[petsc-dev] TR: Contribution proposal about the computation of (harmonic) Ritz pairs within GMRES

[Barry Smith]

  Great, Thanks!

> On Nov 20, 2015, at 8:15 PM, Satish Balay <balay at mcs.anl.gov> wrote:
> 
> added the patch in branch balay/add-KSPComputeRitz-patch [over master]
> 
> ran a build with  alltests - and now merged to next.
> 
> Thanks,
> Satish
> 
> On Fri, 20 Nov 2015, Barry Smith wrote:
> 
>> 
>>  Nicolas,
>> 
>>  Sorry about not responding. It would be easier for me  if this was submitted as a pull request.
>> 
>>  Jed and/or Satish,
>> 
>>     Could you please create a branch from the patch file (since you guys love receiving patch files), look at it and then put it into next for testing? ASAP
>> 
>>   Thanks
>> 
>>   Barry
>> 
>> 
>>> On Nov 20, 2015, at 12:00 PM, TARDIEU Nicolas <nicolas.tardieu at edf.fr> wrote:
>>> 
>>> Dear PETSc Team,
>>> 
>>> May I request your opinion of the development proposal in the following mail.
>>> This work has been carried out in the framework of a PhD thesis ; besides the scientific goals, the proposed features are intended to be integrated in the open-source software Code_Aster, a general purpose finite element solver developed at EDF R&D, in particular for nuclear safety assessment.
>>> In order to ensure the perennity of the development, their integration within PETSc is crucial.
>>> 
>>> This is why I gently request your position on their integration in PETSc. Let us know your policy on the subject and do not hesitate to request for extra integration work if needed.
>>> 
>>> Best regards,
>>> Nicolas
>>> 
>>> <image001.png> 
>>> 
>>> Nicolas Tardieu
>>> Head of the Rotating Machinery Group
>>> EDF - R&D 
>>> 
>>> nicolas.tardieu at edf.fr
>>> Tél. : +33 1 47 65 39 05
>>> 
>>> 
>>> 
>>> 
>>> ---------- Forwarded message ----------
>>> From: Sylvain Mercier <sylvainmercier85 at gmail.com>
>>> Date: 2015-11-03 17:09 GMT+01:00
>>> Subject: [petsc-dev] Contribution proposal about the computation of (harmonic) Ritz pairs within GMRES
>>> To: petsc-dev at mcs.anl.gov
>>> 
>>> 
>>> Hi everyone,
>>> 
>>> During my phd thesis, I have worked on solving sequences of linear
>>> systems with slowly varying matrices using GMRES(restart). In
>>> particular, I have developed a preconditioning technique to improve
>>> the action of an existing "first-level preconditioner". This new
>>> method is defined using Ritz or harmonic Ritz vectors obtained at the
>>> end of the solution of a linear system. Then I have developed two
>>> routines in PETSc (that I've called KSPSetComputeRitz and
>>> KSPComputeRitz) in order to compute the (harmonic) Ritz pairs
>>> associated to the smallest or largest (harmonic) Ritz values in
>>> modulus computed from the Hessenberg matrix of the last complete cycle
>>> in GMRES.
>>> 
>>> Beyond the application to the preconditioning technique that I have
>>> developed, this routine can be used to recover approximated eigenpairs
>>> (and not only eigenvalues as already available in PETSc) of the
>>> preconditioned matrix at the end of a solution with GMRES. That is why
>>> I propose this contribution.
>>> 
>>> Two new routines has been developed, similarly to the existing
>>> routines KSPSetComputeEigenvalues and KSPComputeEigenvalues.
>>> 
>>> The first one is called KSPSetComputeRitz and sets a flag so that the
>>> last complete Hessenberg matrix computed with GMRES(restart) will be
>>> stored. Here is the synopsis of the current version (located in
>>> src/ksp/ksp/interface/itfunc.c)
>>> 
>>> PetscErrorCode  KSPSetComputeEigenvalues(KSP ksp,PetscBool flg)
>>> 
>>>        Input Parameters
>>>            ksp   - iterative context obtained from KSPCreate()
>>>            flg     - PETSC_TRUE or PETSC_FALSE
>>> 
>>> 
>>> The second routine aims at computing the Ritz or harmonic Ritz
>>> associated to the smallest or largest values in modulus. Here is the
>>> synopsis of the current version (located in
>>> src/ksp/ksp/impls/gmres/gmreig.c)
>>> 
>>> PetscErrorCode KSPComputeRitz(KSP ksp,PetscBool ritz,PetscBool
>>> small,PetscInt *nrit,Vec S[],PetscReal tetar[],PetscReal tetai[])
>>> 
>>>        Input Parameter
>>>            ksp     - iterative context obtained from KSPCreate()
>>>            ritz      - PETSC_TRUE or PETSC_FALSE to compute Ritz pairs
>>> and harmonic Ritz pairs, respectively
>>>            small   - PETSC_TRUE or PETSC_FALSE to compute pairs
>>> associated to smallest or largest values in modulus, respectively
>>> 
>>>        Input/Output parameter
>>>            n         - The number of required and recovered pairs
>>> 
>>>        Output Parameters
>>>                    S[]     - a multidimensional PETSc vector to store
>>> the (harmonic) Ritz vectors, provided by user with a dimension of at
>>> least n
>>>            tetar   - real part of computed (harmonic) Ritz values, provided
>>> by user with a dimension of at least n
>>>            tetai   - imaginary part of computed (harmonic) Ritz values,
>>> provided by user with a dimension of at least n
>>> 
>>> This routine has been developed whithin GMRES for real-valued linear
>>> systems. Then the (harmonic) Ritz pairs are possibly complex-valued
>>> and conjugated. In this case, two successive columns of S are equal to
>>> the real and the imaginary parts of the vectors. Finally, the routine
>>> KSPSolve_GMRES (located in src/ksp/ksp/impls/gmres/gmreig.c) has been
>>> modified in order to store the Hessenberg matrix and the basis vectors
>>> of the Krylov subspace as soon as a complete cycle has been performed.
>>> 
>>> To conclude, I propose to contribute to PETSc with these developments
>>> (I have followed the conventions detailed in the developer guide).
>>> Please find attached a patch and the modified files.
>>> 
>>> Regards,
>>> Sylvain
>>> 
>>> 
>>> 
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>>> <Ritz_routines.tar.gz>
>>