[SciPy-User] Incorrect eigenvectors/values from scipy.sparse.linalg.lobpcg
Charanpal Dhanjal
dhanjal@telecom-paristech...
Wed Nov 9 12:55:10 CST 2011
Hi all,
I wanted to use scipy.sparse.linalg.lobpcg and found that it does not
seem to work as described. Here is some code demonstrating the problem:
============================================
import numpy
import scipy.sparse.linalg
numpy.random.seed(21)
n = 20
A = numpy.random.rand(n, n)
A = A.T.dot(A)
s1, U1 = numpy.linalg.eig(A)
print(s1)
k = 5
X = numpy.random.rand(A.shape[0], k)
w, V = scipy.sparse.linalg.lobpcg(A, X, tol=1e-30, largest=True,
maxiter=100)
print(w)
print(numpy.sum(V**2, 0))
print(numpy.linalg.norm(A.dot(V) - V.dot(numpy.diag(w))))
============================================
and the output on my machine is:
[ 106.1436 4.8357 4.6157 3.6735 2.9786 2.7774 2.4734
1.8922 1.8146 1.5884
1.0942 0.985 0.7575 0.6286 0.4411 0.2275 0.0039
0.0501 0.0364 0.136 ]
[ 0.2275+0.j 0.0039+0.j 0.0501+0.j 0.0364+0.j 0.1360+0.j]
[ 2.7735 4.7396 3.8368 4.5054 14.7127]
406.94471445
So, it looks like lobpcg is finding the smallest eigenvalues even
though largest=True. When I change largest=False, then lobpcg returns
the 2nd to 5th largest eigenvectors, i.e. it excludes the very largest
for some reason. Furthermore, the norms of the eigenvectors are not 1
and the last print statement shows the eigenvectors are just not
correct. Any ideas about this? I tried playing around with tol and
maxiter parameters to no avail.
I read that some bugs in this function had been fixed in version 0.9
(the version I am using). Also, I am using python 2.7.2 and numpy 1.6.1
on Ubuntu 11.10, if that helps.
Thanks in advance for any help,
Charanpal
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