What is the easiest and fastest way (with some library, of course) to compute k largest eigenvalues and eigenvectors for a large dense matrix in C++? I'm looking for an equivalent of MATLAB's eigs function; I've looked through Armadillo and Eigen but couldn't find one, and computing all eigenvalues takes forever in my case (I need top 10 eigenvectors for an approx. 30000x30000 dense non-symmetric real matrix).
Desperate, I've even tried to implement power iterations by myself with Armadillo's QR decomposition but ran into complex pairs of eigenvalues and gave up. :)
AFAIK the problem of finding the first k eigenvalues of a generic matrix has no easy solution. The Matlab function eigs you mentioned is supposed to work with sparse matrices.
Matlab probably uses Arnoldi/Lanczos, you might try if it works decently in your case even if your matrix is not sparse. The reference package for Arnlodi is ARPACK which has a C++ interface.
Did you tried https://github.com/yixuan/spectra ?
It similar to ARPACK but with nice Eigen-like interface (it compatible with Eigen!)
I used it for 30kx30k matrices (PCA) and it was quite ok
Eigen has an EigenValues module that works pretty well.. But, I've never used it on anything quite that large.
