[petsc-users] Computing condition number

[Matthew Knepley]

On Tue, Sep 20, 2016 at 6:44 AM, Florian Lindner <mailinglists at xgm.de>
wrote:

> Hello,
>
> to compute / approximate the condition number of a MATSBAIJ, I put
>
> -ksp_view
>
> # Conditon number estimate
> -pc_type none
> -ksp_type gmres
> -ksp_monitor_singular_value
> -ksp_gmres_restart 1000
>
> in my .petscrc
>
> Output is like:
>
> [...]
> 566 KSP Residual norm 1.241765807317e-07 % max 7.020130499234e+02 min
> 6.429054752025e-04 max/min 1.091938203983e+06
> 567 KSP Residual norm 1.219340847328e-07 % max 7.020130499278e+02 min
> 6.423976501709e-04 max/min 1.092801397609e+06
> 568 KSP Residual norm 1.198886059519e-07 % max 7.020130499320e+02 min
> 6.419283878172e-04 max/min 1.093600257062e+06
> 569 KSP Residual norm 1.178377018879e-07 % max 7.020130499362e+02 min
> 6.414517591235e-04 max/min 1.094412853268e+06
> KSP Object: 8 MPI processes
>   type: gmres
>     GMRES: restart=1000, 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: 8 MPI processes
>   type: none
>   linear system matrix = precond matrix:
>   Mat Object:  C   8 MPI processes
>     type: mpisbaij
>     rows=14404, cols=14404
>     total: nonzeros=1059188, allocated nonzeros=1244312
>     total number of mallocs used during MatSetValues calls =75272
>         block size is 1
> (0) 13:30:20 [precice::impl::SolverInterfaceImpl]:380 in initialize: it 1
> of 1 | dt# 1 | t 0 of 1 | dt 1 | max dt 1 |
> ongoing yes | dt complete no |
> (0) 13:30:20 [precice::mapping::PetRadialBasisFctMapping]:519 in map:
> Mapping Data consistent from MeshA (ID 0) to MeshB
> (ID 1)
>   0 KSP Residual norm 1.178378120697e-07 % max 1.000000000000e+00 min
> 1.000000000000e+00 max/min 1.000000000000e+00
> KSP Object: 8 MPI processes
>   type: gmres
>     GMRES: restart=1000, 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: 8 MPI processes
>   type: none
>   linear system matrix = precond matrix:
>   Mat Object:  C   8 MPI processes
>     type: mpisbaij
>     rows=14404, cols=14404
>     total: nonzeros=1059188, allocated nonzeros=1244312
>     total number of mallocs used during MatSetValues calls =75272
>         block size is 1
>
>
> The approximate condition number is the max/min value, 1.094412853268e+06
> here?
>

Yes.

  Thanks,

    Matt


> Just make sure my mathematical illerateracy does not spoil my report...
>
>
> Best thanks,
> Florian
>



-- 
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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