[petsc-users] Slepc eigenvectors not orthonormalized

[Barry Smith]

  Forwarding to slepc-maint

> On Oct 13, 2016, at 5:32 PM, Peetz, Darin T <peetz2 at illinois.edu> wrote:
> 
> I've come across an irregularity when extracting the eigenvectors when using the CISS method to solve the eigenvalue problem.  I'm solving a generalized hermitian problem, and it looks like the resulting eigenvectors are M-orthogonalized with each other (the M-inner products of different eigenvectors are approximately 0, as expected), but are normalized using the L2-inner product, not the M-inner product.  Basically, the matrix V'*M*V (V being a matrix composed of the extracted eigenvectors) is diagonal, but the diagonals are much larger than 1, and the matrix V'*V has non-zero diagonals, but the diagonal elements are exactly equal to 1.  
> 
> This only happens if I use the CISS method.  If I use the Arnoldi method for example, the eigenvectors are normalized as expected.  Is there any particular reason for this, or is this an error in the implementation?
> 
> Thanks,
> Darin