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Rely on LinearAlgebra.eigsort! for sorting eigenvalues of the #151

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Apr 20, 2025
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Rely on LinearAlgebra.eigsort! for sorting eigenvalues of the #151

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92 changes: 61 additions & 31 deletions src/eigenSelfAdjoint.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -162,7 +162,7 @@ function eig2x2!(d::StridedVector, e::StridedVector, j::Integer, vectors::Matrix
return c, s
end

function eigvalsPWK!(S::SymTridiagonal{T}; tol = eps(T), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) where {T<:Real}
function eigvalsPWK!(S::SymTridiagonal{T}; tol = eps(T)) where {T<:Real}
d = S.dv
e = S.ev
n = length(d)
Expand Down Expand Up @@ -217,9 +217,7 @@ function eigvalsPWK!(S::SymTridiagonal{T}; tol = eps(T), sortby::Union{Function,
end
end

# 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)
return d
end

function eigQL!(
Expand Down Expand Up @@ -287,8 +285,8 @@ function eigQL!(
end
end
end
p = sortperm(d)
return d[p], vectors[:, p]

return d, vectors
end

function eigQR!(
Expand Down Expand Up @@ -339,8 +337,8 @@ function eigQR!(
end
end
end
p = sortperm(d)
return d[p], vectors[:, p]

return d, vectors
end

# Own implementation based on Parlett's book
Expand Down Expand Up @@ -575,45 +573,71 @@ function symtriUpper!(
)
end

_eigvals!(A::SymTridiagonal; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) =
LinearAlgebra.sorteig!(eigvalsPWK!(A; tol), sortby == nothing ? LinearAlgebra.eigsortby : sortby)

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

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

_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)
_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)

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

LinearAlgebra.eigvals!(A::Hermitian; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = _eigvals!(A; tol, sortby)
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)
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)...)
LinearAlgebra.Eigen(
LinearAlgebra.sorteig!(
eigQL!(
A.diagonals;
vectors = Array(A.Q),
tol
)...,
sortby == nothing ? LinearAlgebra.eigsortby : sortby
)...
)

_eigen!(A::SymTridiagonal; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) = LinearAlgebra.Eigen(
eigQL!(A, vectors = Matrix{eltype(A)}(I, size(A, 1), size(A, 1)), tol = tol)...,
)
_eigen!(A::SymTridiagonal; tol = eps(real(eltype(A))), sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby) =
LinearAlgebra.Eigen(
LinearAlgebra.sorteig!(
eigQL!(
A;
vectors = Matrix{eltype(A)}(I, size(A, 1), size(A, 1)),
tol
)...,
sortby == nothing ? LinearAlgebra.eigsortby : sortby
)...
)

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

_eigen!(A::Symmetric{<:Real}; tol = eps(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, sortby)

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

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

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


function eigen2!(
Expand All @@ -623,29 +647,35 @@ function eigen2!(
V = zeros(eltype(A), 2, size(A, 1))
V[1] = 1
V[end] = 1
eigQL!(A.diagonals, vectors = rmul!(V, A.Q), tol = tol)
LinearAlgebra.sorteig!(
eigQL!(A.diagonals; vectors = rmul!(V, A.Q), tol)...,
LinearAlgebra.eigsortby
)
end

function eigen2!(A::SymTridiagonal; tol = eps(real(float(one(eltype(A))))))
V = zeros(eltype(A), 2, size(A, 1))
V[1] = 1
V[end] = 1
eigQL!(A, vectors = V, tol = tol)
LinearAlgebra.sorteig!(
eigQL!(A; vectors = V, tol)...,
LinearAlgebra.eigsortby
)
end

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

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


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

eigen2(A::Hermitian, 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)

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

# First method of each type here is identical to the method defined in
# LinearAlgebra but is needed for disambiguation
Expand Down
3 changes: 1 addition & 2 deletions test/eigenselfadjoint.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -26,9 +26,8 @@ using Test, GenericLinearAlgebra, LinearAlgebra, Quaternions
@testset "QR version (QL is default)" begin
vals, vecs =
GenericLinearAlgebra.eigQR!(copy(T), vectors = Matrix{eltype(T)}(I, n, n))
@test issorted(vals)
@test (vecs' * T) * vecs ≈ Diagonal(vals)
@test eigvals(T) ≈ vals
@test eigvals(T) ≈ sort(vals)
@test vecs'vecs ≈ Matrix(I, n, n)
end
end
Expand Down
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