Python numpy compute first eigenvalue and eigenvector

Question

I was wondering if there is a Python package, numpy or otherwise, that has a function that computes the first eigenvalue and eigenvector of a small matrix, say 2x2. I could use the linalg package in numpy as follows.

import numpy as np

def whatever():
    A = np.asmatrix(np.rand(2, 2))
    evals, evecs = np.linalg.eig(A)
    #Assume that the eigenvalues are ordered from large to small and that the
    #eigenvectors are ordered accordingly.
    return evals[0], evecs[:, 0]

But this takes a really long time. I suspect that it's because numpy computes eigenvectors through some sort of iterative process. So I was wondering if there were a much faster algorithm that only returns the first (largest) eigenvalue and eigenvector, since I only need the first.

For 2x2 matrices of course I can write a function myself, that computes the eigenvalue and eigenvector analytically, but then there are problems with floating point computations, for example when I divide a very big number by a very small number, I get infinity or NaN. Does anyone know anything about this? Please help! Thank you in advance!

Umm, what do you mean by "long time"? %timeit np.linalg.eig(np.random.rand(2,2)) gives 10000 loops, best of 3: 208 us per loop. That's reasonably fast, I must say. — Avaris
For 2x2 Matrix numpy is slow due the overhead, just use: math.harvard.edu/archive/21b_fall_04/exhibits/2dmatrices/… — tillsten
@Avaris, don't include a call to a random-number generator in your timing tests! — Ahmed Fasih

Jack Twain Jack Twain · Accepted Answer · 2014-03-19T13:21:27

Use this: http://docs.scipy.org/doc/scipy/reference/sparse.linalg.html

http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigs.html#scipy.sparse.linalg.eigs

Find k eigenvalues and eigenvectors of the square matrix A.

Python numpy compute first eigenvalue and eigenvector

3 Answers