Merge pull request #506 from ginkgo-project/ilu_pteconditioner_assure…

…_linearity

This vector copy ensures linearity of the preconditioner when iterative solvers are used for the triangular systems.

Without the additional copy, the solution vector is used as initial guess to the second solver, no matter its content. When only doing a few iterations, this initial guess still has a strong influence on the result and, depending what is in the respective initial guess vecotrs, we cannot assume the following equality:
prec(x_1) + prec(x_2) = prec(x_1 + x_2)

(here, prec(x) means applying the preconditioner to a vector x)

Especially for preconditioned GMRES, this leads to errors in the result.

Related PR: #506

include/ginkgo/core/preconditioner/ilu.hpp

@@ -176,9 +176,11 @@ class Ilu : public EnableLinOp<
         set_cache_to(b);
         if (!ReverseApply) {
             l_solver_->apply(b, cache_.intermediate.get());
+            x->copy_from(cache_.intermediate.get());
             u_solver_->apply(cache_.intermediate.get(), x);
         } else {
             u_solver_->apply(b, cache_.intermediate.get());
+            x->copy_from(cache_.intermediate.get());
             l_solver_->apply(cache_.intermediate.get(), x);
         }
     }