# MatrixBasedSolver¶

class probnum.linalg.solvers.MatrixBasedSolver(A, b, x0=None)[source]

Bases: abc.ABC

Abstract class for matrix-based probabilistic linear solvers.

Parameters
• A (array-like or LinearOperator or RandomVariable, shape=(n,n)) – A square matrix or linear operator. A prior distribution can be provided as a RandomVariable. If an array or linear operator is given, a prior distribution is chosen automatically.

• b (RandomVariable, shape=(n,) or (n, nrhs)) – Right-hand side vector, matrix or RandomVariable of $$A x = b$$.

• x0 (array-like, shape=(n,) or (n, nrhs)) – Optional. Guess for the solution of the linear system.

Methods Summary

 has_converged(iter, maxiter, **kwargs) Check convergence of a linear solver. solve([callback]) Solve the linear system $$Ax=b$$.

Methods Documentation

has_converged(iter, maxiter, **kwargs)[source]

Check convergence of a linear solver.

Evaluates a set of convergence criteria based on its input arguments to decide whether the iteration has converged.

Parameters
• iter (int) – Current iteration of solver.

• maxiter (int) – Maximum number of iterations

Returns

• has_converged (bool) – True if the method has converged.

• convergence_criterion (str) – Convergence criterion which caused termination.

solve(callback=None, **kwargs)[source]

Solve the linear system $$Ax=b$$.

Parameters
• callback (function, optional) – User-supplied function called after each iteration of the linear solver. It is called as callback(xk, Ak, Ainvk, sk, yk, alphak, resid, **kwargs) and can be used to return quantities from the iteration. Note that depending on the function supplied, this can slow down the solver.

• kwargs – Key-word arguments adjusting the behaviour of the solve iteration. These are usually convergence criteria.

Returns

• x (RandomVariable, shape=(n,) or (n, nrhs)) – Approximate solution $$x$$ to the linear system. Shape of the return matches the shape of b.

• A (RandomVariable, shape=(n,n)) – Posterior belief over the linear operator.

• Ainv (RandomVariable, shape=(n,n)) – Posterior belief over the linear operator inverse $$H=A^{-1}$$.

• info (dict) – Information on convergence of the solver.