Help with ArnoldiMethod.jl

New to Julia
1

Hi everyone. I am trying to solve the general eigenvalue problem closed to a value by computing the eigenvalues of largest magnitude. Using Arpack the command is similar to:

dp,xp=eigs(A,B,nev=3,sigma=ω[o]/rspd);

But I found ArnoldiMethod.jl and someone mentioned it should be faster than the Arpack.jl.

I found this:

https://haampie.github.io/ArnoldiMethod.jl/stable/usage/02_spectral_transformations.html

But I do not know how to set the “sigma” value.

Any help getting the LM eigenvalues and eigenfuncitons faster than Arpack. This is kind of bottlenecking my code.

2

you set it yourself, see here https://github.com/rveltz/BifurcationKit.jl/blob/master/src/EigSolver.jl#L138 for a regular eigenvalue problem.

I also do it in my most recent tutorial

You have also other algo:

1 Like
3

EigSolver calls Arpack for sparse matrixes?

4

Why would it be faster? It is Arnoldi (Lanczos, for symmetric matrices), same as Arpack.

5

I don’t know is what I read.

I am not getting any of the given options to work properly.

Any idea to make Arpack run faster? I was thinking of editing “eigs” to remove a bunch of the “if” in there…

6

There are 4 different eigen solvers in EigSolver.jl based on eig, Arpack, ArnoldiMethod, KrylovKit. They works for matrix-free or sparse linear operators.

7

It difficult to tell without A and B.

8

Dear @rveltz. They are quite sparse matrix…

I would very much appreciate if you can check them and tell me the best way to address my problem. I have uploaded my code here:

https://github.com/marianoarnaiz/SWF

Running: SWF_light.jl (comment using GMT and the plot)

Will make all the computations. The for loop that calls the arpack is in function:

Rayleigh_Forwardsp, between lines 463 and 467