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Eigvecs for specific eigvals for Symmetric/Hermitian #1268

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Apr 30, 2025
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Eigvecs for specific eigvals for Symmetric/Hermitian #1268

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6 changes: 6 additions & 0 deletions src/symmetriceigen.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -331,6 +331,12 @@ function eigvals!(A::Hermitian{T,S}, B::Hermitian{T,S}; sortby::Union{Function,N
end
eigvecs(A::HermOrSym) = eigvecs(eigen(A))

function eigvecs(A::RealHermSymComplexHerm, eigvals::AbstractVector{<:Real})
F = hessenberg(A) # transform to SymTridiagonal form
X = eigvecs(F.H, eigvals)
return F.Q * X # transform eigvecs of F.H back to eigvecs of A
end

function eigvals(A::AbstractMatrix, C::Cholesky; sortby::Union{Function,Nothing}=nothing)
if ishermitian(A)
eigvals!(eigencopy_oftype(Hermitian(A), eigtype(eltype(A))), C; sortby)
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4 changes: 2 additions & 2 deletions src/tridiag.jl
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Expand Up @@ -311,7 +311,7 @@ eigmin(A::SymTridiagonal) = eigvals(A, 1:1)[1]

#Compute selected eigenvectors only corresponding to particular eigenvalues
"""
eigvecs(A::SymTridiagonal[, eigvals]) -> Matrix
eigvecs(A::Union{Symmetric, Hermitian, SymTridiagonal}[, eigvals])::Matrix

Return a matrix `M` whose columns are the eigenvectors of `A`. (The `k`th eigenvector can
be obtained from the slice `M[:, k]`.)
Expand Down Expand Up @@ -346,7 +346,7 @@ julia> eigvecs(A, [1.])
-0.5547001962252291
```
"""
eigvecs(A::SymTridiagonal{<:BlasFloat,<:StridedVector}, eigvals::Vector{<:Real}) = LAPACK.stein!(A.dv, A.ev, eigvals)
eigvecs(A::SymTridiagonal{<:BlasFloat,<:StridedVector}, eigvals::StridedVector{<:Real}) = LAPACK.stein!(A.dv, A.ev, eigvals)

function svdvals!(A::SymTridiagonal)
vals = eigvals!(A)
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19 changes: 19 additions & 0 deletions test/symmetriceigen.jl
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Expand Up @@ -199,4 +199,23 @@ end
end
end

@testset "eigvecs for specific eigvals" begin
function testeigvecs(S, vals)
V = eigvecs(S, vals)
@test S * V ≈ V * Diagonal(vals)
end
for T in (Symmetric, Hermitian)
S = T(rand(3,3))
vals = eigvals(S)
testeigvecs(S, vals)
testeigvecs(S, vals[1:2])
testeigvecs(S, @view vals[2:2])
end
H = Hermitian(rand(ComplexF64,3,3))
vals = eigvals(H)
testeigvecs(H, vals)
testeigvecs(H, vals[1:2])
testeigvecs(H, @view vals[2:2])
end

end # module TestSymmetricEigen