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docs/source/concepts/minimization.rst
View file @ eb3a20e3
......@@ -7,18 +7,25 @@ Description of Minimization
:maxdepth: 1
:caption: Minimization Concepts
Conjugate Gradient <../mod/nifty4.minimization.conjugate_gradient>
Descent Minimizer <../mod/nifty4.minimization.descent_minimizer>
Energy <../mod/nifty4.minimization.energy>
Iteration Controller <../mod/nifty4.minimization.iteration_controller>
Line Energy <../mod/nifty4.minimization.line_energy>
Line Search <../mod/nifty4.minimization.line_search>
Line Search Strong Wolfe <../mod/nifty4.minimization.line_search_strong_wolfe>
QuadraticEnergy <../mod/nifty4.minimization.quadratic_energy>
IterationController <../mod/nifty4.minimization.iteration_controller>
GradientNormController <../mod/nifty4.minimization.gradient_norm_controller>
Minimizer <../mod/nifty4.minimization.minimizer>
Nonlinear Cg <../mod/nifty4.minimization.nonlinear_cg>
Quadratic Energy <../mod/nifty4.minimization.quadratic_energy>
Relaxed Newton <../mod/nifty4.minimization.relaxed_newton>
Scipy Minimizer <../mod/nifty4.minimization.scipy_minimizer>
Steepest Descent <../mod/nifty4.minimization.steepest_descent>
VL BFGS <../mod/nifty4.minimization.vl_bfgs>
Gradient Norm Controller <../mod/nifty4.minimization.gradient_norm_controller>
ConjugateGradient <../mod/nifty4.minimization.conjugate_gradient>
NonlinearCG <../mod/nifty4.minimization.nonlinear_cg>
ScipyMinimizer <../mod/nifty4.minimization.scipy_minimizer>
LineEnergy <../mod/nifty4.minimization.line_energy>
LineSearch <../mod/nifty4.minimization.line_search>
LineSearchStrongWolfe <../mod/nifty4.minimization.line_search_strong_wolfe>
DescentMinimizer <../mod/nifty4.minimization.descent_minimizer>
SteepestDescent <../mod/nifty4.minimization.steepest_descent>
RelaxedNewton <../mod/nifty4.minimization.relaxed_newton>
VL_BFGS <../mod/nifty4.minimization.vl_bfgs>
nifty4/minimization/descent_minimizer.py
View file @ eb3a20e3
......@@ -11,7 +11,7 @@
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2017 Max-Planck-Society
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
......@@ -50,7 +50,7 @@ class DescentMinimizer(Minimizer):
Parameters
----------
nergy : Energy
energy : Energy
Energy object which provides value, gradient and curvature at a
specific position in parameter space.
......@@ -105,4 +105,17 @@ class DescentMinimizer(Minimizer):
@abc.abstractmethod
def get_descent_direction(self, energy):
""" Calculates the next descent direction.
Parameters
----------
energy : Energy
An instance of the Energy class which shall be minimized. The
position of `energy` is used as the starting point of minimization.
Returns
-------
Field
The descent direction.
"""
raise NotImplementedError
nifty4/minimization/energy.py
View file @ eb3a20e3
......@@ -11,7 +11,7 @@
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2017 Max-Planck-Society
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
......@@ -31,19 +31,6 @@ class Energy(with_metaclass(NiftyMeta, type('NewBase', (object,), {}))):
position : Field
The input parameter of the scalar function.
Attributes
----------
position : Field
The Field location in parameter space where value, gradient and
curvature are evaluated.
value : np.float
The value of the energy functional at given `position`.
gradient : Field
The gradient at given `position`.
curvature : LinearOperator, callable
A positive semi-definite operator or function describing the curvature
of the potential at the given `position`.
Notes
-----
An instance of the Energy class is defined at a certain location. If one
......@@ -76,7 +63,7 @@ class Energy(with_metaclass(NiftyMeta, type('NewBase', (object,), {}))):
Returns
-------
out : Energy
Energy
Energy object at new position.
"""
return self.__class__(position)
......@@ -92,14 +79,16 @@ class Energy(with_metaclass(NiftyMeta, type('NewBase', (object,), {}))):
@property
def value(self):
"""
The value of the energy functional at given `position`.
float
The value of the energy functional at given `position`.
"""
raise NotImplementedError
@property
def gradient(self):
"""
The gradient at given `position`.
Field
The gradient at given `position`.
"""
raise NotImplementedError
......@@ -107,14 +96,16 @@ class Energy(with_metaclass(NiftyMeta, type('NewBase', (object,), {}))):
@memo
def gradient_norm(self):
"""
The length of the gradient at given `position`.
float
The length of the gradient at given `position`.
"""
return self.gradient.norm()
@property
def curvature(self):
"""
A positive semi-definite operator or function describing the curvature
of the potential at the given `position`.
LinearOperator
A positive semi-definite operator or function describing the
curvature of the potential at the given `position`.
"""
raise NotImplementedError
nifty4/minimization/line_energy.py
View file @ eb3a20e3
......@@ -11,7 +11,7 @@
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2017 Max-Planck-Society
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
......@@ -37,34 +37,12 @@ class LineEnergy(object):
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.):
......@@ -73,11 +51,11 @@ class LineEnergy(object):
self._line_direction = line_direction
if self._line_position == float(offset):
self.energy = energy
self._energy = energy
else:
pos = energy.position \
+ (self._line_position-float(offset))*self._line_direction
self.energy = energy.at(position=pos)
self._energy = energy.at(position=pos)
def at(self, line_position):
""" Returns LineEnergy at new position, memorizing the zero point.
......@@ -93,24 +71,32 @@ class LineEnergy(object):
"""
return LineEnergy(line_position, self.energy, self.line_direction,
offset=self.line_position)
return LineEnergy(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
def energy(self):
"""
Energy
The underlying Energy object
"""
return self._energy
@property
def line_direction(self):
return self._line_direction
def value(self):
"""
float
The value of the energy functional at given `position`.
"""
return self._energy.value
@property
def directional_derivative(self):
res = self.energy.gradient.vdot(self.line_direction)
"""
float
The directional derivative at the given `position`.
"""
res = self._energy.gradient.vdot(self._line_direction)
if abs(res.imag) / max(abs(res.real), 1.) > 1e-12:
from ..dobj import mprint
mprint("directional derivative has non-negligible "
......
nifty4/minimization/minimizer.py
View file @ eb3a20e3
......@@ -11,7 +11,7 @@
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2017 Max-Planck-Society
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
......@@ -30,7 +30,7 @@ class Minimizer(with_metaclass(NiftyMeta, type('NewBase', (object,), {}))):
Parameters
----------
energy : Energy object
energy : Energy
Energy object which provides value, gradient and curvature at a
specific position in parameter space.
......
nifty4/minimization/relaxed_newton.py
View file @ eb3a20e3
......@@ -11,7 +11,7 @@
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2017 Max-Planck-Society
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
......@@ -21,6 +21,11 @@ from .line_search_strong_wolfe import LineSearchStrongWolfe
class RelaxedNewton(DescentMinimizer):
""" 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.
"""
def __init__(self, controller, line_searcher=LineSearchStrongWolfe()):
super(RelaxedNewton, self).__init__(controller=controller,
line_searcher=line_searcher)
......@@ -28,23 +33,4 @@ class RelaxedNewton(DescentMinimizer):
self.line_searcher.preferred_initial_step_size = 1.
def get_descent_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
An instance of the Energy class which shall be minized. The
position of `energy` is used as the starting point of minization.
Returns
-------
descent_direction : Field
Returns the descent direction with proposed step length. In a
quadratic potential this corresponds to the optimal step.
"""
return -energy.curvature.inverse_times(energy.gradient)
nifty4/minimization/scipy_minimizer.py
View file @ eb3a20e3
......@@ -11,7 +11,7 @@
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2017 Max-Planck-Society
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
......
nifty4/minimization/steepest_descent.py
View file @ eb3a20e3
......@@ -12,7 +12,7 @@ from __future__ import division
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2017 Max-Planck-Society
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
......@@ -22,21 +22,10 @@ from .descent_minimizer import DescentMinimizer
class SteepestDescent(DescentMinimizer):
def get_descent_direction(self, energy):
""" Implementation of the steepest descent minimization scheme.
Also known as 'gradient descent'. This algorithm simply follows the
functional's gradient for minization.
""" Implementation of the steepest descent minimization scheme.
Parameters
----------
energy : Energy
An instance of the Energy class which shall be minized. The
position of `energy` is used as the starting point of minization.
Returns
-------
descent_direction : Field
the descent direction.
"""
Also known as 'gradient descent'. This algorithm simply follows the
functional's gradient for minimization.
"""
def get_descent_direction(self, energy):
return -energy.gradient
nifty4/minimization/vl_bfgs.py
View file @ eb3a20e3
......@@ -11,7 +11,7 @@
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2017 Max-Planck-Society
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
......@@ -25,6 +25,20 @@ from .line_search_strong_wolfe import LineSearchStrongWolfe
class VL_BFGS(DescentMinimizer):
"""Implementation of the Vector-free L-BFGS minimization scheme.
Find the descent direction by using the inverse Hessian.
Instead of storing the whole matrix, it stores only the last few
updates, which are used to do operations requiring the inverse
Hessian product. The updates are represented in a new basis to optimize
the algorithm.
References
----------
W. Chen, Z. Wang, J. Zhou, "Large-scale L-BFGS using MapReduce", 2014,
Microsoft
"""
def __init__(self, controller, line_searcher=LineSearchStrongWolfe(),
max_history_length=5):
super(VL_BFGS, self).__init__(controller=controller,
......@@ -36,41 +50,14 @@ class VL_BFGS(DescentMinimizer):
return super(VL_BFGS, self).__call__(energy)
def get_descent_direction(self, energy):
"""Implementation of the Vector-free L-BFGS minimization scheme.
Find the descent direction by using the inverse Hessian.
Instead of storing the whole matrix, it stores only the last few
updates, which are used to do operations requiring the inverse
Hessian product. The updates are represented in a new basis to optimize
the algorithm.
Parameters
----------
energy : Energy
An instance of the Energy class which shall be minized. The
position of `energy` is used as the starting point of minization.
Returns
-------
descent_direction : Field
Returns the descent direction.
References
----------
W. Chen, Z. Wang, J. Zhou, "Large-scale L-BFGS using MapReduce", 2014,
Microsoft
"""
x = energy.position
gradient = energy.gradient
# initialize the information store if it doesn't already exist
try:
self._information_store.add_new_point(x, gradient)
except AttributeError:
self._information_store = InformationStore(self.max_history_length,
x0=x,
gradient=gradient)
self._information_store = _InformationStore(
self.max_history_length, x0=x, gradient=gradient)
b = self._information_store.b
delta = self._information_store.delta
......@@ -82,7 +69,7 @@ class VL_BFGS(DescentMinimizer):
return descent_direction
class InformationStore(object):
class _InformationStore(object):
"""Class for storing a list of past updates.
Parameters
......
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