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Commit 9d6729d2 authored by Martin Reinecke's avatar Martin Reinecke
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merge better_minimizers

parents 45e3eb9b 576aa27e
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Showing with 484 additions and 422 deletions
nifty/energies/__init__.py
View file @ 9d6729d2
......@@ -17,5 +17,6 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from .energy import Energy
from .quadratic_energy import QuadraticEnergy
from .line_energy import LineEnergy
from .memoization import memo
nifty/energies/energy.py
View file @ 9d6729d2
......@@ -17,6 +17,7 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from ..nifty_meta import NiftyMeta
from .memoization import memo
from keepers import Loggable
from future.utils import with_metaclass
......@@ -41,7 +42,7 @@ class Energy(with_metaclass(NiftyMeta, type('NewBase', (Loggable, object), {})))
value : np.float
The value of the energy functional at given `position`.
gradient : Field
The gradient at given `position` in parameter direction.
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`.
......@@ -108,12 +109,32 @@ class Energy(with_metaclass(NiftyMeta, type('NewBase', (Loggable, object), {})))
@property
def gradient(self):
"""
The gradient at given `position` in parameter direction.
The gradient at given `position`.
"""
raise NotImplementedError
@property
@memo
def gradient_norm(self):
"""
The length of the gradient at given `position`.
"""
return self.gradient.norm()
@property
@memo
def gradient_infnorm(self):
"""
The infinity norm of the gradient at given `position`.
"""
return abs(self.gradient).max()
@property
def curvature(self):
"""
......
nifty/energies/quadratic_energy.py 0 → 100644
View file @ 9d6729d2
from .energy import Energy
from .memoization import memo
class QuadraticEnergy(Energy):
"""The Energy for a quadratic form.
The most important aspect of this energy is that its curvature must be
position-independent.
"""
def __init__(self, position, A, b, grad=None):
super(QuadraticEnergy, self).__init__(position=position)
self._A = A
self._b = b
if grad is not None:
self._Ax = grad + self._b
else:
self._Ax = self._A(self.position)
def at(self, position):
return self.__class__(position=position, A=self._A, b=self._b)
def at_with_grad(self, position, grad):
return self.__class__(position=position, A=self._A, b=self._b,
grad=grad)
@property
@memo
def value(self):
return 0.5*self.position.vdot(self._Ax) - self._b.vdot(self.position)
@property
@memo
def gradient(self):
return self._Ax - self._b
@property
def curvature(self):
return self._A
nifty/minimization/__init__.py
View file @ 9d6729d2
......@@ -17,7 +17,11 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from .line_searching import *
from .iteration_controller import IterationController
from .default_iteration_controller import DefaultIterationController
from .minimizer import Minimizer
from .conjugate_gradient import ConjugateGradient
from .nonlinear_cg import NonlinearCG
from .descent_minimizer import DescentMinimizer
from .steepest_descent import SteepestDescent
from .vl_bfgs import VL_BFGS
......
nifty/minimization/conjugate_gradient.py
View file @ 9d6729d2
......@@ -19,10 +19,10 @@
from __future__ import division
import numpy as np
from keepers import Loggable
from .minimizer import Minimizer
class ConjugateGradient(Loggable, object):
class ConjugateGradient(Minimizer):
""" Implementation of the Conjugate Gradient scheme.
It is an iterative method for solving a linear system of equations:
......@@ -30,43 +30,11 @@ class ConjugateGradient(Loggable, object):
Parameters
----------
convergence_tolerance : float *optional*
Tolerance specifying the case of convergence. (default: 1E-4)
convergence_level : integer *optional*
Number of times the tolerance must be undershot before convergence
is reached. (default: 3)
iteration_limit : integer *optional*
Maximum number of iterations performed (default: None).
reset_count : integer *optional*
Number of iterations after which to restart; i.e., forget previous
conjugated directions (default: None).
controller : IterationController
Object that decides when to terminate the minimization.
preconditioner : Operator *optional*
This operator can be provided which transforms the variables of the
system to improve the conditioning (default: None).
callback : callable *optional*
Function f(energy, iteration_number) supplied by the user to perform
in-situ analysis at every iteration step. When being called the
current energy and iteration_number are passed. (default: None)
Attributes
----------
convergence_tolerance : float
Tolerance specifying the case of convergence.
convergence_level : integer
Number of times the tolerance must be undershot before convergence
is reached. (default: 3)
iteration_limit : integer
Maximum number of iterations performed.
reset_count : integer
Number of iterations after which to restart; i.e., forget previous
conjugated directions.
preconditioner : function
This operator can be provided which transforms the variables of the
system to improve the conditioning (default: None).
callback : callable
Function f(energy, iteration_number) supplied by the user to perform
in-situ analysis at every iteration step. When being called the
current energy and iteration_number are passed. (default: None)
References
----------
......@@ -75,140 +43,73 @@ class ConjugateGradient(Loggable, object):
"""
def __init__(self, convergence_tolerance=1E-4, convergence_level=3,
iteration_limit=None, reset_count=None,
preconditioner=None, callback=None):
self.convergence_tolerance = np.float(convergence_tolerance)
self.convergence_level = np.float(convergence_level)
if iteration_limit is not None:
iteration_limit = int(iteration_limit)
self.iteration_limit = iteration_limit
def __init__(self, controller, preconditioner=None):
self._preconditioner = preconditioner
self._controller = controller
if reset_count is not None:
reset_count = int(reset_count)
self.reset_count = reset_count
if preconditioner is None:
preconditioner = lambda z: z
self.preconditioner = preconditioner
self.callback = callback
def __call__(self, A, b, x0):
def __call__(self, energy):
""" Runs the conjugate gradient minimization.
For `Ax = b` the variable `x` is infered.
Parameters
----------
A : Operator
Operator `A` applicable to a Field.
b : Field
Result of the operation `A(x)`.
x0 : Field
Starting guess for the minimization.
energy : Energy object at the starting point of the iteration.
Its curvature operator must be independent of position, otherwise
linear conjugate gradient minimization will fail.
Returns
-------
x : Field
Latest `x` of the minimization.
convergence : integer
Latest convergence level indicating whether the minimization
has converged or not.
energy : QuadraticEnergy
state at last point of the iteration
status : integer
Can be controller.CONVERGED or controller.ERROR
"""
r = b - A(x0)
d = self.preconditioner(r)
controller = self._controller
status = controller.start(energy)
if status != controller.CONTINUE:
return energy, status
r = -energy.gradient
if self._preconditioner is not None:
d = self._preconditioner(r)
else:
d = r.copy()
previous_gamma = (r.vdot(d)).real
if previous_gamma == 0:
self.logger.info("The starting guess is already perfect solution "
"for the inverse problem.")
return x0, self.convergence_level+1
norm_b = np.sqrt((b.vdot(b)).real)
x = x0.copy()
convergence = 0
iteration_number = 1
self.logger.info("Starting conjugate gradient.")
beta = np.inf
delta = np.inf
return energy, controller.CONVERGED
while True:
if self.callback is not None:
self.callback(x, iteration_number)
q = energy.curvature(d)
ddotq = d.vdot(q).real
if ddotq==0.:
self.logger.error("Alpha became infinite! Stopping.")
return energy, controller.ERROR
alpha = previous_gamma/ddotq
q = A(d)
alpha = previous_gamma/d.vdot(q).real
if alpha < 0:
self.logger.warn("Positive definiteness of A violated!")
return energy, controller.ERROR
if not np.isfinite(alpha):
self.logger.error(
"Alpha became infinite! Stopping. Iteration : %08u "
"alpha = %3.1E beta = %3.1E delta = %3.1E" %
(iteration_number, alpha, beta, delta))
return x0, 0
r -= q * alpha
energy = energy.at_with_grad(energy.position+d*alpha,-r)
x += d * alpha
status = self._controller.check(energy)
if status != controller.CONTINUE:
return energy, status
reset = False
if alpha < 0:
self.logger.warn("Positive definiteness of A violated!")
reset = True
if self.reset_count is not None:
reset += (iteration_number % self.reset_count == 0)
if reset:
self.logger.info("Computing accurate residuum.")
r = b - A(x)
if self._preconditioner is not None:
s = self._preconditioner(r)
else:
r -= q * alpha
s = r
s = self.preconditioner(r)
gamma = r.vdot(s).real
if gamma < 0:
self.logger.warn("Positive definitness of preconditioner "
"violated!")
beta = max(0, gamma/previous_gamma)
delta = np.sqrt(gamma)/norm_b
self.logger.debug("Iteration : %08u alpha = %3.1E "
"beta = %3.1E delta = %3.1E" %
(iteration_number, alpha, beta, delta))
self.logger.warn(
"Positive definiteness of preconditioner violated!")
if gamma == 0:
convergence = self.convergence_level+1
self.logger.info(
"Reached infinite convergence. Iteration : %08u "
"alpha = %3.1E beta = %3.1E delta = %3.1E" %
(iteration_number, alpha, beta, delta))
break
elif abs(delta) < self.convergence_tolerance:
convergence += 1
self.logger.info("Updated convergence level to: %u" %
convergence)
if convergence == self.convergence_level:
self.logger.info(
"Reached target convergence level. Iteration : %08u "
"alpha = %3.1E beta = %3.1E delta = %3.1E" %
(iteration_number, alpha, beta, delta))
break
else:
convergence = max(0, convergence-1)
return energy, controller.CONVERGED
if self.iteration_limit is not None:
if iteration_number == self.iteration_limit:
self.logger.info(
"Reached iteration limit. Iteration : %08u "
"alpha = %3.1E beta = %3.1E delta = %3.1E" %
(iteration_number, alpha, beta, delta))
break
d = s + d * max(0, gamma/previous_gamma)
d = s + d * beta
iteration_number += 1
previous_gamma = gamma
return x, convergence
nifty/minimization/default_iteration_controller.py 0 → 100644
View file @ 9d6729d2
# 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 <http://www.gnu.org/licenses/>.
#
# 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.
from __future__ import print_function
from .iteration_controller import IterationController
class DefaultIterationController(IterationController):
def __init__ (self, tol_abs_gradnorm=None, tol_rel_gradnorm=None,
convergence_level=1, iteration_limit=None, name=None,
verbose=None):
super(DefaultIterationController, self).__init__()
self._tol_abs_gradnorm = tol_abs_gradnorm
self._tol_rel_gradnorm = tol_rel_gradnorm
self._convergence_level = convergence_level
self._iteration_limit = iteration_limit
self._name = name
self._verbose = verbose
def start(self, energy):
self._itcount = -1
self._ccount = 0
if self._tol_rel_gradnorm is not None:
self._tol_rel_gradnorm_now = self._tol_rel_gradnorm \
* energy.gradient_norm
return self.check(energy)
def check(self, energy):
self._itcount += 1
if self._tol_abs_gradnorm is not None:
if energy.gradient_norm <= self._tol_abs_gradnorm:
self._ccount += 1
if self._tol_rel_gradnorm is not None:
if energy.gradient_norm <= self._tol_rel_gradnorm_now:
self._ccount += 1
# report
if self._verbose:
msg = ""
if self._name is not None:
msg += self._name+":"
msg += " Iteration #" + str(self._itcount)
msg += " gradnorm=" + str(energy.gradient_norm)
msg += " convergence level=" + str(self._ccount)
print (msg)
self.logger.info(msg)
# Are we done?
if self._iteration_limit is not None:
if self._itcount >= self._iteration_limit:
return self.CONVERGED
if self._ccount >= self._convergence_level:
return self.CONVERGED
return self.CONTINUE
nifty/minimization/descent_minimizer.py
View file @ 9d6729d2
......@@ -18,17 +18,14 @@
from __future__ import division
import abc
from ..nifty_meta import NiftyMeta
import numpy as np
from keepers import Loggable
from .minimizer import Minimizer
from .line_searching import LineSearchStrongWolfe
from future.utils import with_metaclass
class DescentMinimizer(with_metaclass(NiftyMeta, type('NewBase', (Loggable, object), {}))):
class DescentMinimizer(Minimizer):
""" A base class used by gradient methods to find a local minimum.
Descent minimization methods are used to find a local minimum of a scalar
......@@ -38,60 +35,18 @@ class DescentMinimizer(with_metaclass(NiftyMeta, type('NewBase', (Loggable, obje
Parameters
----------
controller : IterationController
Object that decides when to terminate the minimization.
line_searcher : callable *optional*
Function which infers the step size in the descent direction
(default : LineSearchStrongWolfe()).
callback : callable *optional*
Function f(energy, iteration_number) supplied by the user to perform
in-situ analysis at every iteration step. When being called the
current energy and iteration_number are passed. (default: None)
convergence_tolerance : float *optional*
Tolerance specifying the case of convergence. (default: 1E-4)
convergence_level : integer *optional*
Number of times the tolerance must be undershot before convergence
is reached. (default: 3)
iteration_limit : integer *optional*
Maximum number of iterations performed (default: None).
Attributes
----------
convergence_tolerance : float
Tolerance specifying the case of convergence.
convergence_level : integer
Number of times the tolerance must be undershot before convergence
is reached. (default: 3)
iteration_limit : integer
Maximum number of iterations performed.
line_searcher : LineSearch
Function which infers the optimal step size for functional minization
given a descent direction.
callback : function
Function f(energy, iteration_number) supplied by the user to perform
in-situ analysis at every iteration step. When being called the
current energy and iteration_number are passed.
Notes
------
The callback function can be used to externally stop the minimization by
raising a `StopIteration` exception.
Check `get_descent_direction` of a derived class for information on the
concrete minization scheme.
"""
def __init__(self, line_searcher=LineSearchStrongWolfe(), callback=None,
convergence_tolerance=1E-4, convergence_level=3,
iteration_limit=None):
self.convergence_tolerance = np.float(convergence_tolerance)
self.convergence_level = np.int(convergence_level)
if iteration_limit is not None:
iteration_limit = int(iteration_limit)
self.iteration_limit = iteration_limit
def __init__(self, controller, line_searcher=LineSearchStrongWolfe()):
super(DescentMinimizer, self).__init__()
self._controller = controller
self.line_searcher = line_searcher
self.callback = callback
def __call__(self, energy):
""" Performs the minimization of the provided Energy functional.
......@@ -106,43 +61,29 @@ class DescentMinimizer(with_metaclass(NiftyMeta, type('NewBase', (Loggable, obje
-------
energy : Energy object
Latest `energy` of the minimization.
convergence : integer
Latest convergence level indicating whether the minimization
has converged or not.
status : integer
Can be controller.CONVERGED or controller.ERROR
Note
----
The minimization is stopped if
* the callback function raises a `StopIteration` exception,
* the controller returns controller.CONVERGED or controller.ERROR,
* a perfectly flat point is reached,
* according to the line-search the minimum is found,
* the target convergence level is reached,
* the iteration limit is reached.
"""
convergence = 0
f_k_minus_1 = None
iteration_number = 1
controller = self._controller
status = controller.start(energy)
if status != controller.CONTINUE:
return energy, status
while True:
if self.callback is not None:
try:
self.callback(energy, iteration_number)
except StopIteration:
self.logger.info("Minimization was stopped by callback "
"function.")
break
# compute the the gradient for the current location
gradient = energy.gradient
gradient_norm = gradient.norm()
# check if position is at a flat point
if gradient_norm == 0:
if energy.gradient_norm == 0:
self.logger.info("Reached perfectly flat point. Stopping.")
convergence = self.convergence_level+2
break
return energy, controller.CONVERGED
# current position is encoded in energy object
descent_direction = self.get_descent_direction(energy)
......@@ -157,47 +98,20 @@ class DescentMinimizer(with_metaclass(NiftyMeta, type('NewBase', (Loggable, obje
except RuntimeError:
self.logger.warn(
"Stopping because of RuntimeError in line-search")
break
return energy, controller.ERROR
f_k_minus_1 = energy.value
f_k = new_energy.value
delta = (abs(f_k-f_k_minus_1) /
max(abs(f_k), abs(f_k_minus_1), 1.))
# check if new energy value is bigger than old energy value
if (new_energy.value - energy.value) > 0:
self.logger.info("Line search algorithm returned a new energy "
"that was larger than the old one. Stopping.")
break
return energy, controller.ERROR
energy = new_energy
# check convergence
self.logger.debug("Iteration:%08u "
"delta=%3.1E energy=%3.1E" %
(iteration_number, delta,
energy.value))
if delta == 0:
convergence = self.convergence_level + 2
self.logger.info("Found minimum according to line-search. "
"Stopping.")
break
elif delta < self.convergence_tolerance:
convergence += 1
self.logger.info("Updated convergence level to: %u" %
convergence)
if convergence == self.convergence_level:
self.logger.info("Reached target convergence level.")
break
else:
convergence = max(0, convergence-1)
if self.iteration_limit is not None:
if iteration_number == self.iteration_limit:
self.logger.warn("Reached iteration limit. Stopping.")
break
iteration_number += 1
return energy, convergence