[petsc-dev] GMRES and eigen estimates

[Barry Smith]

  So?

1) You get lucky and CG gives you a zero residual right off the bat while GMRES does not.

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.

   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
>> 
>> 
>