Add eigvals(::Eigen) and eigvecs(::Eigen) methods

Ref: #3021 #12747

Author: jiahao

base/linalg/eigen.jl

@@ -67,8 +67,10 @@ function eig(A::Union{Number, AbstractMatrix}; kwargs...)
     F.values, F.vectors
 end
 #Calculates eigenvectors
-eigvecs(A::Union{Number, AbstractMatrix}, args...; kwargs...) = eigfact(A, args...; kwargs...)[:vectors]
+eigvecs(A::Union{Number, AbstractMatrix}, args...; kwargs...) = eigvecs(eigfact(A, args...; kwargs...))
+eigvecs{T,V,S,U}(F::Union{Eigen{T,V,S,U}, GeneralizedEigen{T,V,S,U}}) = F[:vectors]::S
 
+eigvals{T,V,S,U}(F::Union{Eigen{T,V,S,U}, GeneralizedEigen{T,V,S,U}}) = F[:values]::U
 function eigvals!{T<:BlasReal}(A::StridedMatrix{T}; permute::Bool=true, scale::Bool=true)
     issym(A) && return eigvals!(Symmetric(A))
     _, valsre, valsim, _ = LAPACK.geevx!(permute ? (scale ? 'B' : 'P') : (scale ? 'S' : 'N'), 'N', 'N', 'N', A)

test/linalg/eigen.jl

@@ -29,6 +29,8 @@ debug && println("non-symmetric eigen decomposition")
     f = eigfact(a)
     @test_approx_eq det(a) det(f)
     @test_approx_eq inv(a) inv(f)
+    @test eigvals(f) === f[:values]
+    @test eigvecs(f) === f[:vectors]
 
     num_fact = eigfact(one(eltya))
     @test num_fact.values[1] == one(eltya)
@@ -47,6 +49,8 @@ debug && println("symmetric generalized eigenproblem")
     @test_approx_eq f[:values] eigvals(asym_sg, a_sg'a_sg)
     @test_approx_eq_eps prod(f[:values]) prod(eigvals(asym_sg/(a_sg'a_sg))) 200ε
     @test eigvecs(asym_sg, a_sg'a_sg) == f[:vectors]
+    @test eigvals(f) === f[:values]
+    @test eigvecs(f) === f[:vectors]
     @test_throws KeyError f[:Z]
 
 debug && println("Non-symmetric generalized eigenproblem")