ell1 norm convergence test

[Ryan Yan]

Matt, thanks for letting me be aware of this.

Yan

On Mon, Sep 21, 2009 at 3:33 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Sep 21, 2009 at 2:29 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>>
>>   Likely it is too expensive to use the 1-norm for stopping criteria for
>> fgmres unless you can reformulate fgmres to give you back the residual
>> efficiently.
>>
>
> I have been told that QMR has a natural 1-norm formulation, but I have
> never seen it.
>
>   Matt
>
>
>>   Barry
>>
>> On Sep 21, 2009, at 2:04 PM, Ryan Yan wrote:
>>
>>  Hi Barry,
>>> Thanks for the suggestion.
>>>
>>> I am using FGMRES as the krylov solver.  Is there a direct access to the
>>> residual vector for FGMRES. I guess the answer is yes, since that's the
>>> Krylov method which supports right preconditioning and provides the true
>>> residual 2_Norm monitor, right?
>>>
>>> If so, which header should I include to fetch the residual directly from
>>> KSP_FGMRES?
>>>
>>> Yan
>>>
>>>
>>>
>>> On Mon, Sep 21, 2009 at 2:43 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>>
>>>  Yan,
>>>
>>>   This depends on the Krylov method being used. For example with GMRES
>>> the residual vector is NOT available at each iteration (the 2-norm of the
>>> residual is approximated via a recurrence relationship).
>>>
>>>   You can call KSPBuildResidual() to have the true residual computed for
>>> you. Note: it is expensive because it actually builds the current solution
>>> and computes r = b - A*x
>>>
>>>  What we intended is that if you want the residual efficiently for
>>> example for the CG method, you determine what Krylov method you want to use
>>> the include the appropriate private include file and access the residual
>>> directly from the data structure. This would be efficient. (but like I said
>>> does not work for all methods). For cg include src/ksp/ksp/impls/cg/cgctx.h
>>>
>>>
>>>  Barry
>>>
>>>
>>> On Sep 21, 2009, at 12:44 PM, Ryan Yan wrote:
>>>
>>> Hi All,
>>> The following question is only for test and comparison reason.
>>>
>>> Is there a command line option to set up using 1-Norm(sum of absolute
>>> value of residuals)  as convergence monitor and test.
>>>
>>> Alternatively, if I can get the residual "r" out at the end of each
>>> iteration, then it is going to be much simpler, since I can just call
>>> VecNorm(r, NORM_1, &r_ell1) and pass the r_ell1 into the convergence monitor
>>> and test. Can anyone inform me if PETSc has an interface for the resuidual
>>> r?
>>>
>>> Or one has to call the convergence test:
>>> MyKSPConverged(ksp,n,rnorm,flag,dummy);
>>> and following the steps:
>>> 1. fetch the exact solution:
>>>
>>> KSPBuildSolution(ksp,PETSC_NULL_OBJECT,x,ierr)
>>>
>>> 2. calculate the residual:
>>>
>>> pass the Right Hand side and the Matrix in to calculate the 1-Norm. But
>>> this step is *not* obvious, since the matrix and rhs is already distributed
>>> over each processes.
>>>
>>> 3. set up the convergence test based on the 1_Norm residual.
>>>
>>>
>>> Thank you very much,
>>>
>>>
>>> Yan
>>>
>>>
>>>
>>
>
>
> --
> 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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