Implement sorting for Eigen

base/linalg/eigen.jl

@@ -27,6 +27,9 @@ function getindex(A::Union{Eigen,GeneralizedEigen}, d::Symbol)
  throw(KeyError(d))
 end
 
+eigsortby(λ::Real) = λ
+eigsortby(λ::Complex) = reim(λ)
+
 """
  sort!(F::Base.LinAlg.Eigen; kw...)
 
@@ -52,10 +55,12 @@ julia> F[:values]
  4.0
 ```
 """
-function sort!(F::Eigen; kw...)
- perm = sortperm(F[:values]; kw...)
- permute!(F[:values], perm)
- Base.permutecols!!(F[:vectors], perm)
+function sort!(F::Eigen; by=eigsortby, kw...)
+ if !issorted(F[:values], by=by)
+ perm = sortperm(F[:values]; by=by, kw...)
+ permute!(F[:values], perm)
+ Base.permutecols!!(F[:vectors], perm)
+ end
  return F
 end
 

test/linalg/eigen.jl

@@ -107,7 +107,7 @@ end
 
 let a = rand(10, 10)
  f = eigfact(a)
- sort!(f, by=real)
+ sort!(f)
  @test a ≈ f[:vectors] * Diagonal(f[:values]) / f[:vectors]
 end