ConjugateGradientPolicy

class probnum.linalg.solvers.policies.ConjugateGradientPolicy(reorthogonalization_fn_residual=None, reorthogonalization_fn_action=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 \(i \neq j\).

Parameters

• reorthogonalization_fn_residual (Optional[Callable[[ndarray, Iterable[ndarray], LinearOperator], ndarray]]) – 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.

• reorthogonalization_fn_action (Optional[Callable[[ndarray, Iterable[ndarray], LinearOperator], ndarray]]) – Reorthogonalization function, which takes a vector, an orthogonal basis and optionally an inner product and returns a reorthogonalized vector. If not None the computed action is reorthogonalized.

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 (LinearSolverState) – Current state of the linear solver.

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

Returns

Next action to take.

Return type

action