Implement a method to calculate only largest eigenvalues

[StHagel]

Implement a method to calculate only largest eigenvalues

[sarah-ek]

I've recently been studying iterative solvers so this is on my to-do list for the near future

[guiburon]

Hi,

I am not related to the faer crate but I am curious.

Was your 4096x4096 matrix dense in your example?
Spectra seems to be a sparse eigensolver. I think Arnoldi iteration eigensolvers in general are much more suited to sparse eigenproblems. Also the rule of thumb for Arnoldi iteration is that you need a Krylov subspace 2 times larger than the number of eigenpairs wanted so it is very ill suited to computing all the eigenpairs.

May I suggest taking a look at power iteration and subspace iteration if you want the dominant or the few largest eigenpairs? Otherwise, I think for general dense matrices it is typically not faster to extract less than all of the eigenpairs. I am curious about what would be the faer approach though.

[StHagel]

Hi,

I am not related to the faer crate but I am curious.

Was your 4096x4096 matrix dense in your example? Spectra seems to be a sparse eigensolver. I think Arnoldi iteration eigensolvers in general are much more suited to sparse eigenproblems. Also the rule of thumb for Arnoldi iteration is that you need a Krylov subspace 2 times larger than the number of eigenpairs wanted so it is very ill suited to computing all the eigenpairs.

May I suggest taking a look at power iteration and subspace iteration if you want the dominant or the few largest eigenpairs? Otherwise, I think for general dense matrices it is typically not faster to extract less than all of the eigenpairs. I am curious about what would be the faer approach though.

Spectra does have methods for dense matrices as well (https://spectralib.org/doc/classspectra_1_1geneigssolver), which I have been using in my example benchmarks (the 4096x4096 matrices have all been dense).
Spectra is in fact not well suited for finding all the eigenvalues, but in my applications I only need the leading eigenpairs, hence this issue, asking for a way to get those using faer.

I've recently been studying iterative solvers so this is on my to-do list for the near future

Awesome! Btw, if such a method would also calculate the eigenvectors, that would be even more awesome :)

[StHagel]

Hey there, it's me again.

Did you have time yet to look into this?
If not, is there a way I can help out with it? If you point me towards some specific algorithm(s), which would suite this usecase in faer and point me towards where in the repo such a method would make most sense, I could see if I can write up a draft for a PR to work with.