[petsc-users] SLEPc generalized eigenvalue problem question?

[Vijay S. Mahadevan]

> 2) What is EPS?
Eigenvalue Problem Solver (SLEPc).

The "best" eigensolver is problem dependent. You can use arpack if you
have configured slepc with it or else use Krylov-schur to test the
convergence. There are also Davidson family of solvers implemented in
slepc which are quite effective for symmetric Hermitian systems.

Have a look at ex13 in slepc for a generalized eigenproblem and how
the sparse matrices are constructed using MatSetValue. Just like the
petsc options, you should be able to change the type of solver
dynamically from command line.

On Mon, Aug 1, 2011 at 1:41 PM, Matthew Knepley <knepley at gmail.com> wrote:
> On Mon, Aug 1, 2011 at 6:36 PM, John Chludzinski <jchludzinski at gmail.com>
> wrote:
>>
>> These are definitely not dense matrices (>99% zeros).
>> The way I described storing them just happened to be a way I found that
>> worked (for EPS = LAPACK).  But I want to use methods intended for sparse
>> matrices + MPI.
>>
>> Which is the best canonical PETSc form (for the matrices) and best EPS?
>
> 1) MATAIJ
> 2) What is EPS?
>    Matt
>
>>
>> ---John
>>
>> On Mon, Aug 1, 2011 at 2:27 PM, Matthew Knepley <knepley at gmail.com> wrote:
>>>
>>> On Mon, Aug 1, 2011 at 6:22 PM, John Chludzinski <jchludzinski at gmail.com>
>>> wrote:
>>>>
>>>> I'm a newbie with both PETSc & SLEPc and have had some trouble finding
>>>> examples/tutorials for newbies.  I've looked through the examples in the
>>>> PETSc and SLEPc directories but still am having "issues" seeing how to set
>>>> this up for the type of problem I have.
>>>> SLEPc ex7.c is a good place to start but there's still how best to store
>>>> the matrices and which EPS to use (besides LAPACK).
>>>> Found a PDF, "MATRICES IN PETSc", (after much googling) but not sure
>>>> which of the many forms will work and which is best.
>>>
>>> 1) PETSc and SLEPc are designed to be efficient for sparse matrices. If
>>> you want eigenvalues of dense matrices, use Elemental (as I pointed out in a
>>> previous message)
>>> 2) If you generate matrices with C code, why not just call MatSetValues()
>>> for each row in that code?
>>>    Matt
>>>
>>>>
>>>> ---John
>>>>
>>>> On Mon, Aug 1, 2011 at 2:12 PM, John Chludzinski
>>>> <jchludzinski at gmail.com> wrote:
>>>>>
>>>>> I have 2 files (matrices) in simply binary form (IEEE-754, generated by
>>>>> some C code) and wished to get them into canonical "PETSc binary form". So I
>>>>> did:
>>>>> Mat A;
>>>>> PetscScalar *a;
>>>>> ierr = PetscMalloc(SIZE*SIZE*sizeof(PetscScalar),&a);CHKERRQ(ierr);
>>>>> // stored the file into the space malloc'ed for 'a'.
>>>>> MatCreateSeqDense(PETSC_COMM_SELF, n, n, a, &A);
>>>>> MatView(A,PETSC_VIEWER_BINARY_(PETSC_COMM_WORLD));
>>>>> This works when I use: -eps_type lapack.  As long as I store the matrix
>>>>> in column major order.
>>>>> ---John
>>>>> On Mon, Aug 1, 2011 at 1:40 PM, Matthew Knepley <knepley at gmail.com>
>>>>> wrote:
>>>>>>
>>>>>> On Mon, Aug 1, 2011 at 5:27 PM, John Chludzinski
>>>>>> <jchludzinski at gmail.com> wrote:
>>>>>>>
>>>>>>> I create 2 matrices using:
>>>>>>> MatCreateSeqDense(PETSC_COMM_SELF, n, n, Ka, &A);
>>>>>>> MatCreateSeqDense(PETSC_COMM_SELF, n, n, Kb, &B);
>>>>>>> These matrices are 99% zeros ( 16,016,004 entries and 18660
>>>>>>> non-zeros).  They are symmetric and real.  Their tri-diagonal elements are
>>>>>>> non-zero plus a few other entries.
>>>>>>
>>>>>> Please give some justification for doing this? On the surface, it just
>>>>>> seems perverse.
>>>>>>    Matt
>>>>>>
>>>>>>>
>>>>>>> I tried to use ex7 for the generalized eigenvalue problem:
>>>>>>> ./ex7.exe -f1 k.dat -f2 m.dat -eps_gen_hermitian -eps_smallest_real >
>>>>>>> x.out 2>&1
>>>>>>> without specifying an EPS and get:
>>>>>>> Generalized eigenproblem stored in file.
>>>>>>> Reading REAL matrices from binary files...
>>>>>>> Number of iterations of the method: 500
>>>>>>> Number of linear iterations of the method: 4009
>>>>>>> Solution method: krylovschur
>>>>>>> Number of requested eigenvalues: 1
>>>>>>> Stopping condition: tol=1e-07, maxit=500
>>>>>>> Number of converged approximate eigenpairs: 0
>>>>>>> Is krylovschur inappropriate for this problem or have I set up the
>>>>>>> problem incorrectly by using   MatCreateSeqDense(...) to create the matrix
>>>>>>> input files in PETSc binary form?
>>>>>>> ---John
>>>>>>
>>>>>> --
>>>>>> 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
>>>>>
>>>>
>>>
>>>
>>>
>>> --
>>> 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
>>
>
>
>
> --
> 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
>