nifty8.minimization.conjugate_gradient module

class ConjugateGradient(controller, nreset=20)

Bases: Minimizer

Implementation of the Conjugate Gradient scheme.

It is an iterative method for solving a linear system of equations:

Ax = b

Parameters:

• controller (nifty8.IterationController) – Object that decides when to terminate the minimization.

• nreset (int) – every nreset CG steps the residual will be recomputed accurately by applying the operator instead of updating the old residual

References

Jorge Nocedal & Stephen Wright, “Numerical Optimization”, Second Edition, 2006, Springer-Verlag New York

__call__(energy, preconditioner=None)

Runs the conjugate gradient minimization.

Parameters:

• energy (Energy object at the starting point of the iteration.) – Its metric operator must be independent of position, otherwise linear conjugate gradient minimization will fail.

• preconditioner (Operator optional) – This operator can be provided which transforms the variables of the system to improve the conditioning. Default: None.

Returns:

• QuadraticEnergy – state at last point of the iteration

• int – Can be controller.CONVERGED or controller.ERROR

__init__(controller, nreset=20)