Type{<:AbstractFloat}) = false
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Shouldn't it be

issymmetrictype(::Type{<:Number}) = true

?

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@jishnub jishnub Sep 10, 2025 •
edited
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The exception is NaN, which isn't equal to itself. I didn't want to make this more generic in case the number types contain NaN as a field.

issymmetrictype(::Type{Complex{T}}) where {T} = issymmetrictype(T)

"""
ishermitiantype(T::Type)

Return whether every instance `x` of the type `T` satisfies `ishermitian(x) == tue`,
that is, the fact that the instance is hermitian is known from its type.

!!! note
An instance `x::T` may still be hermitian when `ishermitiantype(T)` returns `false`.
"""
ishermitiantype(::Type) = false
ishermitiantype(::Type{<:Union{Symmetric{<:Real},Hermitian}}) = true
ishermitiantype(::Type{<:Real}) = true
ishermitiantype(::Type{<:AbstractFloat}) = false
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I don't understand this AbstractFloat rule?

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This is to stay consistent with the current behavior

julia> issymmetric(NaN)
false

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@stevengj stevengj Sep 11, 2025 •
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That seems highly questionable to me, as opposed to issymmetric(::Number) = true and ishermitian(x::Number) = isreal(x).

e.g. we have have a type-based issymmetric test for floating-point Symmetric matrices, even though they can also have NaN values.

julia> A = Symmetric(fill(NaN, 3,3))
3×3 Symmetric{Float64, Matrix{Float64}}:
 NaN  NaN  NaN
 NaN  NaN  NaN
 NaN  NaN  NaN

julia> A == A'
false

julia> issymmetric(A)
true


adjoint(A::Hermitian) = A
transpose(A::Symmetric) = A
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4 changes: 2 additions & 2 deletions src/tridiag.jl
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Expand Up @@ -111,14 +111,14 @@ function (::Type{SymTri})(A::AbstractMatrix) where {SymTri <: SymTridiagonal}
checksquare(A)
du = diag(A, 1)
d = diag(A)
if !(_issymmetric(A) || _checksymmetric(d, du, diag(A, -1)))
if !(issymmetrictype(typeof(A)) || _checksymmetric(d, du, diag(A, -1)))
throw(ArgumentError("matrix is not symmetric; cannot convert to SymTridiagonal"))
end
return SymTri(d, du)
end

_checksymmetric(d, du, dl) = all(((x, y),) -> x == transpose(y), zip(du, dl)) && all(issymmetric, d)
_checksymmetric(A::AbstractMatrix) = _issymmetric(A) || _checksymmetric(diagview(A), diagview(A, 1), diagview(A, -1))
_checksymmetric(A::AbstractMatrix) = issymmetrictype(typeof(A)) || _checksymmetric(diagview(A), diagview(A, 1), diagview(A, -1))

SymTridiagonal{T,V}(S::SymTridiagonal{T,V}) where {T,V<:AbstractVector{T}} = S
SymTridiagonal{T,V}(S::SymTridiagonal) where {T,V<:AbstractVector{T}} =
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22 changes: 22 additions & 0 deletions test/symmetric.jl
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Expand Up @@ -1343,4 +1343,26 @@ end
@test_throws msg LinearAlgebra.fillband!(Symmetric(A), 2, 0, 1)
end

@testset "issymmetrictype/ishermitiantype" begin
fsym(x) = Val(LinearAlgebra.issymmetrictype(typeof(x)))
@test @inferred(fsym(Symmetric(ones(2,2)))) == Val(true)
@test @inferred(fsym(Symmetric(ones(ComplexF64,2,2)))) == Val(true)
@test @inferred(fsym(Hermitian(ones(2,2)))) == Val(true)
@test @inferred(fsym(Hermitian(ones(ComplexF64,2,2)))) == Val(false)
@test @inferred(fsym(1)) == Val(true)
@test @inferred(fsym(1.0)) == Val(false)
@test @inferred(fsym(complex(1))) == Val(true)
@test @inferred(fsym(complex(1.0))) == Val(false)

fherm(x) = Val(LinearAlgebra.ishermitiantype(typeof(x)))
@test @inferred(fherm(Symmetric(ones(2,2)))) == Val(true)
@test @inferred(fherm(Symmetric(ones(ComplexF64,2,2)))) == Val(false)
@test @inferred(fherm(Hermitian(ones(2,2)))) == Val(true)
@test @inferred(fherm(Hermitian(ones(ComplexF64,2,2)))) == Val(true)
@test @inferred(fherm(1)) == Val(true)
@test @inferred(fherm(1.0)) == Val(false)
@test @inferred(fherm(complex(1))) == Val(false)
@test @inferred(fherm(complex(1.0))) == Val(false)
end

end # module TestSymmetric
4 changes: 0 additions & 4 deletions test/tridiag.jl
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Expand Up @@ -1155,10 +1155,6 @@ end

@testset "SymTridiagonal from Symmetric" begin
S = Symmetric(reshape(1:9, 3, 3))
@testset "helper functions" begin
@test LinearAlgebra._issymmetric(S)
@test !LinearAlgebra._issymmetric(Array(S))
end
ST = SymTridiagonal(S)
@test ST == SymTridiagonal(diag(S), diag(S,1))
S = Symmetric(Tridiagonal(1:3, 1:4, 1:3))
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