Does ILU(0) applied to a symmetric matrix give a symmetric preconditioner?

[nncarlson]

I'm attempting to use ILU as a preconditioner for a Krylov method (not from Hypre). The matrix is symmetric and I require a symmetric preconditioner. My limited understanding is that a single iteration with ILU(0) ought to be symmetric, however it's immediately evident from the Krylov solver that this isn't the case. When I instead swap in BoomerAMG for ILU everything is good. I'm following the pattern outlined in the manual to configure ILU(0) as a preconditioner:

HYPRE_ILUCreate(&ilu_solver);
HYPRE_ILUSetType(ilu_solver, 0);
HYPRE_ILUSetLevelOfFill(ilu_solver, 0);
HYPRE_ILUSetMaxIter(ilu_solver, 1);
HYPRE_ILUSetTol(ilu_solver, 0.0);
HYPRE_ILUSetup(ilu_solver, parcsr_A, b, x);
HYPRE_ILUSolve(ilu_solver, parcsr_A, b, x);

Am I needing something additional here to ensure symmetry, or am I mistaken about ILU(0) being symmetric given a symmetric matrix?
FWIW, I've tried the exact same code as a preconditioner in a nonlinear iteration where symmetry isn't involved, and it works well.

[liruipeng]

No, it doesn't ensure symmetry given a symmetric matrix. We may add ILDL-type preconditioner in the future to ensure symmetry or IC-type for SPD. But none is available now. Sorry.

[nncarlson]

Thanks for the quick response. If you've got a feature request list, please do add this -- both ILDL (actually my present case) and IC. Do you happen to know whether PILUT or Euclid support this?

[liruipeng]

@nncarlson We will add it. To the best of my knowledge, I don't think PILUT or Euclid supports this. Thanks

[victorapm]

@nncarlson, given the problem is symmetric, you might want to take a look at our sparse approximate inverse (FSAI) preconditioner. It can also be used as relaxation method in BoomerAMG

More info can be found at: https://hypre.readthedocs.io/en/latest/solvers-fsai.html