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

[Ale Foggia]

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?

>
> 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?


> 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
>
>
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