# NIFTy
# Copyright (C) 2017 Theo Steininger
#
# Author: Theo Steininger
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see .
from .quasi_newton_minimizer import QuasiNewtonMinimizer
from .line_searching import LineSearchStrongWolfe
class RelaxedNewton(QuasiNewtonMinimizer):
""" A implementation of the relaxed Newton minimization scheme.
The relaxed Newton minimization exploits gradient and curvature information to
propose a step. A linesearch optimizes along this direction.
Parameter
---------
line_searcher : LineSearch,
An implementation of a line-search algorithm.
callback : function, *optional*
Function f(energy, iteration_number) specified by the user to print
iteration number and energy value at every iteration step. It accepts
an Energy object(energy) and integer(iteration_number). (default: None)
convergence_tolerance : float,
Specifies the required accuracy for convergence. (default : 10e-4)
convergence_level : integer
Specifies the demanded level of convergence. (default : 3)
iteration_limit : integer
Limiting the maximum number of steps. (default : None)
"""
def __init__(self, line_searcher=LineSearchStrongWolfe(), callback=None,
convergence_tolerance=1E-4, convergence_level=3,
iteration_limit=None):
super(RelaxedNewton, self).__init__(
line_searcher=line_searcher,
callback=callback,
convergence_tolerance=convergence_tolerance,
convergence_level=convergence_level,
iteration_limit=iteration_limit)
self.line_searcher.prefered_initial_step_size = 1.
def _get_descend_direction(self, energy):
""" Calculates the descent direction according to a Newton scheme.
The descent direction is determined by weighting the gradient at the
current parameter position with the inverse local curvature, provided by the
Energy object.
Parameters
----------
energy : Energy
The energy object providing implementations of the to be minimized function,
its gradient and curvature.
Returns
-------
out : Field
Returns the descent direction with proposed step length. In a quadratic
potential this corresponds to the optimal step.
"""
gradient = energy.gradient
curvature = energy.curvature
descend_direction = curvature.inverse_times(gradient)
return descend_direction * -1