[petsc-dev] GMRES and eigen estimates

Mark F. Adams mark.adams at columbia.edu
Wed Apr 4 08:38:04 CDT 2012 

On Apr 3, 2012, at 7:16 PM, Barry Smith wrote:

> 
> 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.
> 

        [0]PCSetUp_GAMG 2 levels, grid complexity = 1.00391
  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
Linear solve did not converge due to DIVERGED_INDEFINITE_MAT iterations 8

Perhaps the beta went below zero ....

>> 
>>> 
>>> 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.  

No

> Another use for the debugger to see what convergence test it is using and what norm type
> 

It is not hitting KSPDefaultConverged in the eigen estimate.  Does KSP_NORM_NONE switch to a different converged method ...

Mark

>   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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