Support sortby in eigen

[dlfivefifty]

I ran into this issue:

julia>  eigen(Tridiagonal(SymTridiagonal{BigFloat}(randn(5), randn(4))))
ERROR: MethodError: no method matching eigen!(::Hermitian{BigFloat, Matrix{BigFloat}}; sortby::typeof(LinearAlgebra.eigsortby))

Closest candidates are:
  eigen!(::Hermitian; tol) got unsupported keyword argument "sortby"
   @ GenericLinearAlgebra ~/Projects/GenericLinearAlgebra.jl/src/eigenSelfAdjoint.jl:605
  eigen!(::AbstractMatrix, ::Cholesky; sortby)
   @ LinearAlgebra ~/Projects/julia-1.10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/symmetriceigen.jl:180
  eigen!(::Union{Hermitian{var"#s125", var"#s124"}, Hermitian{Complex{var"#s125"}, var"#s124"}, Symmetric{var"#s125", var"#s124"}} where {var"#s125"<:Union{Float32, Float64}, var"#s124"<:(StridedMatrix{T} where T)}; sortby)
   @ LinearAlgebra ~/Projects/julia-1.10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/symmetriceigen.jl:8
  ...

Stacktrace:
 [1] kwerr(::@NamedTuple{sortby::typeof(LinearAlgebra.eigsortby)}, ::Function, ::Hermitian{BigFloat, Matrix{BigFloat}})
   @ Base ./error.jl:165
 [2] eigen(A::Tridiagonal{BigFloat, Vector{BigFloat}}; permute::Bool, scale::Bool, sortby::typeof(LinearAlgebra.eigsortby))
   @ LinearAlgebra ~/Projects/julia-1.10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/eigen.jl:239
 [3] eigen(A::Tridiagonal{BigFloat, Vector{BigFloat}})
   @ LinearAlgebra ~/Projects/julia-1.10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/eigen.jl:237
 [4] top-level scope
   @ REPL[7]:1

[andreasnoack]

The issue here is actually #77. The sorting would be very simple to add but there is a little more work to finalize eigen!.

[dlfivefifty]

That's not actually my issue nor the issue in the example above: in my case its a custom matrix type that is symmetric. It ends up calling eigen!(::Hermitian{BigFloat}; sortby=sortby) which throws the error.

There is no need for supporting non-symmetric eigen in either case.

[andreasnoack]

I see. I misread the error and thought the Tridiagonal made it hit the general solver. Then it is probably a pretty easy fix.

[dlfivefifty]

Yes its an easy fix I might put together a PR over the weekend.