ConjugateGradientPolicy

class itergp.methods.policies.ConjugateGradientPolicy(precond_inv=None, reorthogonalization_fn_residual=None)

Bases: LinearSolverPolicy

Policy returning \(A\)-conjugate actions.

Selects the negative gradient / residual as an initial action \(s_0 = b - A x_0\) and then successively generates \(A\)-conjugate actions, i.e. the actions satisfy \(s_i^\top A s_j = 0\) iff \(i \neq j\). If a preconditioner inverse \(P^{-1}\) is supplied, the actions are orthogonal with respect to the \(P^{-\frac{1}{2}}AP^{-\frac{\top}{2}}\) inner product.

Parameters

• precond_inv (Optional[LinearOperatorLike]) – Preconditioner inverse.

• reorthogonalization_fn_residual (Optional[Callable[[backend.Array, Iterable[backend.Array], linops.LinearOperator], backend.Array]]) – Reorthogonalization function, which takes a vector, an orthogonal basis and optionally an inner product and returns a reorthogonalized vector. If not None the residuals are reorthogonalized before the action is computed.

Return type

None

Methods Summary

__call__(solver_state[, rng])

Return an action for a given solver state.

Methods Documentation

__call__(solver_state, rng=None)

Return an action for a given solver state.

Parameters

• solver_state (probnum.linalg.solvers.LinearSolverState) – Current state of the linear solver.

• rng (Optional[Generator]) – Random number generator.

Returns

Next action to take.

Return type

action