Cholesky

class itergp.methods.Cholesky(atol=1e-06, rtol=1e-06, maxrank=None)

Bases: ProbabilisticLinearSolver

Cholesky decomposition.

Parameters

• atol – Absolute tolerance.

• rtol – Relative tolerance.

• maxrank – Maximum rank of the factorization.

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.

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

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

Tuple[LinearSystemBelief, LinearSolverState]

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.

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

Yields

solver_state – State of the probabilistic linear solver.

Return type

Generator[LinearSolverState, None, None]