Repository: JuliaLang/julia
File: stdlib/LinearAlgebra/src/symmetric.jl (Julia)

Code before:
!!! compat "Julia 1.8"
    This function requires Julia 1.8 or later.
"""
symmetricpart(A::AbstractMatrix{T}, uplo=:U) where {T} =
    symmetricpart!(copyto!(similar(A, typeof(one(T) / 2)), A), uplo)

"""
    symmetricpart!(A, uplo=:U)

Overwrite the square matrix `A` with its symmetric part, `(A + transpose(A)) / 2`,
and return `Symmetric(A, uplo)`.

!!! compat "Julia 1.8"
    This function requires Julia 1.8 or later.
"""
symmetricpart!(A::AbstractMatrix, uplo::Symbol=:U) =
    Symmetric(_hermorsympart!(identity, identity, A, char_uplo(uplo)), uplo)

"""
    hermitianpart(A, uplo=:U)

Return the Hermitian part of the square matrix `A`, defined as `(A + A') / 2`,
as a [`Hermitian`](@ref) matrix.

!!! compat "Julia 1.8"
    This function requires Julia 1.8 or later.
"""
hermitianpart(A::AbstractMatrix{T}, uplo=:U) where {T} =
    hermitianpart!(copyto!(similar(A, typeof(one(T) / 2)), A), uplo)

"""
    hermitianpart!(A, uplo=:U)

Overwrite the square matrix `A` with its Hermitian part, `(A + A') / 2`,
and return `Hermitian(A, uplo)`.

!!! compat "Julia 1.8"
    This function requires Julia 1.8 or later.
"""
hermitianpart!(A::AbstractMatrix, uplo::Symbol=:U) =
    Hermitian(_hermorsympart!(real, conj, A, char_uplo(uplo)), uplo)

function _hermorsympart!(real::Function, conj::Function, A::AbstractMatrix, uplo::Char)
    require_one_based_indexing(A)
    n = checksquare(A)
    triangle = uplo === 'U' ? (j -> 1:(j - 1)) : (j -> (j + 1):n)
    @inbounds for j in 1:n
        A[j, j] = real(A[j, j])
        for i in triangle(j)
            A[i, j] = (A[i, j] + conj(A[j, i])) / 2
        end

Review comment (suggestion):
```suggestion
!!! compat "Julia 1.10"
    This function requires Julia 1.10 or later.
```

Code after:
            end
            return Symmetric(retmat)
        end

        function ($func)(A::Hermitian{T}; $(rtolarg...)) where {T<:Complex}
            n = checksquare(A)
            F = eigen(A)
            λ₀ = $rtolval # treat λ ≥ λ₀ as "zero" eigenvalues up to roundoff
            if all(λ -> λ ≥ λ₀, F.values)
                retmat = (F.vectors * Diagonal(($func).(max.(0, F.values)))) * F.vectors'
                for i = 1:n
                    retmat[i,i] = real(retmat[i,i])
                end
                return Hermitian(retmat)
            else
                retmat = (F.vectors * Diagonal(($func).(complex(F.values)))) * F.vectors'
                return retmat
            end
        end
    end
end

"""
    hermitianpart(A, uplo=:U) -> Hermitian

Return the Hermitian part of the square matrix `A`, defined as `(A + A') / 2`, as a
[`Hermitian`](@ref) matrix. For real matrices `A`, this is also known as the symmetric part
of `A`; it is also sometimes called the "operator real part". The optional argument `uplo` controls the corresponding argument of the
[`Hermitian`](@ref) view. For real matrices, the latter is equivalent to a
[`Symmetric`](@ref) view.

See also [`hermitianpart!`](@ref) for the corresponding in-place operation.

!!! compat "Julia 1.10"
    This function requires Julia 1.10 or later.
"""
hermitianpart(A::AbstractMatrix, uplo::Symbol=:U) = Hermitian(_hermitianpart(A), uplo)

"""
    hermitianpart!(A, uplo=:U) -> Hermitian

Overwrite the square matrix `A` in-place with its Hermitian part `(A + A') / 2`, and return
[`Hermitian(A, uplo)`](@ref). For real matrices `A`, this is also known as the symmetric
part of `A`.

See also [`hermitianpart`](@ref) for the corresponding out-of-place operation.

!!! compat "Julia 1.10"
    This function requires Julia 1.10 or later.
"""
hermitianpart!(A::AbstractMatrix, uplo::Symbol=:U) = Hermitian(_hermitianpart!(A), uplo)