[petsc-users] Incorrect Eigenvalues when Setting KSP and PC types

[Jose E. Roman]

Greg,

The linear solver table probably needs to be updated. I have tried several Cholesky solvers. With mkl_pardiso I get an explicit error message that it does not support Cholesky with complex scalars. The rest (PETSc, MUMPS, CHOLMOD) give a wrong answer (without error message). The problem is not related to your matrix, nor to shift-and-invert in SLEPc. I tried with ex1.c under PETSC_DIR/src/ksp/ksp/examples/tutorials. The example works in complex scalars, but the matrix is real. As soon as you add complex entries Cholesky fails, for instance adding this:
  ierr = MatSetValue(A,0,1,1.0+PETSC_i,INSERT_VALUES);CHKERRQ(ierr);
  ierr = MatSetValue(A,1,0,1.0-PETSC_i,INSERT_VALUES);CHKERRQ(ierr);

I don't know if it is a bug or that the algorithm cannot support complex Hermitian matrices. Maybe Hong can confirm any of these. In the latter case, I agree that all packages should give an error message, as mkl_pardiso does.

As a side comment, I would suggest using LU instead of Cholesky. Cholesky performs less flops but it does not mean it will be faster - I have seen many cases where it is slower than LU, maybe because in shift-and-invert computations the matrix is often indefinite, so an indefinite factorization is computed rather than Cholesky. Some SLEPc eigensolvers (e.g. LOBPCG) require that the preconditioner is symmetric (Hermitian), but the default solver (Krylov-Schur) is quite robust when you use LU instead of Cholesky in Hermitian problems. And you can always solve the problem as non-Hermitian (the difference in accuracy should not be too noticeable).

Jose


> El 25 sept 2017, a las 7:17, Greg Meyer <gregory.meyer at gmail.com> escribió:
> 
> Hi all,
> 
> Hong--looking at your link, there may be no special algorithm for Hermitian matrices in MUMPS, but that doesn't mean it can't solve them like it would any matrix. Furthermore it appears that Cholesky of complex matrices is supported from this link: https://www.mcs.anl.gov/petsc/documentation/linearsolvertable.html
> 
> So do you or anyone have any idea why I get incorrect eigenvalues?
> 
> Thanks,
> Greg
> 
> On Thu, Sep 21, 2017 at 5:51 PM Greg Meyer <gregory.meyer at gmail.com> wrote:
> Ok, thanks. It seems that PETSc clearly should throw an error in this case instead of just giving incorrect answers? I am surprised that it does not throw an error...
> 
> On Thu, Sep 21, 2017 at 5:24 PM Hong <hzhang at mcs.anl.gov> wrote:
> Greg :
> Yes, they are Hermitian.
>  
> PETSc does not support  Cholesky factorization for Hermitian.
> It seems mumps does not support Hermitian either
> https://lists.mcs.anl.gov/mailman/htdig/petsc-users/2015-November/027541.html
> 
> Hong
> 
> 
> On Thu, Sep 21, 2017 at 3:43 PM Hong <hzhang at mcs.anl.gov> wrote:
> Greg:
> 
> OK, the difference is whether LU or Cholesky factorization is used. But I would hope that neither one should give incorrect eigenvalues, and when I run with the latter it does!
> Are your matrices symmetric/Hermitian?
> Hong
> 
> On Thu, Sep 21, 2017 at 2:05 PM Hong <hzhang at mcs.anl.gov> wrote:
> Gregory :
> Use '-eps_view' for both runs to check the algorithms being used. 
> Hong
> 
> Hi all,
> 
> I'm using shift-invert with EPS to solve for eigenvalues. I find that if I do only
> 
> ...
>   ierr = EPSGetST(eps,&st);CHKERRQ(ierr);
>   ierr = STSetType(st,STSINVERT);CHKERRQ(ierr);
> ...
> 
> in my code I get correct eigenvalues. But if I do 
> 
> ...
>   ierr = EPSGetST(eps,&st);CHKERRQ(ierr);
>   ierr = STSetType(st,STSINVERT);CHKERRQ(ierr);
>   ierr = STGetKSP(st,&ksp);CHKERRQ(ierr);
>   ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
>   ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
>   ierr = PCSetType(pc,PCCHOLESKY);CHKERRQ(ierr);
> ...
> 
> the eigenvalues found by EPS are completely wrong! Somehow I thought I was supposed to do the latter, from the examples etc, but I guess that was not correct? I attach the full piece of test code and a test matrix.
> 
> Best,
> Greg
>