# SymMatrixBasedPLS¶

Symmetric matrix-based probabilistic linear solver.

Probabilistic linear solver updating beliefs over the symmetric system matrix and its inverse. The solver makes use of prior information and iteratively infers the matrix and its inverse by matrix-vector multiplication.

This code implements the method described in Wenger et al. [1].

Parameters:
• policy – Policy returning actions taken by the solver.

• stopping_criterion – Stopping criterion determining when a desired terminal condition is met.

References

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 (Generator | None) – 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:
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 (Generator | None) – Random number generator.

Yields:

solver_state – State of the probabilistic linear solver.

Return type:

Generator[LinearSolverState, None, None]