[petsc-users] SLEPc generalized eigenvalue problem question?

[John Chludzinski]

Jose,

I used:

MatCreateSeqAIJ(PETSC_COMM_SELF, n, n, 0, cnt, &A);
MatSetValue(A, i, j, *(a+i*SIZE+j), INSERT_VALUES);

to create the input matrices.  Their sizes collapsed dramatically: from
192208072 to 239944. But again, using: ./ex7.exe -f1 k.dat -f2 m.dat
-eps_gen_hermitian -eps_smallest_real > x.out 2>&1, I 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

I'm really only interested in the least 50 eigenvalues.

Smallest 10 eigenvalues
-0.000019
-0.000004
-0.000000
0.000005
0.000012
0.000016
2.795284
2.795307
21.235339
21.235340
81.582017

Largest 10 eigenvalues
176431487319.625000
176431532012.467468
176431562378.361359
176435480628.136292
176435488209.944031
176435555689.747253
176435563270.922424
663312473823.916260
663312473823.917969
663312666285.928589
663312666285.929810

On Mon, Aug 1, 2011 at 1:46 PM, Jose E. Roman <jroman at dsic.upv.es> wrote:

El 01/08/2011, a las 19:27, John Chludzinski escribió:
>
> > 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.
> >
> > 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
>
>
>
> The solver has reached the maximum number of iterations. Do you want to
> compute the leftmost part of the spectrum? Are those eigenvalues
> (relatively) large in magnitude? I guess not. If you need the smallest
> eigenvalues, instead of computing the smallest eigenvalues of (K,M) try
> computing the largest eigenvalues of (M,K) and then compute the reciprocals.
> Also, have a look at the chapter on spectral transformations.
>
> And of course do not use dense matrices, as pointed out by Matt.
>  Jose
>
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