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improve eigvals & co docstrings #43904

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improve eigvals & co docstrings
st-- Jan 23, 2022
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docstrings
st-- Jan 26, 2022
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18 changes: 10 additions & 8 deletions stdlib/LinearAlgebra/src/eigen.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -140,7 +140,8 @@ end
sorteig!(λ::AbstractVector, sortby::Union{Function,Nothing}=eigsortby) = sortby === nothing ? λ : sort!(λ, by=sortby)

"""
eigen!(A, [B]; permute, scale, sortby)
eigen!(A; permute, scale, sortby)
eigen!(A, B; sortby)

Same as [`eigen`](@ref), but saves space by overwriting the input `A` (and
`B`), instead of creating a copy.
Expand Down Expand Up @@ -179,7 +180,7 @@ end
"""
eigen(A; permute::Bool=true, scale::Bool=true, sortby) -> Eigen

Computes the eigenvalue decomposition of `A`, returning an [`Eigen`](@ref) factorization object `F`
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
matrix `F.vectors`. (The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Expand Down Expand Up @@ -316,7 +317,7 @@ Return the eigenvalues of `A`.

For general non-symmetric matrices it is possible to specify how the matrix is balanced
before the eigenvalue calculation. The `permute`, `scale`, and `sortby` keywords are
the same as for [`eigen!`](@ref).
the same as for [`eigen`](@ref).

# Examples
```jldoctest
Expand Down Expand Up @@ -462,17 +463,18 @@ function eigen!(A::StridedMatrix{T}, B::StridedMatrix{T}; sortby::Union{Function
end

"""
eigen(A, B) -> GeneralizedEigen
eigen(A, B; sortby) -> GeneralizedEigen

Computes the generalized eigenvalue decomposition of `A` and `B`, returning a
Compute the generalized eigenvalue decomposition of `A` and `B`, returning a
[`GeneralizedEigen`](@ref) factorization object `F` which contains the generalized eigenvalues in
`F.values` and the generalized eigenvectors in the columns of the matrix `F.vectors`.
(The `k`th generalized eigenvector can be obtained from the slice `F.vectors[:, k]`.)

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

Any keyword arguments passed to `eigen` are passed through to the lower-level
[`eigen!`](@ref) function.
By default, the eigenvalues and vectors are sorted lexicographically by `(real(λ),imag(λ))`.
A different comparison function `by(λ)` can be passed to `sortby`, or you can pass
`sortby=nothing` to leave the eigenvalues in an arbitrary order.

# Examples
```jldoctest
Expand Down Expand Up @@ -563,7 +565,7 @@ end
"""
eigvals(A, B) -> values

Computes the generalized eigenvalues of `A` and `B`.
Compute the generalized eigenvalues of `A` and `B`.

# Examples
```jldoctest
Expand Down
8 changes: 4 additions & 4 deletions stdlib/LinearAlgebra/src/symmetriceigen.jl
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Expand Up @@ -16,7 +16,7 @@ eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, irange::UnitRange)
"""
eigen(A::Union{SymTridiagonal, Hermitian, Symmetric}, irange::UnitRange) -> Eigen

Computes the eigenvalue decomposition of `A`, returning an [`Eigen`](@ref) factorization object `F`
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
matrix `F.vectors`. (The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Expand All @@ -42,7 +42,7 @@ eigen!(A::RealHermSymComplexHerm{T,<:StridedMatrix}, vl::Real, vh::Real) where {
"""
eigen(A::Union{SymTridiagonal, Hermitian, Symmetric}, vl::Real, vu::Real) -> Eigen

Computes the eigenvalue decomposition of `A`, returning an [`Eigen`](@ref) factorization object `F`
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
matrix `F.vectors`. (The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Expand Down Expand Up @@ -86,7 +86,7 @@ eigvals!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, irange::UnitRang
"""
eigvals(A::Union{SymTridiagonal, Hermitian, Symmetric}, irange::UnitRange) -> values

Returns the eigenvalues of `A`. It is possible to calculate only a subset of the
Return 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.

Expand Down Expand Up @@ -127,7 +127,7 @@ eigvals!(A::RealHermSymComplexHerm{T,<:StridedMatrix}, vl::Real, vh::Real) where
"""
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
Return 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
Expand Down