[petsc-users] Nullspaces

[Marco Cisternino]

Hello Jose and Stefano.
Thank you, Jose for your hints.
I computed the two smallest eigenvalues of my operator and they are tiny but not zero.
The smallest 0 eigenvalue is = (4.71506e-08, 0) with abs error = 3.95575e-07
The smallest 1 eigenvalue is = (1.95628e-07, 0) with abs error = 4.048e-07
As Stefano remarked, I would have expected much tinier values, closer to zero.
Probably something is wrong in what I do:
    EPS eps;
    EPSCreate(PETSC_COMM_WORLD, &eps);
    EPSSetOperators( eps, matrix, NULL );
    EPSSetWhichEigenpairs(eps, EPS_SMALLEST_MAGNITUDE);
    EPSSetProblemType( eps, EPS_NHEP );
    EPSSetConvergenceTest(eps,EPS_CONV_ABS);
    EPSSetTolerances(eps, 1.0e-10, 1000);
    EPSSetDimensions(eps,2,PETSC_DEFAULT,PETSC_DEFAULT);
    EPSSetFromOptions( eps );
    EPSSolve( eps );

Even commenting " EPSSetTolerances(eps, 1.0e-10, 1000);" and use default values, the results are exactly the same.

Am I correctly computing the 2 smallest eigenvalues?

They should be zeros but they are not. Any suggestions about how understanding why? 

In a previous email Mark remarked: "Also you say you divide by the cell volume. Maybe I am not understanding this but that is basically diagonal scaling and that will change the null space (ie, not a constant anymore)", therefore why does the null space built with MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, nullptr, &nullspace); passes the MatNullSpaceTest??

Thank you all!

Marco Cisternino 

-----Original Message-----
From: Jose E. Roman <jroman at dsic.upv.es> 
Sent: martedì 4 gennaio 2022 19:30
To: Marco Cisternino <marco.cisternino at optimad.it>
Cc: Stefano Zampini <stefano.zampini at gmail.com>; petsc-users <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Nullspaces

To compute more than one eigenpair, call EPSSetDimensions(eps,nev,PETSC_DEFAULT,PETSC_DEFAULT).

To compute zero eigenvalues you may want to use an absolute convergence criterion, with EPSSetConvergenceTest(eps,EPS_CONV_ABS), but then a tolerance of 1e-12 is probably too small. You can try without this, anyway.

Jose


> El 4 ene 2022, a las 18:44, Marco Cisternino <marco.cisternino at optimad.it> escribió:
> 
> Hello Stefano and thank you for your support.
> I never used SLEPc before but I did this:
> right after the matrix loading from file I added the following lines to my shared tiny code
>     MatLoad(matrix, v);
>  
>     EPS eps;
>     EPSCreate(PETSC_COMM_WORLD, &eps);
>     EPSSetOperators( eps, matrix, NULL );
>     EPSSetWhichEigenpairs(eps, EPS_SMALLEST_MAGNITUDE);
>     EPSSetProblemType( eps, EPS_NHEP );
>     EPSSetTolerances(eps, 1.0e-12, 1000);
>     EPSSetFromOptions( eps );
>     EPSSolve( eps );
>  
>     Vec xr, xi; /* eigenvector, x */
>     PetscScalar kr, ki; /* eigenvalue, k */
>     PetscInt j, nconv;
>     PetscReal error;
>     EPSGetConverged( eps, &nconv );
>     for (j=0; j<nconv; j++) {
>         EPSGetEigenpair( eps, j, &kr, &ki, xr, xi );
>         EPSComputeError( eps, j, EPS_ERROR_ABSOLUTE, &error );
>         std::cout << "The smallest eigenvalue is = (" << kr << ", " << ki << ") with error = " << error << std::endl;
>     }
>  
> I launched using
> mpirun -n 1 ./testnullspace -eps_monitor
>  
> and the output is
>  
>   1 EPS nconv=0 first unconverged value (error) -1499.29 (6.57994794e+01)
>   2 EPS nconv=0 first unconverged value (error) -647.468 (5.39939262e+01)
>   3 EPS nconv=0 first unconverged value (error) -177.157 (9.49337698e+01)
>   4 EPS nconv=0 first unconverged value (error) 59.6771 (1.62531943e+02)
>   5 EPS nconv=0 first unconverged value (error) 41.755 (1.41965990e+02)
>   6 EPS nconv=0 first unconverged value (error) -11.5462 (3.60453662e+02)
>   7 EPS nconv=0 first unconverged value (error) -6.04493 (4.60890030e+02)
>   8 EPS nconv=0 first unconverged value (error) -22.7362 (8.67630086e+01)
>   9 EPS nconv=0 first unconverged value (error) -12.9637 
> (1.08507821e+02)
> 10 EPS nconv=0 first unconverged value (error) 7.7234 (1.53561979e+02) 
> …
> 111 EPS nconv=0 first unconverged value (error) -2.27e-08 
> (6.84762319e+00)
> 112 EPS nconv=0 first unconverged value (error) -2.60619e-08 
> (4.45245528e+00)
> 113 EPS nconv=0 first unconverged value (error) -5.49592e-09 
> (1.87798984e+01)
> 114 EPS nconv=0 first unconverged value (error) -9.9456e-09 
> (7.96711076e+00)
> 115 EPS nconv=0 first unconverged value (error) -1.89779e-08 
> (4.15471472e+00)
> 116 EPS nconv=0 first unconverged value (error) -2.05288e-08 
> (2.52953194e+00)
> 117 EPS nconv=0 first unconverged value (error) -2.02919e-08 
> (2.90090711e+00)
> 118 EPS nconv=0 first unconverged value (error) -3.8706e-08 
> (8.03595736e-01)
> 119 EPS nconv=1 first unconverged value (error) -61751.8 
> (9.58036571e-07) Computed 1 pairs The smallest eigenvalue is = 
> (-3.8706e-08, 0) with error = 4.9707e-07
>  
> Am I using SLEPc in the right way at least for the first smallest eigenvalue? If I’m on the right way I can find out how to compute the second one.
>  
> Thanks a lot
>  
> Marco Cisternino