[SciPy-user] bug in ARPACK from scipy.sandbox?

lorenzo bolla lbolla@gmail....
Thu Aug 23 02:46:32 CDT 2007


I have problems with the ARPACK wrappers in scipy.sandbox.
take a look at this snippet of code.

---------------------------------------------------------------------------------------------------------

In [295]: A = numpy.array([[1,2,3,4],[0,2,3,4],[0,0,3,4],[0,0,0,4]],
dtype=float)

In [296]: A
Out[296]:
array([[ 1.,  2.,  3.,  4.],
       [ 0.,  2.,  3.,  4.],
       [ 0.,  0.,  3.,  4.],
       [ 0.,  0.,  0.,  4.]])

In [297]: [w,v] = arpack.eigen(A,2)
In [298]: w
Out[298]: array([ 4.+0.j,  3.+0.j,  0.+0.j])

--> WRONG: I get 3 eigenvalues instead of two!

In [299]: v
Out[299]:
array([[ 0.+0.j,  0.+0.j,  0.+0.j],
       [ 0.+0.j,  0.+0.j,  0.+0.j],
       [ 0.+0.j,  0.+0.j,  0.+0.j],
       [ 0.+0.j,  0.+0.j,  0.+0.j]])
--> WRONG: all the eigenvectors are null!

In [300]: [w,v] = arpack.eigen(A.astype(numpy.complex),2)

In [301]: w
Out[301]: array([ 4. -2.41126563e-15j,  3. +1.34425147e-15j])
--> CORRECT: casting the matrix to complex type gives the correct result and
the correct numbers of eigenvalues

In [302]: v
Out[302]:
array([[ -1.37221970e-01-0.75187207j,  -7.50019180e-01-0.32694452j],
       [ -1.02916477e-01-0.56390405j,  -5.00012787e-01-0.21796301j],
       [ -5.14582387e-02-0.28195202j,  -1.66670929e-01-0.07265434j],
       [ -1.28645597e-02-0.07048801j,   2.49800181e-16+0.j        ]])
--> MAYBE: and the eigenvectors are not null, but...

In [303]: [w,v] = arpack.eigen(A.astype(numpy.complex128),2)

In [304]: w
Out[304]: array([ 4. +7.28583860e-16j,  3. +2.23881966e-16j])

In [305]: v
Out[305]:
array([[ -6.65958925e-01 -3.75020242e-01j,
          8.08076904e-01 +1.28192062e-01j],
       [ -4.99469194e-01 -2.81265182e-01j,
          5.38717936e-01 +8.54613743e-02j],
       [ -2.49734597e-01 -1.40632591e-01j,
          1.79572645e-01 +2.84871248e-02j],
       [ -6.24336492e-02 -3.51581477e-02j,
         -5.20417043e-16 -2.39391840e-16j]])
 --> WRONG: casting to a complex128 changes the values of the
eigenvectors!!!

---------------------------------------------------------------------------------------------------------

in any case, the result for the eigenvectors are different than Matlab
(while the eigenvalues are ok):

v =

   -8.181818181818171e-001    7.642914835078907e-001
   -5.454545454545460e-001    5.732186126309180e-001
   -1.818181818181832e-001    2.866093063154587e-001
   -6.938893903907228e-018    7.165232657886386e-002


w =

    3.000000000000010e+000                         0
                         0    3.999999999999995e+000

Can someone explain me what's wrong?
Thanks in advance,
lorenzo.
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