In-place eigvals for complex Hermitian BandedMatrix

[jishnub]

After this,

julia> A = Hermitian(brand(ComplexF64, 6, 6, 2, 2))
6×6 Hermitian{ComplexF64, BandedMatrix{ComplexF64, Matrix{ComplexF64}, Base.OneTo{Int64}}}:
 0.539725+0.0im          0.25559+0.00579831im  0.559341+0.114413im            ⋅                      ⋅                      ⋅    
  0.25559-0.00579831im  0.784935+0.0im         0.378323+0.837163im   0.337384+0.392795im             ⋅                      ⋅    
 0.559341-0.114413im    0.378323-0.837163im    0.744348+0.0im        0.153074+0.0727464im   0.420417+0.0808449im            ⋅    
          ⋅             0.337384-0.392795im    0.153074-0.0727464im  0.267722+0.0im         0.377242+0.541864im    0.690377+0.470517im
          ⋅                      ⋅             0.420417-0.0808449im  0.377242-0.541864im     0.67322+0.0im        0.0208153+0.151669im
          ⋅                      ⋅                      ⋅            0.690377-0.470517im   0.0208153-0.151669im    0.850139+0.0im

julia> eigvals!(copy(A))
6-element Vector{Float64}:
 -0.8404525797103768
 -0.1783975827526587
  0.459438228060648
  0.7997670633406646
  1.4132897571114231
  2.2064446339423642

julia> eigen!(copy(A))
Eigen{ComplexF64, Float64, Matrix{ComplexF64}, Vector{Float64}}
values:
6-element Vector{Float64}:
 -0.8404525797103773
 -0.17839758275265893
  0.4594382280606475
  0.7997670633406677
  1.4132897571114234
  2.2064446339423593
vectors:
6×6 Matrix{ComplexF64}:
 -0.148603+0.0im        -0.425349+0.0im           0.749991+0.0im         0.287983+0.0im        -0.294169+0.0im       0.255028+0.0im
   0.10547-0.376109im   -0.157143-0.329141im     -0.383595-0.338108im    0.217697-0.218831im   -0.202174-0.142623im  0.448417+0.308796im
   0.33548+0.102147im    0.619659+0.0252785im    0.0926653+0.13952im    0.0500393+0.0875024im  -0.340514+0.136919im  0.507191-0.249498im
  0.206242+0.622302im   -0.254169-0.337529im   -0.00461372-0.041927im    -0.13238-0.072834im    0.449047-0.102082im   0.37728-0.112541im
 -0.392573-0.0638003im  0.0315878-0.0271654im    -0.107969-0.313205im    0.045246+0.761045im   0.0967334-0.195571im  0.201939-0.24638im
 -0.246861-0.231159im    0.328377+0.115492im      0.185982+0.0433029im   0.184487-0.416562im    0.416109-0.533607im  0.128546-0.214531im

[codecov]

Codecov Report

Patch coverage: 100.00% and project coverage change: +1.94 🎉

Comparison is base (fc3575f) 83.44% compared to head (11da89c) 85.39%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #359      +/-   ##
==========================================
+ Coverage   83.44%   85.39%   +1.94%     
==========================================
  Files          24       24              
  Lines        3353     3389      +36     
==========================================
+ Hits         2798     2894      +96     
+ Misses        555      495      -60     

Impacted Files	Coverage Δ
src/symbanded/symbanded.jl	93.02% <ø> (-0.79%)	⬇️
src/lapack.jl	88.11% <100.00%> (+1.75%)	⬆️
src/symbanded/bandedeigen.jl	77.77% <100.00%> (+7.73%)	⬆️
src/symbanded/tridiagonalize.jl	98.73% <100.00%> (+0.34%)	⬆️

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[jishnub]

This PR overlaps with #185, but given that the other one is stalled, perhaps it's better to get this version with dense eigenvectors working, and subsequently change the type of the eigenvector matrix as an implementation detail.

[jishnub]

The eigvals methods are moved to bandedeigen.jl from symbanded.jl so that they're in the same file as eigen and are easy to discover.