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Move alg to a keyword argument in symmetric eigen #1214

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Mar 1, 2025
Merged

Move alg to a keyword argument in symmetric eigen #1214

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f5412d7
Move `alg` to a keyword argument in symmetric eigen
jishnub Feb 20, 2025
e25f2b9
Move alg to kwarg in test
jishnub Feb 20, 2025
f1fbdab
Merge branch 'master' into jishnub/symeigen_alg
ViralBShah Mar 1, 2025
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32 changes: 19 additions & 13 deletions src/symmetriceigen.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -6,10 +6,16 @@ eigencopy_oftype(A::Hermitian, S) = Hermitian(copytrito!(similar(parent(A), S, s
eigencopy_oftype(A::Symmetric, S) = Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo(A.uplo))
eigencopy_oftype(A::Symmetric{<:Complex}, S) = copyto!(similar(parent(A), S), A)

default_eigen_alg(A) = DivideAndConquer()
"""
default_eigen_alg(A)

Return the default algorithm used to solve the eigensystem `A v = λ v` for a symmetric matrix `A`.
Defaults to `LinearAlegbra.DivideAndConquer()`, which corresponds to the LAPACK function `LAPACK.syevd!`.
"""
default_eigen_alg(@nospecialize(A)) = DivideAndConquer()

# Eigensolvers for symmetric and Hermitian matrices
function eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, alg::Algorithm = default_eigen_alg(A); sortby::Union{Function,Nothing}=nothing)
function eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}; alg::Algorithm = default_eigen_alg(A), sortby::Union{Function,Nothing}=nothing)
if alg === DivideAndConquer()
Eigen(sorteig!(LAPACK.syevd!('V', A.uplo, A.data)..., sortby)...)
elseif alg === QRIteration()
Expand All @@ -22,7 +28,7 @@ function eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, alg::Algo
end

"""
eigen(A::Union{Hermitian, Symmetric}, alg::Algorithm = default_eigen_alg(A)) -> Eigen
eigen(A::Union{Hermitian, Symmetric}; alg::LinearAlgebra.Algorithm = LinearAlgebra.default_eigen_alg(A)) -> Eigen

Compute the eigenvalue decomposition of `A`, returning an [`Eigen`](@ref) factorization object `F`
which contains the eigenvalues in `F.values` and the eigenvectors in the columns of the
Expand All @@ -45,19 +51,19 @@ The default `alg` used may change in the future.

The following functions are available for `Eigen` objects: [`inv`](@ref), [`det`](@ref), and [`isposdef`](@ref).
"""
function eigen(A::RealHermSymComplexHerm, alg::Algorithm = default_eigen_alg(A); sortby::Union{Function,Nothing}=nothing)
_eigen(A, alg; sortby)
function eigen(A::RealHermSymComplexHerm; alg::Algorithm = default_eigen_alg(A), sortby::Union{Function,Nothing}=nothing)
_eigen(A; alg, sortby)
end

# we dispatch on the eltype in an internal method to avoid ambiguities
function _eigen(A::RealHermSymComplexHerm, alg::Algorithm; sortby)
function _eigen(A::RealHermSymComplexHerm; alg::Algorithm, sortby)
S = eigtype(eltype(A))
eigen!(eigencopy_oftype(A, S), alg; sortby)
eigen!(eigencopy_oftype(A, S); alg, sortby)
end

function _eigen(A::RealHermSymComplexHerm{Float16}, alg::Algorithm; sortby::Union{Function,Nothing}=nothing)
function _eigen(A::RealHermSymComplexHerm{Float16}; alg::Algorithm, sortby::Union{Function,Nothing}=nothing)
S = eigtype(eltype(A))
E = eigen!(eigencopy_oftype(A, S), alg, sortby=sortby)
E = eigen!(eigencopy_oftype(A, S); alg, sortby)
values = convert(AbstractVector{Float16}, E.values)
vectors = convert(AbstractMatrix{isreal(E.vectors) ? Float16 : Complex{Float16}}, E.vectors)
return Eigen(values, vectors)
Expand Down Expand Up @@ -114,7 +120,7 @@ function eigen(A::RealHermSymComplexHerm, vl::Real, vh::Real)
end


function eigvals!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, alg::Algorithm = default_eigen_alg(A); sortby::Union{Function,Nothing}=nothing)
function eigvals!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}; alg::Algorithm = default_eigen_alg(A), sortby::Union{Function,Nothing}=nothing)
vals::Vector{real(eltype(A))} = if alg === DivideAndConquer()
LAPACK.syevd!('N', A.uplo, A.data)
elseif alg === QRIteration()
Expand All @@ -129,7 +135,7 @@ function eigvals!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, alg::Al
end

"""
eigvals(A::Union{Hermitian, Symmetric}, alg::Algorithm = default_eigen_alg(A))) -> values
eigvals(A::Union{Hermitian, Symmetric}; alg::Algorithm = default_eigen_alg(A))) -> values

Return the eigenvalues of `A`.

Expand All @@ -143,9 +149,9 @@ a comparison of the accuracy and performance of different methods.

The default `alg` used may change in the future.
"""
function eigvals(A::RealHermSymComplexHerm, alg::Algorithm = default_eigen_alg(A); sortby::Union{Function,Nothing}=nothing)
function eigvals(A::RealHermSymComplexHerm; alg::Algorithm = default_eigen_alg(A), sortby::Union{Function,Nothing}=nothing)
S = eigtype(eltype(A))
eigvals!(eigencopy_oftype(A, S), alg; sortby)
eigvals!(eigencopy_oftype(A, S); alg, sortby)
end


Expand Down
15 changes: 0 additions & 15 deletions test/symmetric.jl
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Expand Up @@ -720,21 +720,6 @@ end
end
end

@testset "eigendecomposition Algorithms" begin
using LinearAlgebra: DivideAndConquer, QRIteration, RobustRepresentations
for T in (Float64, ComplexF64, Float32, ComplexF32)
n = 4
A = T <: Real ? Symmetric(randn(T, n, n)) : Hermitian(randn(T, n, n))
d, v = eigen(A)
for alg in (DivideAndConquer(), QRIteration(), RobustRepresentations())
@test (@inferred eigvals(A, alg)) ≈ d
d2, v2 = @inferred eigen(A, alg)
@test d2 ≈ d
@test A * v2 ≈ v2 * Diagonal(d2)
end
end
end

const BASE_TEST_PATH = joinpath(Sys.BINDIR, "..", "share", "julia", "test")
isdefined(Main, :ImmutableArrays) || @eval Main include(joinpath($(BASE_TEST_PATH), "testhelpers", "ImmutableArrays.jl"))
using .Main.ImmutableArrays
Expand Down
17 changes: 16 additions & 1 deletion test/symmetriceigen.jl
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Expand Up @@ -3,6 +3,7 @@
module TestSymmetricEigen

using Test, LinearAlgebra
using LinearAlgebra: DivideAndConquer, QRIteration, RobustRepresentations

@testset "chol-eigen-eigvals" begin
## Cholesky decomposition based
Expand Down Expand Up @@ -173,7 +174,7 @@ end
@test D.vectors ≈ D32.vectors

# ensure that different algorithms dispatch correctly
λ, V = eigen(C, LinearAlgebra.QRIteration())
λ, V = eigen(C; alg=LinearAlgebra.QRIteration())
@test λ isa Vector{Float16}
@test C * V ≈ V * Diagonal(λ)
end
Expand All @@ -184,4 +185,18 @@ end
@test S * v ≈ v * Diagonal(λ)
end

@testset "eigendecomposition Algorithms" begin
for T in (Float64, ComplexF64, Float32, ComplexF32)
n = 4
A = T <: Real ? Symmetric(randn(T, n, n)) : Hermitian(randn(T, n, n))
d, v = eigen(A)
for alg in (DivideAndConquer(), QRIteration(), RobustRepresentations())
@test (@inferred eigvals(A; alg)) ≈ d
d2, v2 = @inferred eigen(A; alg)
@test d2 ≈ d
@test A * v2 ≈ v2 * Diagonal(d2)
end
end
end

end # module TestSymmetricEigen