[SciPy-dev] ARPACK wrapper
Nils Wagner
nwagner at iam.uni-stuttgart.de
Mon Nov 20 08:47:54 CST 2006
Aric Hagberg wrote:
> On Mon, Nov 20, 2006 at 09:45:47AM +0100, Nils Wagner wrote:
>
>> Hi Neilen,
>>
>> In order to compare the results with the workhorse eig I have used a
>> very small
>> order n. The number of desired eigenpairs is equal to k=4 in my example,
>> but the
>> shape of the array of eigenvectors is (n,k+1) and for the eigenvalues it
>> is (k+1,).
>> The eigenvectors returned by arpack.eigen are zero.
>>
>> Nils
>>
>
> Hi Nils,
>
> The size of the return arrays are intentional (k+1). This is
> the way ARPACK returns eigenvalues and eigenvectors for nonsymmetric
> matrices. I think the idea is that the k'th eigenvalue
> (largest, smallest, etc) might be a complex conjugate pair and
> then you might want k+1 (the conjugate). Else, if the k'th
> eigenvalue is real that entry is zero.
>
> I can run your test example successfully. Do the tests in
> arpack/tests/test_arpack.py work for you?
>
> Aric
>
>
>
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help (arpack.eigen) yields
eigen(A, k=6, M=None, ncv=None, which='LM', maxiter=None, tol=0,
return_eigenvectors=True)
Return k eigenvalues and eigenvectors of the matrix A.
Solves A * x[i] = w[i] * x[i], the standard eigenvalue problem for
w[i] eigenvalues with corresponding eigenvectors x[i].
Inputs:
A -- A matrix, array or an object with matvec(x) method to perform
the matrix vector product A * x. The sparse matrix formats
in scipy.sparse are appropriate for A.
k -- The number of eigenvalue/eigenvectors desired
M -- (Not implemented)
A symmetric positive-definite matrix for the generalized
eigenvalue problem A * x = w * M * x
Outputs:
w -- An array of k eigenvalues
v -- An array of k eigenvectors, k[i] is the eigenvector corresponding
to the eigenvector w[i]
This info doesn't match with your explanation.
Concerning the tests I get
/usr/bin/python
/usr/lib64/python2.4/site-packages/scipy/sandbox/arpack/tests/test_speigs.py
Found 1 tests for __main__
_naupd: Number of update iterations taken
-----------------------------------------
1 - 1: 17
_naupd: Number of wanted "converged" Ritz values
------------------------------------------------
1 - 1: 4
_naupd: Real part of the final Ritz values
------------------------------------------
1 - 4: 1.033E+00 7.746E-01 5.164E-01 2.582E-01
_naupd: Imaginary part of the final Ritz values
-----------------------------------------------
1 - 4: 0.000E+00 0.000E+00 0.000E+00 0.000E+00
_naupd: Associated Ritz estimates
---------------------------------
1 - 4: 4.508E-17 7.450E-22 7.087E-26 4.834E-29
=============================================
= Nonsymmetric implicit Arnoldi update code =
= Version Number: 2.4 =
= Version Date: 07/31/96 =
=============================================
= Summary of timing statistics =
=============================================
Total number update iterations = 17
Total number of OP*x operations = 59
Total number of B*x operations = 0
Total number of reorthogonalization steps = 58
Total number of iterative refinement steps = 0
Total number of restart steps = 0
Total time in user OP*x operation = 0.004000
Total time in user B*x operation = 0.000000
Total time in Arnoldi update routine = 0.008000
Total time in naup2 routine = 0.008000
Total time in basic Arnoldi iteration loop = 0.004000
Total time in reorthogonalization phase = 0.000000
Total time in (re)start vector generation = 0.000000
Total time in Hessenberg eig. subproblem = 0.000000
Total time in getting the shifts = 0.000000
Total time in applying the shifts = 0.000000
Total time in convergence testing = 0.000000
Total time in computing final Ritz vectors = 0.000000
.
----------------------------------------------------------------------
Ran 1 test in 0.107s
OK
/usr/bin/python
/usr/lib64/python2.4/site-packages/scipy/sandbox/arpack/tests/test_arpack.py
Found 5 tests for __main__
.....
----------------------------------------------------------------------
Ran 5 tests in 0.039s
OK
Nils
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