[petsc-dev] strangness in Chebyshev estimate of eigenvalues

[Matthew Knepley]

On Tue, Aug 25, 2015 at 12:13 PM, Mark Adams <mfadams at lbl.gov> wrote:

>
>
> On Sat, Aug 22, 2015 at 10:39 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>>
>> > On Aug 22, 2015, at 9:26 PM, Mark Adams <mfadams at lbl.gov> wrote:
>> >
>> > Good point.  I can not see any reason to use the initial guess for the
>> eigen estimate.
>>
>>    Why not, won't it better select for the eigen space actually seen by
>> the linear solver since the linear solver starts with that guess? I am just
>> making this up because I haven't looked how the initial guess affects
>> eigenanalysis for Chebyshev  it but ...
>>
>
> I've not looked at it, and it would be hard to because it is not a well
> defined problem.  But, if the initial guess is low frequency then it will
> give a poor estimate for the highest eigen value.  It is not clear to me
> what the relationship is, generally, of an initial guess and the solution,
> spectrally.  Initial guesses will change as the problem evolves but we
> don't update the eigen estimates.  If the user's initial guess happens to
> be zero then god knows what happens. (This is actually the case for the
> XGC1 code!!!)  It adds one more variable in debugging AMG, which is hard
> enough as it is.
>
>
>>
>> >  I would vote for (1).
>> >
>> > Also, I hope cheb->random is the default.
>>
>>    Well then different machines will produce different convergence
>> histories which is annoying for any kind of "no change" daily testing.
>> Except for you, most of the rest of us don't like the random default, sorry
>> :-)
>>
>
> We can use the determinate random number that I added to GAMG (eg, v(i) =
> ((double)(gid(i)*51)%100) - 50.)/50.
>

Wait, why are you doing this? Why not just create a PetscRandom and set the
seed?

   Matt


>
>> >  One of my apps uses a zero RHS for the first solve, just because they
>> did not care about adding some logic like: if (.not. first_solve) solve()
>> Using a zero RHS would be catastrophic.
>>
>>    There code be a check that rhs norm is zero (cost of a global
>> reduction?) and then use a nonzero initial guess to do the eigenanalysis
>>
>
> Too complicated for little gain, or loss even, and requires a reduction.
>
>
>>
>> >  I trust this is true, because the code works, but we should make
>> sure.  And perhaps Cheby should check that that KSPSolve did all of its
>> iterations (ie, DIVERGE_ITS, or whatever).  Getting this wrong leads to
>> silent errors that are a pain to debug.
>>
>>    Good point, the KSPChebyshevComputeExtremeEigenvalues_Private()
>> routine should check that n returned from  KSPGetIterationNumber() is not
>> zero etc.
>>
>>   Barry
>>
>
> So I think we should:
>
> 1) set the initial guess with my new sort of random number (we don't need
> good quality random number here)
> 2) add the check for DIVERGE_ITS, or something, in
> KSPChebyshevComputeExtremeEigenvalues_Private.  Should it stop?  Probably.
>
> Mark
>
>
>>
>> >
>> > I can do this.
>> >
>> > Mark
>> >
>> >
>> >
>> > On Sat, Aug 22, 2015 at 6:35 PM, Barry Smith <bsmith at mcs.anl.gov>
>> wrote:
>> >
>> >    From KSPSolve_Chebyshev()
>> >
>> >      X = ksp->work[0];
>> >       if (cheb->random) {
>> >         B    = ksp->work[1];
>> >         ierr = VecSetRandom(B,cheb->random);CHKERRQ(ierr);
>> >       } else {
>> >         B = ksp->vec_rhs;
>> >       }
>> >       ierr = KSPSolve(cheb->kspest,B,X);CHKERRQ(ierr);
>> >
>> >       if (ksp->guess_zero) {
>> >         ierr = VecZeroEntries(X);CHKERRQ(ierr);
>> >       }
>> >       ierr =
>> KSPChebyshevComputeExtremeEigenvalues_Private(cheb->kspest,&min,&max);CHKERRQ(ierr);
>> >
>> >    This seems to do strange stuff with the initial guess for the
>> eigenanalysis. ksp->work[0] is a work vector used within the Chebyshev
>> algorithm, so at this point in the code it will have just whatever stuff it
>> had in it from a previous Chebyshev solver or a zero the first time
>> through. It seems bad to use this vector as the initial guess for
>> estimator. Then AFTER the KSPSolve() it zeros  ksp->work[0], sometimes? If
>> the original system being solved has zero initial guess, even though the
>> values in X will not be used again. WTF?
>> >
>> >    Shouldn't the code either
>> >
>> > 1) zero X = ksp->work[0] everytime BEFORE the KSPSolve() or
>> > 2) zero X if ksp->guess_zero and otherwise copy into X the initial
>> guess vec_sol from the caller before computing the eigenvalues to use that
>> initial guess in estimating the eigenvalues?
>> >
>> >   Barry
>> >
>> >
>>
>>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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