> El 1 abr 2017, a las 0:01, Toon Weyens <[email protected]> escribió:
>
> Dear jose,
>
> I have saved the matrices in Matlab format and am sending them to you using
> pCloud. If you want another format, please tell me. Please also note that
> they are about 1.4GB each.
>
> I also attach a typical output of eps_view and log_view in output.txt, for 8
> processes.
>
> Thanks so much for helping me out! I think Petsc and Slepc are amazing
> inventions that really have saved me many months of work!
>
> Regards
I played a little bit with your matrices.
With Krylov-Schur I can solve the problem quite easily. Note that in
generalized eigenvalue problems it is always better to use STSINVERT because
you have to invert a matrix anyway. So instead of setting which=smallest_real,
use shift-and-invert with a target that is close to the wanted eigenvalue. For
instance, with target=-0.005 I get convergence with just one iteration:
$ ./ex7 -f1 A.bin -f2 B.bin -st_ksp_type preonly -st_pc_type lu
-st_pc_factor_mat_solver_package mumps -eps_tol 1e-5 -st_type sinvert
-eps_target -0.005
Generalized eigenproblem stored in file.
Reading COMPLEX matrices from binary files...
Number of iterations of the method: 1
Number of linear iterations of the method: 16
Solution method: krylovschur
Number of requested eigenvalues: 1
Stopping condition: tol=1e-05, maxit=7500
Linear eigensolve converged (1 eigenpair) due to CONVERGED_TOL; iterations 1
---------------------- --------------------
k ||Ax-kBx||/||kx||
---------------------- --------------------
-0.004809-0.000000i 8.82085e-05
---------------------- --------------------
Of course, you don't know a priori where your eigenvalue is. Alternatively, you
can set the target at 0 and get rid of positive eigenvalues with a region
filtering. For instance:
$ ./ex7 -f1 A.bin -f2 B.bin -st_ksp_type preonly -st_pc_type lu
-st_pc_factor_mat_solver_package mumps -eps_tol 1e-5 -st_type sinvert
-eps_target 0 -rg_type interval -rg_interval_endpoints -1,0,-.05,.05 -eps_nev 2
Generalized eigenproblem stored in file.
Reading COMPLEX matrices from binary files...
Number of iterations of the method: 8
Number of linear iterations of the method: 74
Solution method: krylovschur
Number of requested eigenvalues: 2
Stopping condition: tol=1e-05, maxit=7058
Linear eigensolve converged (2 eigenpairs) due to CONVERGED_TOL; iterations 8
---------------------- --------------------
k ||Ax-kBx||/||kx||
---------------------- --------------------
-0.000392-0.000000i 2636.4
-0.004809+0.000000i 318441
---------------------- --------------------
In this case, the residuals seem very bad. But this is due to the fact that
your matrices have huge norms. Adding the option -eps_error_backward
::ascii_info_detail will show residuals relative to the matrix norms:
---------------------- --------------------
k eta(x,k)
---------------------- --------------------
-0.000392-0.000000i 3.78647e-11
-0.004809+0.000000i 5.61419e-08
---------------------- --------------------
Regarding the GD solver, I am also getting the correct solution. I don't know
why you are not getting convergence to the wanted eigenvalue:
$ ./ex7 -f1 A.bin -f2 B.bin -st_ksp_type preonly -st_pc_type lu
-st_pc_factor_mat_solver_package mumps -eps_tol 1e-5 -eps_smallest_real
-eps_ncv 32 -eps_type gd
Generalized eigenproblem stored in file.
Reading COMPLEX matrices from binary files...
Number of iterations of the method: 132
Number of linear iterations of the method: 0
Solution method: gd
Number of requested eigenvalues: 1
Stopping condition: tol=1e-05, maxit=120000
Linear eigensolve converged (1 eigenpair) due to CONVERGED_TOL; iterations 132
---------------------- --------------------
k ||Ax-kBx||/||kx||
---------------------- --------------------
-0.004809+0.000000i 2.16223e-05
---------------------- --------------------
Again, it is much better to use a target instead of smallest_real:
$ ./ex7 -f1 A.bin -f2 B.bin -st_ksp_type preonly -st_pc_type lu
-st_pc_factor_mat_solver_package mumps -eps_tol 1e-5 -eps_type gd -eps_target
-0.005
Generalized eigenproblem stored in file.
Reading COMPLEX matrices from binary files...
Number of iterations of the method: 23
Number of linear iterations of the method: 0
Solution method: gd
Number of requested eigenvalues: 1
Stopping condition: tol=1e-05, maxit=120000
Linear eigensolve converged (1 eigenpair) due to CONVERGED_TOL; iterations 23
---------------------- --------------------
k ||Ax-kBx||/||kx||
---------------------- --------------------
-0.004809-0.000000i 2.06572e-05
---------------------- --------------------
Jose
