BayesCG¶
- class probnum.linalg.solvers.BayesCG(stopping_criterion=<probnum.LambdaStoppingCriterion object>)¶
Bases:
ProbabilisticLinearSolverBayesian conjugate gradient method.
Probabilistic linear solver taking prior information about the solution and choosing \(A\)-conjugate actions to gain information about the solution by projecting the current residual.
This code implements the method described in Cockayne et al. 1.
- Parameters
stopping_criterion – Stopping criterion determining when a desired terminal condition is met.
References
- 1
Cockayne, J. et al., A Bayesian Conjugate Gradient Method, Bayesian Analysis, 2019
Methods Summary
solve(prior, problem[, rng])Solve the linear system.
solve_iterator(prior, problem[, rng])Generator implementing the solver iteration.
Methods Documentation
- solve(prior, problem, rng=None)¶
Solve the linear system.
- Parameters
prior (LinearSystemBelief) – Prior belief about the quantities of interest \((x, A, A^{-1}, b)\) of the linear system.
problem (LinearSystem) – Linear system to be solved.
- Returns
belief – Posterior belief \((\mathsf{x}, \mathsf{A}, \mathsf{H}, \mathsf{b})\) over the solution \(x\), the system matrix \(A\), its (pseudo-)inverse \(H=A^\dagger\) and the right hand side \(b\).
solver_state – Final state of the solver.
- Return type
- solve_iterator(prior, problem, rng=None)¶
Generator implementing the solver iteration.
This function allows stepping through the solver iteration one step at a time and exposes the internal solver state.
- Parameters
prior (LinearSystemBelief) – Prior belief about the quantities of interest \((x, A, A^{-1}, b)\) of the linear system.
problem (LinearSystem) – Linear system to be solved.
- Yields
solver_state – State of the probabilistic linear solver.
- Return type
Generator[LinearSolverState, None, None]