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

General Usage
1

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!

2

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
3

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.

4

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}:
 18.15660395791398
 -1.1566039579139824
  5.197454115860898e-16

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