# 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 .
#
# Copyright(C) 2013-2017 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
class LineEnergy:
""" Evaluates an underlying Energy along a certain line direction.
Given an Energy class and a line direction, its position is parametrized by
a scalar step size along the descent direction relative to a zero point.
Parameters
----------
line_position : float
Defines the full spatial position of this energy via
self.energy.position = zero_point + line_position*line_direction
energy : Energy
The Energy object which will be evaluated along the given direction.
line_direction : Field
Direction used for line evaluation. Does not have to be normalized.
offset : float *optional*
Indirectly defines the zero point of the line via the equation
energy.position = zero_point + offset*line_direction
(default : 0.).
Attributes
----------
line_position : float
The position along the given line direction relative to the zero point.
value : float
The value of the energy functional at the given position
directional_derivative : float
The directional derivative at the given position
line_direction : Field
Direction along which the movement is restricted. Does not have to be
normalized.
energy : Energy
The underlying Energy at the given position
Raises
------
NotImplementedError
Raised if
* value, gradient or curvature of the attribute energy are not
implemented.
Notes
-----
The LineEnergy is used in minimization schemes in order perform line
searches. It describes an underlying Energy which is restricted along one
direction, only requiring the step size parameter to determine a new
position.
"""
def __init__(self, line_position, energy, line_direction, offset=0.):
self._line_position = float(line_position)
self._line_direction = line_direction
pos = energy.position \
+ (self._line_position-float(offset))*self._line_direction
self.energy = energy.at(position=pos)
def at(self, line_position):
""" Returns LineEnergy at new position, memorizing the zero point.
Parameters
----------
line_position : float
Parameter for the new position on the line direction.
Returns
-------
LineEnergy object at new position with same zero point as `self`.
"""
return self.__class__(line_position,
self.energy,
self.line_direction,
offset=self.line_position)
@property
def value(self):
return self.energy.value
@property
def line_position(self):
return self._line_position
@property
def line_direction(self):
return self._line_direction
@property
def directional_derivative(self):
res = self.energy.gradient.vdot(self.line_direction)
if abs(res.imag) / max(abs(res.real), 1.) > 1e-12:
print "directional derivative has non-negligible " \
"imaginary part:", res
return res.real