Largest eigenvalues (and corresponding eigenvectors) in C++

Question

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. :)

Answer 1

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.

Answer 2

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

Answer 3

Eigen has an EigenValues module that works pretty well.. But, I've never used it on anything quite that large.

Answer 4

Here is how I get the k largest eigenvectors of a NxN real-valued (float), dense, symmetric matrix A in C++ Eigen:

#include <Eigen/Dense>
...
Eigen::MatrixXf A(N,N);
...
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXf> solver(N);
solver.compute(A);
Eigen::VectorXf lambda = solver.eigenvalues().reverse();
Eigen::MatrixXf X = solver.eigenvectors().block(0,N-k,N,k).rowwise().reverse();

Note that the eigenvalues and associated eigenvectors are returned in ascending order so I reverse them to get the largest values first.

If you want eigenvalues and eigenvectors for other (non-symmetric) matrices they will, in general, be complex and you will need to use the Eigen::EigenSolver class instead.