[petsc-users] BVNormColumn

[Bikash Kanungo]

Thank you so much, Jose. Loosening the tolerance did the trick!

Thanks again,
Bikash

On Tue, Oct 25, 2016 at 5:25 AM, Jose E. Roman <jroman at dsic.upv.es> wrote:

>
> > El 19 oct 2016, a las 9:54, Jose E. Roman <jroman at dsic.upv.es> escribió:
> >
> >>
> >> El 19 oct 2016, a las 0:26, Bikash Kanungo <bikash at umich.edu> escribió:
> >>
> >> Hi Jose,
> >>
> >> Thanks for the pointers. Here's what I observed on probing it further:
> >>
> >>      • The ||B - B^H|| norm was 1e-18. So I explicitly made it
> Hermitian by setting B = 0.5(B+B^H). However, this didn't help.
> >>      • Next, I checked for the conditioning of B by computing the ratio
> of the highest and lowest eigenvalues. The conditioning of the order 1e-9.
> >>      • I monitored the imaginary the imaginary part of VecDot(y,x,
> dotXY) where y = B*x and noted that only when the imaginary part is more
> than 1e-16 in magnitude, the error of "The inner product is not well
> defined" is flagged. For the first few iterations of orhtogonalization
> (i.e., the one where orthogonization is successful), the values of
> VecDot(y,x, dotXY) are all found to be lower than 1e-16. I guess this small
> imaginary part might be the cause of the error.
> >> Let me know if there is a way to bypass the abort by changing the
> tolerance for imaginary part.
> >>
> >>
> >>
> >> Regards,
> >> Bikash
> >>
> >
> > There is something wrong: the condition number is greater than 1 by
> definition, so it cannot be 1e-9. Anyway, maybe what happens is that your
> matrix has a very small norm. The SLEPc code needs a fix for the case when
> the norm of B or the norm of the vector x is very small. Please send the
> matrix to my personal email and I will make some tests.
> >
> > Jose
>
> I tested with your matrix and vector with two different machines, with
> different compilers, and in both cases the computation did not fail. The
> imaginary part is below the machine precision, as expected. I don't know
> why you are getting larger roundoff error. Anyway, the check that we
> currently have in SLEPc is too strict. You can try relaxing it, by editing
> function BV_SafeSqrt (in $SLEPC_DIR/include/slepc/private/bvimpl.h), for
> instance with this:
>
>   if (PetscAbsReal(PetscImaginaryPart(alpha))>PETSC_MACHINE_EPSILON &&
> PetscAbsReal(PetscImaginaryPart(alpha))/absal>100*PETSC_MACHINE_EPSILON)
> SETERRQ1(PetscObjectComm((PetscObject)bv),1,"The inner product is not
> well defined: nonzero imaginary part %g",PetscImaginaryPart(alpha));
>
> Let us know if this works for you.
> Thanks.
> Jose
>
>


-- 
Bikash S. Kanungo
PhD Student
Computational Materials Physics Group
Mechanical Engineering
University of Michigan
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