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add methods for symmetric real eigen #145

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Jan 15, 2025
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add methods for symmetric real eigen #145

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0bc96bc
add methods for symmetric real eigen
araujoms Jan 15, 2025
1927f88
remove superfluous real (and type parametrization)
araujoms Jan 15, 2025
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13 changes: 11 additions & 2 deletions src/eigenSelfAdjoint.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -448,8 +448,7 @@ function singleShiftQR!(
end

symtri!(A::Hermitian) = A.uplo == 'L' ? symtriLower!(A.data) : symtriUpper!(A.data)
symtri!(A::Symmetric{T}) where {T<:Real} =
A.uplo == 'L' ? symtriLower!(A.data) : symtriUpper!(A.data)
symtri!(A::Symmetric{<:Real}) = A.uplo == 'L' ? symtriLower!(A.data) : symtriUpper!(A.data)

# Assume that lower triangle stores the relevant part
function symtriLower!(
Expand Down Expand Up @@ -580,6 +579,7 @@ _eigvals!(A::SymTridiagonal; tol = eps(real(eltype(A))), sortby::Union{Function,

_eigvals!(A::Hermitian; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = eigvals!(symtri!(A); tol, sortby)

_eigvals!(A::Symmetric{<:Real}; tol = eps(eltype(A)), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = eigvals!(symtri!(A); tol, sortby)

LinearAlgebra.eigvals!(A::SymmetricTridiagonalFactorization; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) =
_eigvals!(A; tol, sortby)
Expand All @@ -589,6 +589,7 @@ LinearAlgebra.eigvals!(A::SymTridiagonal; tol = eps(real(eltype(A))), sortby::Un

LinearAlgebra.eigvals!(A::Hermitian; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = _eigvals!(A; tol, sortby)

LinearAlgebra.eigvals!(A::Symmetric{<:Real}; tol = eps(eltype(A)), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = _eigvals!(A; tol, sortby)

_eigen!(A::SymmetricTridiagonalFactorization; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) =
LinearAlgebra.Eigen(LinearAlgebra.sorteig!(eigQL!(A.diagonals, vectors = Array(A.Q), tol = tol)..., sortby)...)
Expand All @@ -599,6 +600,7 @@ _eigen!(A::SymTridiagonal; tol = eps(real(eltype(A))), sortby::Union{Function,No

_eigen!(A::Hermitian; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = _eigen!(symtri!(A), tol = tol)

_eigen!(A::Symmetric{<:Real}; tol = eps(eltype(A)), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = _eigen!(symtri!(A), tol = tol)

LinearAlgebra.eigen!(A::SymmetricTridiagonalFactorization; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) =
_eigen!(A; tol, sortby)
Expand All @@ -607,6 +609,8 @@ LinearAlgebra.eigen!(A::SymTridiagonal; tol = eps(real(eltype(A))), sortby::Unio

LinearAlgebra.eigen!(A::Hermitian; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = _eigen!(A; tol, sortby)

LinearAlgebra.eigen!(A::Symmetric{<:Real}; tol = eps(eltype(A)), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = _eigen!(A; tol, sortby)


function eigen2!(
A::SymmetricTridiagonalFactorization;
Expand All @@ -628,12 +632,17 @@ end
eigen2!(A::Hermitian; tol = eps(float(real(one(eltype(A)))))) =
eigen2!(symtri!(A), tol = tol)

eigen2!(A::Symmetric{<:Real}; tol = eps(float(one(eltype(A))))) =
eigen2!(symtri!(A), tol = tol)


eigen2(A::SymTridiagonal; tol = eps(float(real(one(eltype(A)))))) =
eigen2!(copy(A), tol = tol)

eigen2(A::Hermitian, tol = eps(float(real(one(eltype(A)))))) = eigen2!(copy(A), tol = tol)

eigen2(A::Symmetric{<:Real}, tol = eps(float(one(eltype(A))))) = eigen2!(copy(A), tol = tol)

# First method of each type here is identical to the method defined in
# LinearAlgebra but is needed for disambiguation
const _eigencopy_oftype = if VERSION >= v"1.9"
Expand Down
2 changes: 1 addition & 1 deletion test/eigenselfadjoint.jl
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Expand Up @@ -34,7 +34,7 @@ using Test, GenericLinearAlgebra, LinearAlgebra, Quaternions
end

@testset "(full) Symmetric" for uplo in (:L, :U)
A = Hermitian(big.(randn(n, n)), uplo)
A = Symmetric(big.(randn(n, n)), uplo)
vals, vecs = eigen(A)
@testset "default" begin
@test vecs' * A * vecs ≈ diagm(0 => vals)
Expand Down
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