" Adjusting nev from # to # ". eigs() on a Sparse Array using Arpack

Hi there!
I’m trying to solve an eigenvalues problem. Originally I have a 792x792 matrix that I turned into a Sparse Array. For that purpose I’m using Arpack and eigs( ). The dimension of that array is 792 so I expect that number of eigenvalues, but I get 791. I’m specifying de number of eigenvalues (nev = 792), but I get this warning:

┌ Warning: Adjusting nev from 792 to 791
└ @ Arpack ~/.julia/packages/Arpack/UiiMc/src/Arpack.jl:99

I mean, I tried the same in Mathematica and I got 792 values without any problem.
My code is some heavy, so I made another one with a 3x3 array. And I get the same problem.

using Arpack
foo = [[1, 2, 3] [5, 6, 7] [8, 9, 10]] #dummy array
eigs(foo, nev = 3)[1] #I know and I tried in Mathematica this one and I got 3 eigenvalues

But the same warning appears again!

┌ Warning: Adjusting nev from 3 to 1
└ @ Arpack ~/.julia/packages/Arpack/UiiMc/src/Arpack.jl:99

Does anyone know why I’m getting less eigenvalues that I expect?
Is there any way to avoid that auto adjusting of the nev?

By the way, I’m using version 1.1.0 of Julia on my Mac.

Thank you!

You don’t need sparse matrices or arpack for a matrix that small - just use standard dense linear algebra in the LinearAlgebra standard library.

1 Like

Yes, I totally agree with you. But 792 is just one case, my code should be able to solve arrays of bigger dimensions than that, in some cases I will need Sparse Arrays to deal with a lot of zeros. That’s my point.
For that reason I’m looking for a way to get all my eigenvalues from a Sparse Matrix.

AFAIK, ARPACK simply isn’t made for what you’re asking. It is a tool to calculate a bunch of extremal eigenvalues for huge sparse matrices and not for calculating all of them. Getting all eigenvalues of a large sparse matrix is an expensive problem!

Anyways, there are iterative solvers implemented in Julia that give you what you want. For example, using KrylovKit.jl I get:

julia> using KrylovKit

julia> foo = [[1, 2, 3] [5, 6, 7] [8, 9, 10]];

julia> eigvals(foo) # using Julia's regular solver
3-element Array{Float64,1}:

julia> λ, ϕ = eigsolve(sparse(foo)); # using KrylovKit

julia> λ
3-element Array{Complex{Float64},1}:
      18.156603957913973 + 0.0im
      -1.156603957913983 + 0.0im
 -3.1400729958893956e-16 + 0.0im

See also IterativeSolvers.jl and ArnoldiMethod.jl for alternatives.

1 Like