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pythonsparse-matrixeigenvalueeigenvector

Python - How can linalg.eigsh find *all* the eigenvectors?

I am using the example code on the documenation page for linalg.eigsh, here:

import scipy.sparse.linalg as sp
import numpy as np

id = np.eye(13)
vals, vecs = sp.eigsh(id, k=6)

len(vals)
# 6
len(vecs)
# 13

I am asking it for 6 eigenvalues (k=6) and it does return 6, but it gives me 13 (i.e. all) the eigenvectors.
In the documentation, right when it talks about k, it says:

The number of eigenvalues and eigenvectors desired. k must be smaller than N. It is not possible to compute all eigenvectors of a matrix.

And indeed I thought that the speed of the Lanczos method, underlying eighsh was due to it finding only a subset of the eigvectors.

So how can it return all the eigenvectors?

Solution

  • You're interpreting the results wrong. The eigenvectors are the columns of vecs, but you're counting the rows. vecs has six columns, as expected.