[Trilinos-Users] Sparse matrix and Anasazi Solvers,

[Alicia Klinvex]

Hello Mike,

I'm pretty sure your Trilinos code is NOT using shift-and-invert with BKS.
 (Shift-and-invert is the spectral transformation I described before.)  If
you want to use shift-and-invert, you must construct the linear solver
yourself and give it to the BKS solver manager.  Some examples of that can
be found on this page:
http://trilinos.org/docs/r11.12/packages/anasazi/doc/html/examples.html

If you want to use a sparse factorization, then the Amesos example should
be of interest to you.  If you want to use a preconditioned Krylov method
to solve the linear systems that arise at each iteration of BKS, then look
at the Belos example.  Let me know if those examples don't make sense to
you.

Best wishes,
Alicia

Disclaimer: I am an external collaborator at Sandia, and I did not write
the BKS code.  I can help you with the mechanics of getting things to run,
but Heidi Thornquist and Rich Lehoucq (who are also on the user mailing
list) would probably know more about how to get good performance out of BKS
and block Davidson.

On Thu, Feb 5, 2015 at 1:50 PM, Mike Atambo <mikeat4999 at gmail.com> wrote:

> Alicia,
> Im still trying to figure  out what exactly im facing. Maybe what you
> described be the issue, but  at this
> point i would prefer to try out what you have suggested, if it works, then
> it would be certain thats what im facing,
> if not, then i can rule that out.
> Please let me know how to  set the krylov-shur  solver   as you suggested,
> here are the parameters i pass to  the anasaziPL   for Krylov-Shur at the
> moment:
>
>   const double tol = 1.0e-8;
>   const int maxIters = 500;
>   anasaziPL.set ("Which", "SR");
>   anasaziPL.set ("Block Size",1 );
>   //anasaziPL.set ("Maximum Iterations", maxIters);
>   anasaziPL.set ("Convergence Tolerance", tol);
>   anasaziPL.set ("Full Ortho", true);
>   anasaziPL.set ("Use Locking", true);
>
> Mike.
>
>
> On Thu, Feb 5, 2015 at 5:47 PM, Alicia Klinvex <aklinvex at purdue.edu>
> wrote:
>
>> Hi Mike,
>>
>> If ARPACK is working for you and block Krylov-Schur is not, I suspect
>> that one is using a spectral transformation and the other is not.
>>
>> I don't know much about scipy's eigs, but I assume it is similar to
>> Matlab's eigs (which also uses ARPACK).  When you ask Matlab's eigs to find
>> the smallest eigenvalues of a matrix, it will automatically transform the
>> problem of finding the smallest eigenpairs of A x = \lambda x into the
>> equivalent problem of finding the largest eigenpairs of A^{-1} x =
>> \lambda^{-1}x.  Anasazi's Krylov Schur does not do that unless you
>> explicitly tell it to.  Could that be the problem you're having?  If so, we
>> can discuss how to tell Krylov-Schur that's what you want to do.
>>
>> Best wishes,
>> Alicia Klinvex
>>
>> On Thu, Feb 5, 2015 at 11:21 AM, Mike Atambo <mikeat4999 at gmail.com>
>> wrote:
>>
>>> Hi,
>>> Im unable to get matrices,  ( say a sparse matrix with
>>> 885500 non zeros  out of  about  2822796900 )   to converge
>>> with the block davison or the krylov solver,
>>>
>>> I had a look at the condition number reported by the 'ILUT'
>>> preconditioner and it seems to grow rather quickly for my  problems,  ( 9x9
>>>  with 39 non zeros has  condition number= 10,   and at    25*25 and 100 non
>>> zeros the condition number is at 250).
>>>
>>> Im able to solve all these examples here using scipy.sparse.eigs  (it
>>> uses ARPACK),  so there is probably something that im not doing right.
>>>
>>> The block-davidson solver with 'ILUT' pre-conditioner   work for the
>>> small systems above,   but  beyond  300*300 matrix size,  this is not
>>> longer true.
>>>
>>> At the moment im  following these steps.
>>>
>>> 1.  Create and initialize a matrix,
>>> 2.  Create an anasazi basic eigenproblem,
>>> 3.  Create a  solver (either block davidson or krylov-shur)
>>> 4.   Get solution,
>>>
>>> Id like to find out whether there is a way to tell why the system  im
>>> working on seems
>>> to be  unable to converge.  Any help would be appreciated.
>>>
>>> Mike
>>>
>>>
>>> --
>>> M. O. Atambo
>>> mikeat4999 at gmail.com
>>> matambo at ictp.it
>>> Ext .139
>>>
>>>
>>>
>>> _______________________________________________
>>> Trilinos-Users mailing list
>>> Trilinos-Users at software.sandia.gov
>>> https://software.sandia.gov/mailman/listinfo/trilinos-users
>>>
>>>
>>
>
>
> --
> M. O. Atambo
> mikeat4999 at gmail.com
> matambo at ictp.it
> Ext .139
> Room 209.
>
>
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