[petsc-users] Condition number of matrix

[Song Gao]

condition number is max_eigenvalue/min_eigenvalue.

so I guess it is max/min 2.829815526858e+06?

2016-08-30 10:03 GMT-04:00 Florian Lindner <mailinglists at xgm.de>:

> Hi,
>
> Am 30.08.2016 um 14:05 schrieb Barry Smith:
> >
> >    The format of .petscrc requires each option to be on its own line
> >
> >> -ksp_view
> >> -pc_type none
> >> -ksp_type gmres
> >> -ksp_monitor_singular_value
> >> -ksp_gmres_restart 1000
>
> Oh man, didn't know that. Sorry! Is using a hash # ok for comments in
> .petscrc?
>
> I added the option accordingly:
>
> -ksp_view
> -pc_type none
> -ksp_type gmres
> -ksp_monitor_singular_value
> -ksp_gmres_restart 1000
>
> petsc outputs a line like:
>
> 550 KSP Residual norm 1.374922291162e-07 % max 1.842011038215e+03 min
> 6.509297234157e-04 max/min 2.829815526858e+06
>
> for each iteration. Sorry about my mathematical illerateness, but where
> can I see the condition number of the matrix?
>
> Thanks,
> Florian
>
> >
> >
> >
> >> On Aug 30, 2016, at 7:01 AM, Florian Lindner <mailinglists at xgm.de>
> wrote:
> >>
> >> Hello,
> >>
> >> there is a FAQ and a Stackoverflow article about getting the condition
> number of a petsc matrix:
> >>
> >> http://www.mcs.anl.gov/petsc/documentation/faq.html#conditionnumber
> >> http://scicomp.stackexchange.com/questions/34/how-can-i-
> estimate-the-condition-number-of-a-large-sparse-matrix-using-petsc
> >>
> >> Both tell me to add:
> >>
> >> -pc_type none -ksp_type gmres -ksp_monitor_singular_value
> -ksp_gmres_restart 1000
> >>
> >> to my options.
> >>
> >> I add the line to .petscrc but nothing happens, no additional output at
> all. I added -ksp_view, so my .petscrc looks
> >> like that:
> >>
> >> -ksp_view
> >> -pc_type none -ksp_type gmres -ksp_monitor_singular_value
> -ksp_gmres_restart 1000
> >>
> >> The complete output is below, but something I wonder about:
> >>
> >> GMRES: restart=30, shouldn't that be 1000
> >>
> >> And where can I read out the condition number approximation?
> >>
> >> Thanks,
> >> Florian
> >>
> >>
> >> KSP Object: 1 MPI processes
> >>  type: gmres
> >>    GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> >>    GMRES: happy breakdown tolerance 1e-30
> >>  maximum iterations=10000
> >>  tolerances:  relative=1e-09, absolute=1e-50, divergence=10000.
> >>  left preconditioning
> >>  using nonzero initial guess
> >>  using PRECONDITIONED norm type for convergence test
> >> PC Object: 1 MPI processes
> >>  type: none
> >>  linear system matrix = precond matrix:
> >>  Mat Object:  C   1 MPI processes
> >>    type: seqsbaij
> >>    rows=14403, cols=14403
> >>    total: nonzeros=1044787, allocated nonzeros=1123449
> >>    total number of mallocs used during MatSetValues calls =72016
> >>        block size is 1
> >> (0) 13:58:35 [precice::impl::SolverInterfaceImpl]:395 in initialize:
> it 1 of 1 | dt# 1 | t 0 of 1 | dt 1 | max dt 1 |
> >> ongoing yes | dt complete no |
> >> (0) 13:58:35 [precice::impl::SolverInterfaceImpl]:446 in advance:
> Iteration #1
> >> KSP Object: 1 MPI processes
> >>  type: gmres
> >>    GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> >>    GMRES: happy breakdown tolerance 1e-30
> >>  maximum iterations=10000
> >>  tolerances:  relative=1e-09, absolute=1e-50, divergence=10000.
> >>  left preconditioning
> >>  using nonzero initial guess
> >>  using PRECONDITIONED norm type for convergence test
> >> PC Object: 1 MPI processes
> >>  type: none
> >>  linear system matrix = precond matrix:
> >>  Mat Object:  C   1 MPI processes
> >>    type: seqsbaij
> >>    rows=14403, cols=14403
> >>    total: nonzeros=1044787, allocated nonzeros=1123449
> >>    total number of mallocs used during MatSetValues calls =72016
> >>        block size is 1
> >
>
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