AsymmetricMatrixBasedSolver

class probnum.linalg.AsymmetricMatrixBasedSolver(A, b, x0)

Bases: probnum.linalg.ProbabilisticLinearSolver

Asymmetric matrix-based probabilistic linear solver.

Parameters

• A (array-like or LinearOperator or RandomVariable, shape=(n,n)) – The square matrix or linear operator of the linear system.

• b (array_like, shape=(n,) or (n, nrhs)) – Right-hand side vector or matrix in \(A x = b\).

Methods Summary

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

Methods Documentation

has_converged(iter, maxiter, **kwargs)

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, maxiter=None, atol=None)

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.