# [petsc-users] Nullspaces

Barry Smith bsmith at petsc.dev
Wed Jan 5 16:17:10 CST 2022

```  What do you get for the two eigenvectors ?

> On Jan 5, 2022, at 11:21 AM, Marco Cisternino <marco.cisternino at optimad.it> wrote:
>
> 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
>>
>>    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
>

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