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Mar 26, 2021
Merged

Support for using matrices of different types in generalized eigendecomposition #39301

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62c1341
Support generalized eigendecomposition of matrices of different types…
schneiderfelipe Jan 18, 2021
f5364ca
Solve U' \ A / A in-place in generalized eigen! for mixed types
schneiderfelipe Jan 20, 2021
e92a888
Transfer eigensolvers from symmetric.jl to symmetriceigen.jl
schneiderfelipe Jan 21, 2021
7e42143
Fix generalized eigen! (mixed types) tests for Real and Complex
schneiderfelipe Jan 22, 2021
c15c933
Fix and test the behavior of UtiAUi! for complex matrices
schneiderfelipe Feb 3, 2021
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1 change: 1 addition & 0 deletions stdlib/LinearAlgebra/src/LinearAlgebra.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -374,6 +374,7 @@ include("cholesky.jl")
include("lu.jl")
include("bunchkaufman.jl")
include("diagonal.jl")
include("symmetriceigen.jl")
include("bidiag.jl")
include("uniformscaling.jl")
include("hessenberg.jl")
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168 changes: 0 additions & 168 deletions stdlib/LinearAlgebra/src/symmetric.jl
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Expand Up @@ -676,174 +676,6 @@ end
inv(A::Hermitian{<:Any,<:StridedMatrix}) = Hermitian(_inv(A), sym_uplo(A.uplo))
inv(A::Symmetric{<:Any,<:StridedMatrix}) = Symmetric(_inv(A), sym_uplo(A.uplo))

eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}; sortby::Union{Function,Nothing}=nothing) = Eigen(sorteig!(LAPACK.syevr!('V', 'A', A.uplo, A.data, 0.0, 0.0, 0, 0, -1.0)..., sortby)...)

function eigen(A::RealHermSymComplexHerm; sortby::Union{Function,Nothing}=nothing)
T = eltype(A)
S = eigtype(T)
eigen!(S != T ? convert(AbstractMatrix{S}, A) : copy(A), sortby=sortby)
end

eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, irange::UnitRange) = Eigen(LAPACK.syevr!('V', 'I', A.uplo, A.data, 0.0, 0.0, irange.start, irange.stop, -1.0)...)

"""
eigen(A::Union{SymTridiagonal, Hermitian, Symmetric}, irange::UnitRange) -> Eigen

Computes 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
matrix `F.vectors`. (The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Iterating the decomposition produces the components `F.values` and `F.vectors`.

The following functions are available for `Eigen` objects: [`inv`](@ref), [`det`](@ref), and [`isposdef`](@ref).

The [`UnitRange`](@ref) `irange` specifies indices of the sorted eigenvalues to search for.

!!! note
If `irange` is not `1:n`, where `n` is the dimension of `A`, then the returned factorization
will be a *truncated* factorization.
"""
function eigen(A::RealHermSymComplexHerm, irange::UnitRange)
T = eltype(A)
S = eigtype(T)
eigen!(S != T ? convert(AbstractMatrix{S}, A) : copy(A), irange)
end

eigen!(A::RealHermSymComplexHerm{T,<:StridedMatrix}, vl::Real, vh::Real) where {T<:BlasReal} =
Eigen(LAPACK.syevr!('V', 'V', A.uplo, A.data, convert(T, vl), convert(T, vh), 0, 0, -1.0)...)

"""
eigen(A::Union{SymTridiagonal, Hermitian, Symmetric}, vl::Real, vu::Real) -> Eigen

Computes 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
matrix `F.vectors`. (The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Iterating the decomposition produces the components `F.values` and `F.vectors`.

The following functions are available for `Eigen` objects: [`inv`](@ref), [`det`](@ref), and [`isposdef`](@ref).

`vl` is the lower bound of the window of eigenvalues to search for, and `vu` is the upper bound.

!!! note
If [`vl`, `vu`] does not contain all eigenvalues of `A`, then the returned factorization
will be a *truncated* factorization.
"""
function eigen(A::RealHermSymComplexHerm, vl::Real, vh::Real)
T = eltype(A)
S = eigtype(T)
eigen!(S != T ? convert(AbstractMatrix{S}, A) : copy(A), vl, vh)
end

eigvals!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}) =
LAPACK.syevr!('N', 'A', A.uplo, A.data, 0.0, 0.0, 0, 0, -1.0)[1]

function eigvals(A::RealHermSymComplexHerm)
T = eltype(A)
S = eigtype(T)
eigvals!(S != T ? convert(AbstractMatrix{S}, A) : copy(A))
end

"""
eigvals!(A::Union{SymTridiagonal, Hermitian, Symmetric}, irange::UnitRange) -> values

Same as [`eigvals`](@ref), but saves space by overwriting the input `A`, instead of creating a copy.
`irange` is a range of eigenvalue *indices* to search for - for instance, the 2nd to 8th eigenvalues.
"""
eigvals!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, irange::UnitRange) =
LAPACK.syevr!('N', 'I', A.uplo, A.data, 0.0, 0.0, irange.start, irange.stop, -1.0)[1]

"""
eigvals(A::Union{SymTridiagonal, Hermitian, Symmetric}, irange::UnitRange) -> values

Returns the eigenvalues of `A`. It is possible to calculate only a subset of the
eigenvalues by specifying a [`UnitRange`](@ref) `irange` covering indices of the sorted eigenvalues,
e.g. the 2nd to 8th eigenvalues.

# Examples
```jldoctest
julia> A = SymTridiagonal([1.; 2.; 1.], [2.; 3.])
3×3 SymTridiagonal{Float64, Vector{Float64}}:
1.0 2.0 ⋅
2.0 2.0 3.0
⋅ 3.0 1.0

julia> eigvals(A, 2:2)
1-element Vector{Float64}:
0.9999999999999996

julia> eigvals(A)
3-element Vector{Float64}:
-2.1400549446402604
1.0000000000000002
5.140054944640259
```
"""
function eigvals(A::RealHermSymComplexHerm, irange::UnitRange)
T = eltype(A)
S = eigtype(T)
eigvals!(S != T ? convert(AbstractMatrix{S}, A) : copy(A), irange)
end

"""
eigvals!(A::Union{SymTridiagonal, Hermitian, Symmetric}, vl::Real, vu::Real) -> values

Same as [`eigvals`](@ref), but saves space by overwriting the input `A`, instead of creating a copy.
`vl` is the lower bound of the interval to search for eigenvalues, and `vu` is the upper bound.
"""
eigvals!(A::RealHermSymComplexHerm{T,<:StridedMatrix}, vl::Real, vh::Real) where {T<:BlasReal} =
LAPACK.syevr!('N', 'V', A.uplo, A.data, convert(T, vl), convert(T, vh), 0, 0, -1.0)[1]

"""
eigvals(A::Union{SymTridiagonal, Hermitian, Symmetric}, vl::Real, vu::Real) -> values

Returns the eigenvalues of `A`. It is possible to calculate only a subset of the eigenvalues
by specifying a pair `vl` and `vu` for the lower and upper boundaries of the eigenvalues.

# Examples
```jldoctest
julia> A = SymTridiagonal([1.; 2.; 1.], [2.; 3.])
3×3 SymTridiagonal{Float64, Vector{Float64}}:
1.0 2.0 ⋅
2.0 2.0 3.0
⋅ 3.0 1.0

julia> eigvals(A, -1, 2)
1-element Vector{Float64}:
1.0000000000000009

julia> eigvals(A)
3-element Vector{Float64}:
-2.1400549446402604
1.0000000000000002
5.140054944640259
```
"""
function eigvals(A::RealHermSymComplexHerm, vl::Real, vh::Real)
T = eltype(A)
S = eigtype(T)
eigvals!(S != T ? convert(AbstractMatrix{S}, A) : copy(A), vl, vh)
end

eigmax(A::RealHermSymComplexHerm{<:Real,<:StridedMatrix}) = eigvals(A, size(A, 1):size(A, 1))[1]
eigmin(A::RealHermSymComplexHerm{<:Real,<:StridedMatrix}) = eigvals(A, 1:1)[1]

function eigen!(A::HermOrSym{T,S}, B::HermOrSym{T,S}; sortby::Union{Function,Nothing}=nothing) where {T<:BlasReal,S<:StridedMatrix}
vals, vecs, _ = LAPACK.sygvd!(1, 'V', A.uplo, A.data, B.uplo == A.uplo ? B.data : copy(B.data'))
GeneralizedEigen(sorteig!(vals, vecs, sortby)...)
end
function eigen!(A::Hermitian{T,S}, B::Hermitian{T,S}; sortby::Union{Function,Nothing}=nothing) where {T<:BlasComplex,S<:StridedMatrix}
vals, vecs, _ = LAPACK.sygvd!(1, 'V', A.uplo, A.data, B.uplo == A.uplo ? B.data : copy(B.data'))
GeneralizedEigen(sorteig!(vals, vecs, sortby)...)
end

eigvals!(A::HermOrSym{T,S}, B::HermOrSym{T,S}) where {T<:BlasReal,S<:StridedMatrix} =
LAPACK.sygvd!(1, 'N', A.uplo, A.data, B.uplo == A.uplo ? B.data : copy(B.data'))[1]
eigvals!(A::Hermitian{T,S}, B::Hermitian{T,S}) where {T<:BlasComplex,S<:StridedMatrix} =
LAPACK.sygvd!(1, 'N', A.uplo, A.data, B.uplo == A.uplo ? B.data : copy(B.data'))[1]

eigvecs(A::HermOrSym) = eigvecs(eigen(A))

function svd(A::RealHermSymComplexHerm, full::Bool=false)
vals, vecs = eigen(A)
I = sortperm(vals; by=abs, rev=true)
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