krypy.recycling - Recycling Linear Systems Solvers

The recycling module provides functions for the solution of sequences of linear algebraic systems. Once a linear system has been solved, the generated data is examined and a deflation space is determined automatically for the solution of the next linear system. Several selection strategys are available.

class krypy.recycling.RecyclingCg(*args, **kwargs)

Bases: krypy.recycling.linsys._RecyclingSolver

Recycling preconditioned CG method.

See _RecyclingSolver for the documentation of the available parameters.

class krypy.recycling.RecyclingMinres(*args, **kwargs)

Bases: krypy.recycling.linsys._RecyclingSolver

Recycling preconditioned MINRES method.

See _RecyclingSolver for the documentation of the available parameters.

class krypy.recycling.RecyclingGmres(*args, **kwargs)

Bases: krypy.recycling.linsys._RecyclingSolver

Recycling preconditioned GMRES method.

See _RecyclingSolver for the documentation of the available parameters.

class krypy.recycling.linsys._RecyclingSolver(DeflatedSolver)

Base class for recycling solvers.

Initialize recycling solver base.

Parameters:DeflatedSolver – a deflated solver from deflation.

After a run of the provided DeflatedSolver via solve(), the resulting instance of the DeflatedSolver is available in the attribute last_solver.

last_solver = None

DeflatedSolver instance from last run of solve().

Instance of DeflatedSolver that resulted from the last call to solve(). Initialized with None before the first run.

last_timings = None

Timings from last run of solve().

Timings have to be filled after each run of solve() and has to be a dictionary holding the time needed for applying A, M, Ml, Mr, ip, axpy.

solve(linear_system, vector_factory=None, *args, **kwargs)

Solve the given linear system with recycling.

The deflation vectors and the Krylov subspace of the last solve() call are examined and considered for deflation according to the provided deflation_vector_factory.


All remaining arguments are passed to the DeflatedSolver.

Returns:instance of DeflatedSolver which was used to obtain the approximate solution. The approximate solution is available under the attribute xk.