[petsc-dev] GMRES and eigen estimates

Barry Smith bsmith at mcs.anl.gov
Tue Apr 3 18:16:25 CDT 2012 

On Apr 3, 2012, at 5:40 PM, Mark F. Adams wrote:

> 
> On Apr 3, 2012, at 5:05 PM, Barry Smith wrote:
> 
>> 
>> 
>> So?
>> 
>> 1) You get lucky and CG gives you a zero residual right off the bat while GMRES does not.
> 
> I don't quite understand the CG results.  I assume that CG applies the preconditioner before the iteration (I recall seeing that in the code at one point) and so it never sees a residual.

   Since with CG Norm_none turns off computation of norms the monitor number printed is meaningless (happens to be zero so you see zero).  I suppose we could error out if norm_none is used with monitor

>  GMRES seems to have different behavior ...

    GMRES ignores the norm_none option since the algorithm needs the norm so it is computed and is printed out with monitoring.

> CG also seems to stop after 7 iterations. Not clear why that happens (max its is set to 10).

   You could run with -ksp_converged_reason or in the debugger to see why it is stopping at 7.

> 
>> 
>> 2)  "I turn off norms for this -- its in the eigen estimate -- because I don't usually want them. "    But doesn't GMRES compute the norms always? So why not have the GMRES version still kick out early if the norm reduces by same 10^10 before it ran out of its? (Since the norm is "free" for GMRES there is no harm done, and good things occasionly like your case below.
>> 
> 
> I use this code:
> 
>          ierr = KSPSetNormType( eksp, KSP_NORM_NONE );                 CHKERRQ(ierr);
>          ierr = KSPSetOptionsPrefix(eksp,((PetscObject)pc)->prefix);CHKERRQ(ierr);
>          ierr = KSPAppendOptionsPrefix( eksp, "gamg_est_");         CHKERRQ(ierr);
>          ierr = KSPSetFromOptions( eksp );    CHKERRQ(ierr);
> 
> So I assume that the KSP_NORM_NONE turns off convergence checking.

PetscErrorCode  KSPDefaultConverged(KSP ksp,PetscInt n,PetscReal rnorm,KSPConvergedReason *reason,void *ctx)
{
  PetscErrorCode         ierr;
  KSPDefaultConvergedCtx *cctx = (KSPDefaultConvergedCtx*) ctx;
  KSPNormType            normtype;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ksp,KSP_CLASSID,1);
  PetscValidPointer(reason,4);
  *reason = KSP_CONVERGED_ITERATING;
  
  ierr = KSPGetNormType(ksp,&normtype);CHKERRQ(ierr);
  if (normtype == KSP_NORM_NONE) SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_ARG_WRONGSTATE,"Use KSPSkipConverged() with KSPNormType of KSP_NORM_NONE");

   So I do not understand why it isn't generating that error message for you? Are you using KSPSkipConverged in the code or something.  Another use for the debugger to see what convergence test it is using and what norm type

   Barry

> 
> Mark
> 
> 
>>  Barry
>> 
>> 
>> On Apr 3, 2012, at 3:46 PM, Mark F. Adams wrote:
>> 
>>> Sorry false alarm.
>>> 
>>> Running in KSP tutorials (this creates a GASM PC that is just one block with the whole domain):
>>> 
>>> ./ex54 -ne 5 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_verbose 2 -pc_gamg_use_agg_gasm -mat_coarsen_type hem -pc_gamg_square_graph false -mg_levels_sub_pc_type lu -gamg_est_ksp_type gmres -options_left -ksp_monitor -gamg_est_ksp_monitor_singular_value -gamg_est_ksp_view
>>> 
>>> I get:
>>> 
>>> 0 KSP Residual norm 6.446415297424e+01 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>> 1 KSP Residual norm 2.366096117202e-14 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>> 2 KSP Residual norm 1.540964857879e-14 % max 1.693380955892e+00 min 7.781997678493e-01 max/min 2.176023465763e+00
>>> 3 KSP Residual norm 1.241326996942e-14 % max 2.530597391197e+00 min 7.364405777662e-01 max/min 3.436254692636e+00
>>> 4 KSP Residual norm 1.063574617851e-14 % max 3.476067169257e+00 min 7.236790329140e-01 max/min 4.803327181195e+00
>>> 5 KSP Residual norm 9.458672353406e-15 % max 4.436589616128e+00 min 7.159721822673e-01 max/min 6.196594959987e+00
>>> 6 KSP Residual norm 8.601272732515e-15 % max 5.409099625105e+00 min 7.111665034107e-01 max/min 7.605953878822e+00
>>> 7 KSP Residual norm 7.941524085286e-15 % max 6.390434791698e+00 min 7.078275282801e-01 max/min 9.028237157187e+00
>>> 8 KSP Residual norm 7.413487448731e-15 % max 7.377240678599e+00 min 7.053779875665e-01 max/min 1.045856378939e+01
>>> 9 KSP Residual norm 6.978470326179e-15 % max 8.367510521210e+00 min 7.035029387897e-01 max/min 1.189406619339e+01
>>> 10 KSP Residual norm 6.612020575839e-15 % max 9.360078579306e+00 min 7.020212846961e-01 max/min 1.333304101080e+01
>>> 
>>> The problem is that I turn off norms for this -- its in the eigen estimate -- because I don't usually want them.  Here they would have stopped the iterations and all would have been good.
>>> 
>>> BTW, CG does this:
>>> 
>>> 0 KSP Residual norm 0.000000000000e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>> 1 KSP Residual norm 0.000000000000e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>> 2 KSP Residual norm 0.000000000000e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>> 3 KSP Residual norm 0.000000000000e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>> 4 KSP Residual norm 0.000000000000e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>> 5 KSP Residual norm 0.000000000000e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>> 6 KSP Residual norm 0.000000000000e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>> 7 KSP Residual norm 0.000000000000e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>>                      PCSetUp_GAMG PC setup max eigen=1.000000e+00 min=0.000000e+00 on level 1 (N=36)
>>> 
>>> Is it using a preconditioned norm perhaps....
>>> 
>>> Mark
>>> 
>>> On Apr 3, 2012, at 2:06 PM, Barry Smith wrote:
>>> 
>>>> 
>>>> barry-smiths-macbook-pro:tutorials barrysmith$ ./ex10 -f0 ~/Datafiles/Matrices/arco1 -pc_type lu -ksp_type gmres -ksp_monitor_singular_value
>>>> 0 KSP Residual norm 2.544968574075e+03 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>>> 1 KSP Residual norm 2.708628636814e-10 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>>> Number of iterations =   1
>>>> Residual norm 2.36559e-11
>>>> barry-smiths-macbook-pro:tutorials barrysmith$ ./ex10 -f0 ~/Datafiles/Matrices/arco1 -pc_type lu -ksp_type fgmres -ksp_monitor_singular_value
>>>> 0 KSP Residual norm 7.410897708964e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>>> 1 KSP Residual norm 2.157675690523e-11 % max 9.999999999999e-01 min 9.999999999999e-01 max/min 1.000000000000e+00
>>>> Number of iterations =   1
>>>> Residual norm 2.26094e-11
>>>> barry-smiths-macbook-pro:tutorials barrysmith$ ./ex10 -f0 ~/Datafiles/Matrices/arco1 -pc_type lu -ksp_type cg -ksp_monitor_singular_value
>>>> 0 KSP Residual norm 2.544968574075e+03 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
>>>> 1 KSP Residual norm 3.135993325987e-10 % max 9.999999999999e-01 min 9.999999999999e-01 max/min 1.000000000000e+00
>>>> Number of iterations =   1
>>>> Residual norm 2.22684e-11
>>>> 
>>>> Mark,
>>>> 
>>>> Could you provide the exact specifications on how you obtained this bad highest eigen estimate? What code you ran with what options?
>>>> 
>>>> Thanks
>>>> 
>>>> barry
>>>> 
>>>> 
>>>> On Mar 30, 2012, at 10:22 AM, Mark F. Adams wrote:
>>>> 
>>>>> I've had problems with GMRES and eigen estimates in the past but I now have a smoking gun.  It seems that if you give GMRES an operator preconditioned with LU (ie, the preconditioned operator is the identity) GMRES gives me a highest eigen estimate of ~10 (way off).  With CG I get a prefect max=1.0, min=0.0.
>>>>> 
>>>>> Any thoughts?
>>>>> 
>>>>> Mark
>>>> 
>>>> 
>>> 
>> 
>> 
>

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