/usr/lib/python3/dist-packages/csb/numeric/integrators.py is in python3-csb 1.2.2+dfsg-2ubuntu1.
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provides various integration schemes and an abstract gradient class.
"""
import numpy
from abc import ABCMeta, abstractmethod
from csb.statistics.samplers.mc import State, TrajectoryBuilder
from csb.numeric import InvertibleMatrix
class AbstractIntegrator(object):
"""
Abstract integrator class. Subclasses implement different integration
schemes for solving deterministic equations of motion.
@param timestep: Integration timestep
@type timestep: float
@param gradient: Gradient of potential energy
@type gradient: L{AbstractGradient}
"""
__metaclass__ = ABCMeta
def __init__(self, timestep, gradient):
self._timestep = timestep
self._gradient = gradient
def integrate(self, init_state, length, mass_matrix=None, return_trajectory=False):
"""
Integrates equations of motion starting from an initial state a certain
number of steps.
@param init_state: Initial state from which to start integration
@type init_state: L{State}
@param length: Nubmer of integration steps to be performed
@type length: int
@param mass_matrix: Mass matrix
@type mass_matrix: n-dimensional L{InvertibleMatrix} with n being the dimension
of the configuration space, that is, the dimension of
the position / momentum vectors
@param return_trajectory: Return complete L{Trajectory} instead of the initial
and final states only (L{PropagationResult}). This reduces
performance.
@type return_trajectory: boolean
@rtype: L{AbstractPropagationResult}
"""
builder = TrajectoryBuilder.create(full=return_trajectory)
builder.add_initial_state(init_state)
state = init_state.clone()
for i in range(length - 1):
state = self.integrate_once(state, i, mass_matrix=mass_matrix)
builder.add_intermediate_state(state)
state = self.integrate_once(state, length - 1, mass_matrix=mass_matrix)
builder.add_final_state(state)
return builder.product
@abstractmethod
def integrate_once(self, state, current_step, mass_matrix=None):
"""
Integrates one step starting from an initial state and an initial time
given by the product of the timestep and the current_step parameter.
The input C{state} is changed in place.
@param state: State which to evolve one integration step
@type state: L{State}
@param current_step: Current integration step
@type current_step: int
@param mass_matrix: mass matrix
@type mass_matrix: n-dimensional numpy array with n being the dimension
of the configuration space, that is, the dimension of
the position / momentum vectors
@return: the altered state
@rtype: L{State}
"""
pass
def _get_inverse(self, mass_matrix):
inverse_mass_matrix = None
if mass_matrix is None:
inverse_mass_matrix = 1.0
else:
if mass_matrix.is_unity_multiple:
inverse_mass_matrix = mass_matrix.inverse[0][0]
else:
inverse_mass_matrix = mass_matrix.inverse
return inverse_mass_matrix
class LeapFrog(AbstractIntegrator):
"""
Leap Frog integration scheme implementation that calculates position and
momenta at equal times. Slower than FastLeapFrog, but intermediate points
in trajectories obtained using
LeapFrog.integrate(init_state, length, return_trajectoy=True) are physical.
"""
def integrate_once(self, state, current_step, mass_matrix=None):
inverse_mass_matrix = self._get_inverse(mass_matrix)
i = current_step
if i == 0:
self._oldgrad = self._gradient(state.position, 0.)
momentumhalf = state.momentum - 0.5 * self._timestep * self._oldgrad
state.position = state.position + self._timestep * numpy.dot(inverse_mass_matrix, momentumhalf)
self._oldgrad = self._gradient(state.position, (i + 1) * self._timestep)
state.momentum = momentumhalf - 0.5 * self._timestep * self._oldgrad
return state
class FastLeapFrog(LeapFrog):
"""
Leap Frog integration scheme implementation that calculates position and
momenta at unequal times by concatenating the momentum updates of two
successive integration steps.
WARNING: intermediate points in trajectories obtained by
FastLeapFrog.integrate(init_state, length, return_trajectories=True)
are NOT to be interpreted as phase-space trajectories, because
position and momenta are not given at equal times! In the initial and the
final state, positions and momenta are given at equal times.
"""
def integrate(self, init_state, length, mass_matrix=None, return_trajectory=False):
inverse_mass_matrix = self._get_inverse(mass_matrix)
builder = TrajectoryBuilder.create(full=return_trajectory)
builder.add_initial_state(init_state)
state = init_state.clone()
state.momentum = state.momentum - 0.5 * self._timestep * self._gradient(state.position, 0.)
for i in range(length-1):
state.position = state.position + self._timestep * numpy.dot(inverse_mass_matrix, state.momentum)
state.momentum = state.momentum - self._timestep * \
self._gradient(state.position, (i + 1) * self._timestep)
builder.add_intermediate_state(state)
state.position = state.position + self._timestep * numpy.dot(inverse_mass_matrix, state.momentum)
state.momentum = state.momentum - 0.5 * self._timestep * \
self._gradient(state.position, length * self._timestep)
builder.add_final_state(state)
return builder.product
class VelocityVerlet(AbstractIntegrator):
"""
Velocity Verlet integration scheme implementation.
"""
def integrate_once(self, state, current_step, mass_matrix=None):
inverse_mass_matrix = self._get_inverse(mass_matrix)
i = current_step
if i == 0:
self._oldgrad = self._gradient(state.position, 0.)
state.position = state.position + self._timestep * numpy.dot(inverse_mass_matrix, state.momentum) \
- 0.5 * self._timestep ** 2 * numpy.dot(inverse_mass_matrix, self._oldgrad)
newgrad = self._gradient(state.position, (i + 1) * self._timestep)
state.momentum = state.momentum - 0.5 * self._timestep * (self._oldgrad + newgrad)
self._oldgrad = newgrad
return state
class AbstractGradient(object):
"""
Abstract gradient class. Implementations evaluate the gradient of an energy
function.
"""
__metaclass__ = ABCMeta
@abstractmethod
def evaluate(self, q, t):
"""
Evaluates the gradient at position q and time t.
@param q: Position array
@type q: One-dimensional numpy array
@param t: Time
@type t: float
@rtype: numpy array
"""
pass
def __call__(self, q, t):
"""
Evaluates the gradient at position q and time t.
@param q: Position array
@type q: One-dimensional numpy array
@param t: Time
@type t: float
@rtype: numpy array
"""
State.check_flat_array(q)
return self.evaluate(q, t)
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