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 2×2. 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 2×2 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!
Answers:
There doesn’t appear to be a numpy equivalent of Matlab’s eigs(A,B,k) for finding the k largest eigenvectors.
If you’re interested, Enthought has compiled a table showing the differences between Matlab and numpy. That should be helpful for answering questions like this one: Link
One other thought, for 2×2 matrices, I don’t think eigs(A,B,1) would help anyway. The effort involved in computing the first eigenpair leaving the matrix transformed to where the second emerges directly. There is only benefit for 3×3 and larger.
According to the docs:
http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html
and also to my own experience, numpy.linalg.eig(A) does NOT sort the eigenvectors in any particular order, which is what the OP and subsequent seem to be assuming. I suggest something like:
rearrangedEvalsVecs = sorted(zip(evals,evecs.T),
key=lambda x: x[0].real, reverse=True)
Use this: http://docs.scipy.org/doc/scipy/reference/sparse.linalg.html
Find k eigenvalues and eigenvectors of the square matrix A.
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 2×2. 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 2×2 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!
There doesn’t appear to be a numpy equivalent of Matlab’s eigs(A,B,k) for finding the k largest eigenvectors.
If you’re interested, Enthought has compiled a table showing the differences between Matlab and numpy. That should be helpful for answering questions like this one: Link
One other thought, for 2×2 matrices, I don’t think eigs(A,B,1) would help anyway. The effort involved in computing the first eigenpair leaving the matrix transformed to where the second emerges directly. There is only benefit for 3×3 and larger.
According to the docs:
http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html
and also to my own experience, numpy.linalg.eig(A) does NOT sort the eigenvectors in any particular order, which is what the OP and subsequent seem to be assuming. I suggest something like:
rearrangedEvalsVecs = sorted(zip(evals,evecs.T),
key=lambda x: x[0].real, reverse=True)
Use this: http://docs.scipy.org/doc/scipy/reference/sparse.linalg.html
Find k eigenvalues and eigenvectors of the square matrix A.