[Trilinos-Users] PyTrilinos + Anasazi - Generalized eigenproblem
mbudisic at engineering.ucsb.edu
Mon Dec 22 14:38:51 MST 2008
yes, after I rescaled the auxiliary vector to unit norm, everything
seems to work just fine on the larger problems, even without changing
the "Orthogonalization" setting.
I believe I am set right now. If I run into some other problems, I will
e-mail to the list. Thanks a lot once again for all your help.
Chris Baker wrote:
> Hi Marko,
> It looks like the problem where the solver would freeze with an
> auxiliary vector is some combination of the orthogonalization routine
> and the small problem size. I suggest you start running with a larger
> sample problem, at least 10 x 10. For the case that the solver seems to
> freeze, it should be possible to fix this via:
> I played around on some row-stochastic matrices to verify that deflating
> against the (normalized) ones() vector worked.
> On Mon, Dec 22, 2008 at 13:28, Marko Budisic
> <mbudisic at engineering.ucsb.edu <mailto:mbudisic at engineering.ucsb.edu>>
> Hi Chris,
> thank you for all your responses, especially those over the weekend.
> I wasn't trying to rush you in my last e-mail, I was just
> summarizing all my questions because I wanted to make them clear at
> the end of the e-mail so you didn't have to decode what I was
> actually asking for in the end. The discussion with you was
> extremely helpful with my understanding of the code and it's a
> pleasure to have such responsive support on the other end.
> As for the problem, I resorted to solving the generalized
> eigenproblem in the exact way you suggested and I'm glad to say that
> it is working well. My original matrix A might end up being
> symmetric in some cases too, so I will try the Davidson solver in
> those cases.
> All of the things being said, it seems that it is only Monday and
> that the prospects are good for my problems to be resolved, thanks
> to you and Heidi in the past weeks, so I am glad that is the case.
> Chris Baker wrote:
> Hello Marko,
> I am currently looking into the reason that Anasazi+PyTrilinos
> becomes unresponsive when using Auxilliary vectors.
> Am I right to assume that one use of AuxVecs would be to used for
> removing "known" eigenvectors from the process? In my case, I
> often have row-stochastic matrices. Most of the times, they will
> have the largest eigenvalue at 1 with eigenspace being the vector
> filled with ones (the diagonal of the vector space). Would
> passing a
> vector filled with ones ( via say PutScalar(1.0) ) to AuxVecs
> choosing "LM" as the sorting method) make the code return the
> largest evalue/evector as the result (assuming NEV = 1)?
> In any case, I have tried working a bit more with the AuxVecs
> to see
> why the code was not responsive before. It seems that AuxVecs
> vectors have to be of length 1
> Also correct. In fact, for multiple auxiliary vectors, they must
> form an orthonormal basis.
> In this case however, this is the last thing the code prints
> to the
> screen (even with all verbosity options turned on) but it still
> continues to run at 100% CPU. I waited for some time but it never
> exited or printed other messages so I ended up killing the
> Yeah, I'm currently investigating this. We don't see this
> problem with Anasazi in general, so I am leaning toward some
> Python issue.
> When I pass the unit length vector to AuxVecs, the code runs but
> fails (and exits to command prompt) with
> Anasazi::SVQBOrthoManager::findBasis(): Orthogonalization
> constraints not feasible
> This is because the auxiliary vectors add another constraint on
> the orthogonalization routine. Your 5x5 example just doesn't
> have enough room to move around: 1 vector for the auxiliary
> vector plus 3 vectors minimum for BKS plus 1 additional vector
> because the problem is non-Hermitian (this gives us extra room
> to keep from splitting a conjugate pair).
> Having said that, I don't believe this is the cause for the
> problem with setAuxVecs(). I ran on a larger matrix and still
> saw the freezing.
> To summarize, my main question is the one stated at the
> about the use ot AuxVecs, the rest of the e-mail was more of a
> followup to your answer. Of course, I am still interested in an
> answer to my previous question about why the generalized
> eigenproblem acts as the regular eigenproblem in PyTrilinos
> (explained in my previous e-mails).
> Solving generalized eigenvalue problems with BlockKrylovSchur
> requires a little more work. I neglected to tell you this in my
> previous email, because my brain doesn't work properly on the
> weekend. In short, the generalized eigenvalue problem must be
> transformed into a standard eigenvalue problem to work with BKS.
> (/This is not the case with the other Anasazi eigensolvers, but
> they don't solve non-Hermitian problems, so they are not
> relevant to you./)
> In your particular case (searching for the largest magnitude
> eigenvalues of (W,Dsum)), construct a linear operator
> Op = inv(Dsum) W
> This transforms the eigenvalue problem to
> inv(Dsum) W v = v lambda
> The eigenvectors and eigenvalues are unchanged from the
> generalized eigenvalue problem.
> Pass Op to the BasicEigenproblem class, either by setOp() or
> setA(). If a matrix is passed via setM(), it is used for the
> inner product defining orthogonality. The benefit of doing that
> is to restore symmetry in Op and to handle certain special
> cases. In your case, W was not symmetric, so that symmetry in
> inv(Dsum) W cannot be easily restored. I would not pass anything
> to setM().
> However, in your case, because Dsum is a diagonal matrix,
> applying the operator inv(Dsum) W serves to implicitly scale the
> entries of W on every application of the operator. In this case,
> it is probably better to simply scale them once in situ, as you
> were doing before, and consider simply the standard eigenvalue
> I hope this helps. Even more, I hope this is correct; after all,
> it is only Monday.
> I'm still looking at the setAuxVecs() problem with
> Anasazi+PyTrilinos. I will respond to you and the list when it
> is diagnosed.
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