partial_schur not respecting argument nev
jpfairbanks opened this issue · comments
This is an unintuitive behavior for me given the way that eigs used to work.
julia> A = randn(100,21); A = A*A';
julia> schur_to_eigen(partial_schur(A, nev=8, which=LM())[1])[1]
9-element Array{Float64,1}:
181.35175628108203
174.42634344552079
142.31044226550978
132.80295154586017
126.68141410737701
121.75800101083811
109.79068655370247
104.68006588968174
100.09676418940714
julia> schur_to_eigen(partial_schur(A, nev=12, which=LM())[1])[1]
21-element Array{Float64,1}:
181.3517562810819
174.42634344552076
142.31044226550975
...I expected partial_schur to return a schur decomposition of order exactly nev, or schur_to_eigen to take an argument of nev too.
You're right, it is a bit unintuitive. What happens is that multiple eigenvalues converge simultaneously, so that nev is rather a lower bound for the number of converged eigenvalues than an exact number; the upper bound would be max. And in fact this is sometimes desirable behaviour, for instance when you have a complex conjugate pair of eigenvalues, then you probably need both of them -- might exceed nev by 1 then.
But in case unwanted eigenvalues converge, it turns out there are numerical issues when removing them in the obvious way (losing a lot of precision in the other eigenvalues is what @NymanLauri and I observed). In ARPACK there is this concept of purging unwanted eigenvalues, but when I looked at it it seemed rather convoluted. It is in the todo list of #67 however!
The simplest solution is indeed to do some post-processing in this schur_to_eigen function. I'll try something soon!
My use case only needs real eigenvalues, both LR for matrices with +/- (adjacency matrix) eigenvalues and SR for when they are all positive (Laplacian matrix). Can I just use nev=k and then sort and take the first k? I usually need the eigenvector too.
Yeah, so sortperm should work then. I think schur_to_eigen is type unstable btw, but that is on Julia's side (eigen is type-unstable). So maybe wrap the vector of eigenvalues in real(...) to be sure.
Closed via #81