[petsc-users] [SLEPc] Number of iterations changes with MPI processes in Lanczos

[Ale Foggia]

I've tried the option that you gave me but I still get different number of
iterations when changing the number of MPI processes: I did 960 procs and
1024 procs and I got 435 and 176 iterations, respectively.

El mar., 23 oct. 2018 a las 16:48, Jose E. Roman (<jroman at dsic.upv.es>)
escribió:

>
>
> > El 23 oct 2018, a las 15:46, Ale Foggia <amfoggia at gmail.com> escribió:
> >
> >
> >
> > El mar., 23 oct. 2018 a las 15:33, Jose E. Roman (<jroman at dsic.upv.es>)
> escribió:
> >
> >
> > > El 23 oct 2018, a las 15:17, Ale Foggia <amfoggia at gmail.com> escribió:
> > >
> > > Hello Jose, thanks for your answer.
> > >
> > > El mar., 23 oct. 2018 a las 12:59, Jose E. Roman (<jroman at dsic.upv.es>)
> escribió:
> > > There is an undocumented option:
> > >
> > >   -bv_reproducible_random
> > >
> > > It will force the initial vector of the Krylov subspace to be the same
> irrespective of the number of MPI processes. This should be used for
> scaling analyses as the one you are trying to do.
> > >
> > > What about when I'm not doing the scaling? Now I would like to ask for
> computing time for bigger size problems, should I also use this option in
> that case? Because, what happens if I have a "bad" configuration? Meaning,
> I ask for some time, enough if I take into account the "correct" scaling,
> but when I run it takes double the time/iterations, like it happened before
> when changing from 960 to 1024 processes?
> >
> > When you increase the matrix size the spectrum of the matrix changes and
> probably also the convergence, so the computation time is not easy to
> predict in advance.
> >
> > Okey, I'll keep that in mine. I thought that, even if the spectrum
> changes, if I had a behaviour/tendency for 6 or 7 smaller cases I could
> predict more or less the time. It was working this way until I found this
> "iterations problem" which doubled the time of execution for the same size
> problem. To be completely sure, do you suggest me or not to use this
> run-time option when going in production? Can you elaborate a bit in the
> effect this option? Is the (huge) difference I got in the number of
> iterations something expected?
>
> Ideally if you have a rough approximation of the eigenvector, you set it
> as the initial vector with EPSSetInitialSpace(). Otherwise, SLEPc generates
> a random initial vector, that is start the search blindly. The difference
> between using one random vector or another may be large, depending on the
> problem. Krylov-Schur is usually less sensitive to the initial vector.
>
> Jose
>
> >
> >
> > >
> > > An additional comment is that we strongly recommend to use the default
> solver (Krylov-Schur), which will do Lanczos with implicit restart. It is
> generally faster and more stable.
> > >
> > > I will be doing Dynamical Lanczos, that means that I'll need the
> "matrix whose rows are the eigenvectors of the tridiagonal matrix" (so,
> according to the Lanczos Technical Report notation, I need the "matrix
> whose rows are the eigenvectors of T_m", which should be the same as the
> vectors y_i). I checked the Technical Report for Krylov-Schur also and I
> think I can get the same information also from that solver, but I'm not
> sure. Can you confirm this please?
> > > Also, as the vectors I want are given by V_m^(-1)*x_i=y_i (following
> the notation on the Report), my idea to get them was to retrieve the
> invariant subspace V_m (with EPSGetInvariantSubspace), invert it, and then
> multiply it with the eigenvectors that I get with EPSGetEigenvector. Is
> there another easier (or with less computations) way to get this?
> >
> > In Krylov-Schur the tridiagonal matrix T_m becomes
> arrowhead-plus-tridiagonal. Apart from this, it should be equivalent. The
> relevant information can be obtained with EPSGetBV() and EPSGetDS(). But
> this is a "developer level" interface. We could help you get this running.
> Send a small problem matrix to slepc-maint together with a more detailed
> description of what you need to compute.
> >
> > Thanks! When I get to that part I'll write to slepc-maint for help.
> >
> >
> > Jose
> >
> > >
> > >
> > > Jose
> > >
> > >
> > >
> > > > El 23 oct 2018, a las 12:13, Ale Foggia <amfoggia at gmail.com>
> escribió:
> > > >
> > > > Hello,
> > > >
> > > > I'm currently using Lanczos solver (EPSLANCZOS) to get the smallest
> real eigenvalue (EPS_SMALLEST_REAL) of a Hermitian problem (EPS_HEP). Those
> are the only options I set for the solver. My aim is to be able to
> predict/estimate the time-to-solution. To do so, I was doing a scaling of
> the code for different sizes of matrices and for different number of MPI
> processes. As I was not observing a good scaling I checked the number of
> iterations of the solver (given by EPSGetIterationNumber). I've encounter
> that for the **same size** of matrix (that meaning, the same problem), when
> I change the number of MPI processes, the amount of iterations changes, and
> the behaviour is not monotonic. This are the numbers I've got:
> > > >
> > > > # procs   # iters
> > > > 960          157
> > > > 992          189
> > > > 1024        338
> > > > 1056        190
> > > > 1120        174
> > > > 2048        136
> > > >
> > > > I've checked the mailing list for a similar situation and I've found
> another person with the same problem but in another solver ("[SLEPc] GD is
> not deterministic when using different number of cores", Nov 19 2015), but
> I think the solution this person finds does not apply to my problem
> (removing "-eps_harmonic" option).
> > > >
> > > > Can you give me any hint on what is the reason for this behaviour?
> Is there a way to prevent this? It's not possible to estimate/predict any
> time consumption for bigger problems if the number of iterations varies
> this much.
> > > >
> > > > Ale
> > >
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20181024/43159f99/attachment.html>