By default, it is solving the problem as B^{-1}*A*x=lambda*x (see chapter on
Spectral Transformation). That is why A can be a shell matrix without problem.
But B needs to be an explicit matrix in order to compute an LU factorization.
If B is also a shell matrix then you should set an iterative solver for the
associated KSP (see examples in the chapter).
An alternative is to create a shell matrix M that computes the action of
B^{-1}*A, then pass M to the EPS solver as a standard eigenproblem.
Jose
> El 12 jul 2023, a las 19:04, Quentin Chevalier
> <quentin.cheval...@polytechnique.edu> escribió:
>
> Hello PETSc Users,
>
> I have a generalised eigenvalue problem : Ax= lambda Bx
> I used to have only A as a matrix-free method, I used mumps and an LU
> preconditioner, everything worked fine.
>
> Now B is matrix-free as well, and my solver is returning an error :
> "MatSolverType mumps does not support matrix type python", which is ironic
> given it seem to handle A quite fine.
>
> I have read in the user manual here that there some methods may require
> additional methods to be supplied for B like MATOP_GET_DIAGONAL but it's
> unclear to me exactly what I should be implementing and what is the best
> solver for my case.
>
> A is hermitian, B is hermitian positive but not positive-definite or real.
> Therefore I have specified a GHEP problem type to the EPS object.
>
> I use PETSc in complex mode through the petsc4py bridge.
>
> Any help on how to get EPS to work for a generalised matrix-free case would
> be welcome. Performance is not a key issue here - I have a tractable high
> value case on hand.
>
> Thank you for your time,
>
> Quentin
