/usr/lib/python3/dist-packages/csb/statistics/samplers/mc/propagators.py is in python3-csb 1.2.3+dfsg-3.
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Provides various deterministic and stochastic propagators.
"""
import numpy
from abc import ABCMeta, abstractmethod
from csb.statistics.samplers.mc import TrajectoryBuilder
from csb.numeric.integrators import FastLeapFrog, VelocityVerlet
from csb.numeric import InvertibleMatrix
class AbstractPropagator(object):
"""
Abstract propagator class. Subclasses serve to propagate
an inital state by some dynamics to a final state.
"""
__metaclass__ = ABCMeta
@abstractmethod
def generate(self, init_state, length, return_trajectory=False):
"""
Generate a trajectory, starting from an initial state with a certain length.
@param init_state: Initial state from which to propagate
@type init_state: L{State}
@param length: Length of the trajectory (in integration steps or stochastic moves)
@type length: int
@param return_trajectory: Return complete L{Trajectory} instead of the initial
and final states only (L{PropagationResult})
@type return_trajectory: boolean
@rtype: L{AbstractPropagationResult}
"""
pass
class MDPropagator(AbstractPropagator):
"""
Molecular Dynamics propagator. Generates a trajectory
by integration of Hamiltionian equations of motion.
@param gradient: Gradient of potential energy. Guides the dynamics.
@type gradient: L{AbstractGradient}
@param timestep: Timestep to be used for integration
@type timestep: float
@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 integrator: Subclass of L{AbstractIntegrator} to be used to integrate
Hamiltonian equations of motion
@type integrator: type
"""
def __init__(self, gradient, timestep, mass_matrix=None, integrator=FastLeapFrog):
super(MDPropagator, self).__init__()
self._gradient = None
self.gradient = gradient
self._mass_matrix = mass_matrix
self._timestep = None
self.timestep = timestep
self._integrator = integrator
self._first_run = True
@property
def gradient(self):
return self._gradient
@gradient.setter
def gradient(self, value):
self._gradient = value
@property
def timestep(self):
return self._timestep
@timestep.setter
def timestep(self, value):
self._timestep = float(value)
@property
def mass_matrix(self):
return self._mass_matrix
@mass_matrix.setter
def mass_matrix(self, value):
self._mass_matrix = value
def generate(self, init_state, length, return_trajectory=False):
integrator = self._integrator(self.timestep, self.gradient)
result = integrator.integrate(init_state, length,
mass_matrix=self.mass_matrix,
return_trajectory=return_trajectory)
return result
class Looper(object):
"""
Implements an iterable list with a ring-like topology,
that is, if the iterator points on the last element,
next() returns the first element.
"""
def __init__(self, items):
self._items = items
self._n_items = len(self._items)
self._current = 0
def __iter__(self):
return self
def next(self):
if self._current == self._n_items:
self._current = 0
self._current += 1
return self._items[self._current - 1]
class ThermostattedMDPropagator(MDPropagator):
"""
Thermostatted Molecular Dynamics propagator. Employs the Andersen thermostat
which simulates collision with particles of a heat bath at a given temperature.
@param gradient: Gradient of potential energy. Guides the dynamics.
@type gradient: L{AbstractGradient}
@param timestep: Timestep to be used for integration
@type timestep: float
@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 temperature: Time-dependent temperature
@type temperature: Real-valued function
@param collision_probability: collision probability within duration of one timestep
@type collision_probability: float
@param update_interval: Interval with which momenta are redrawn
@type update_interval: int
@param integrator: Subclass of L{AbstractIntegrator} to be used to perform
integration steps between momentum updates
@type integrator: type
"""
def __init__(self, gradient, timestep, mass_matrix=None, temperature=lambda t: 1.,
collision_probability=0.1, update_interval=1, integrator=VelocityVerlet):
super(ThermostattedMDPropagator, self).__init__(gradient, timestep,
mass_matrix, integrator)
self._collision_probability = collision_probability
self._update_interval = update_interval
self._temperature = temperature
def _update(self, momentum, T, collision_probability):
"""
Simulate collision with heat bath particles.
@param momentum: Momentum
@type momentum: one-dimensional numpy array of numbers
@param T: Temperature of the heat bath
@type T: float
@param collision_probability: collision probability within duration of one timestep
@type collision_probability: float
@rtype: tuple (updated momentum, heat induced by the update)
"""
d = len(momentum)
heat = 0.
update_list = numpy.where(numpy.random.random(d) < collision_probability)[0]
if len(update_list) > 0:
K = None
if self.mass_matrix.is_unity_multiple:
K = lambda x: 0.5 * sum(x ** 2) / self.mass_matrix[0][0]
else:
K = lambda x: 0.5 * numpy.dot(x.T, numpy.dot(self.mass_matrix.inverse, x))
ke_old = K(momentum)
updated_momentum = [numpy.sqrt(T) * self._random_loopers[i].next() for i in update_list]
momentum[update_list] = updated_momentum
heat = (K(momentum) - ke_old) / T
return momentum, heat
def _step(self, i, state, heat, integrator):
"""
Performs one step consisting of an integration step
and possibly a momentum update
@param i: integration step count
@type i: int
@param state: state to be updated
@type state: L{State}
@param heat: heat produced up to the current integration step
@type heat: float
@param integrator: integration scheme used to evolve the state deterministically
@type integrator: L{AbstractIntegrator}
"""
state = integrator.integrate_once(state, i, mass_matrix=self.mass_matrix)
if i % self._update_interval == 0:
state.momentum, stepheat = self._update(state.momentum,
self._temperature(i * self.timestep),
self._collision_probability)
heat += stepheat
return state, heat
def generate(self, init_state, length, return_trajectory=False):
if self._first_run == True and self.mass_matrix is None:
d = len(init_state.position)
self.mass_matrix = InvertibleMatrix(numpy.eye(d), numpy.eye(d))
integrator = self._integrator(self.timestep, self.gradient)
builder = TrajectoryBuilder.create(full=return_trajectory)
builder.add_initial_state(init_state)
heat = 0.
state = init_state.clone()
d = len(state.position)
n_randoms = int(1.5 * length * self._collision_probability / float(self._update_interval))
if n_randoms < 5:
n_randoms = 5
if not self.mass_matrix.is_unity_multiple:
randoms = numpy.random.multivariate_normal(mean=numpy.zeros(d),
cov=self.mass_matrix,
size=n_randoms).T
else:
randoms = numpy.random.normal(scale=numpy.sqrt(self.mass_matrix[0][0]),
size=(d, n_randoms))
self._random_loopers = [Looper(x) for x in randoms]
for i in range(length - 1):
state, heat = self._step(i, state, heat, integrator)
builder.add_intermediate_state(state)
state, heat = self._step(length - 1, state, heat, integrator)
builder.add_final_state(state)
traj = builder.product
traj.heat = heat
return traj
class AbstractMCPropagator(AbstractPropagator):
"""
Provides the interface for MC trajectory generators. Implementations
generate a sequence of states according to some implementation of
L{AbstractSingleChainMC}.
@param pdf: PDF to sample from
@type pdf: L{AbstractDensity}
@param temperature: See documentation of L{AbstractSingleChainMC}
@type temperature: float
"""
__metaclass__ = ABCMeta
def __init__(self, pdf, temperature=1.):
self._pdf = pdf
self._temperature = temperature
self._acceptance_rate = 0.0
def generate(self, init_state, length, return_trajectory=True):
self._init_sampler(init_state)
self._sampler.state = init_state
builder = TrajectoryBuilder.create(full=return_trajectory)
builder.add_initial_state(init_state)
for i in range(length):
self._sampler.sample()
if i != length - 1:
builder.add_intermediate_state(self._sampler.state)
builder.add_final_state(self._sampler.state)
self._acceptance_rate = self._sampler.acceptance_rate
return builder.product
@abstractmethod
def _init_sampler(self, init_state):
"""
Initializes the sampler with which to obtain the MC state
trajectory.
"""
pass
@property
def acceptance_rate(self):
"""
Acceptance rate of the MC sampler that generated the
trajectory.
"""
return self._acceptance_rate
class RWMCPropagator(AbstractMCPropagator):
"""
Draws a number of samples from a PDF using the L{RWMCSampler} and
returns them as a L{Trajectory}.
@param pdf: PDF to sample from
@type pdf: L{AbstractDensity}
@param stepsize: Serves to set the step size in
proposal_density, e.g. for automatic acceptance
rate adaption
@type stepsize: float
@param proposal_density: The proposal density as a function f(x, s)
of the current state x and the stepsize s.
By default, the proposal density is uniform,
centered around x, and has width s.
@type proposal_density: callable
@param temperature: See documentation of L{AbstractSingleChainMC}
@type temperature: float
"""
def __init__(self, pdf, stepsize=1., proposal_density=None, temperature=1.):
super(RWMCPropagator, self).__init__(pdf, temperature)
self._stepsize = stepsize
self._proposal_density = proposal_density
def _init_sampler(self, init_state):
from csb.statistics.samplers.mc.singlechain import RWMCSampler
self._sampler = RWMCSampler(self._pdf, init_state, self._stepsize,
self._proposal_density, self._temperature)
class HMCPropagator(AbstractMCPropagator):
"""
Draws a number of samples from a PDF using the L{HMCSampler} and
returns them as a L{Trajectory}.
@param pdf: PDF to sample from
@type pdf: L{AbstractDensity}
@param gradient: Gradient of the negative log-probability
@type gradient: L{AbstractGradient}
@param timestep: Timestep used for integration
@type timestep: float
@param nsteps: Number of integration steps to be performed in
each iteration
@type nsteps: 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 integrator: Subclass of L{AbstractIntegrator} to be used for
integrating Hamiltionian equations of motion
@type integrator: type
@param temperature: See documentation of L{AbstractSingleChainMC}
@type temperature: float
"""
def __init__(self, pdf, gradient, timestep, nsteps, mass_matrix=None,
integrator=FastLeapFrog, temperature=1.):
super(HMCPropagator, self).__init__(pdf, temperature)
self._gradient = gradient
self._timestep = timestep
self._nsteps = nsteps
self._mass_matrix = mass_matrix
self._integrator = integrator
def _init_sampler(self, init_state):
from csb.statistics.samplers.mc.singlechain import HMCSampler
self._sampler = HMCSampler(self._pdf, init_state, self._gradient,
self._timestep, self._nsteps,
mass_matrix=self.mass_matrix,
integrator=self._integrator, temperature=self._temperature)
@property
def mass_matrix(self):
return self._mass_matrix
@mass_matrix.setter
def mass_matrix(self, value):
self._mass_matrix = value
class AbstractNCMCPropagator(AbstractMCPropagator):
"""
Draws a number of samples from a PDF using the L{AbstractNCMCSampler}.
@param protocol: The nonequilibrium protocol specifying a sequence of
perturbation and propagation steps
@type protocol: L{Protocol}
@param reverse_protocol: The protocol with the order of perturbation and
propagation reversed in each step.
@type reverse_protocol: L{Protocol}
"""
__metaclass__ = ABCMeta
def __init__(self, protocol, reverse_protocol):
self._protocol = None
self.protocol = protocol
self._reverse_protocol = None
self.reverse_protocol = reverse_protocol
pdf = self.protocol.steps[0].perturbation.sys_before.hamiltonian
temperature = self.protocol.steps[0].perturbation.sys_before.hamiltonian.temperature
super(AbstractNCMCPropagator, self).__init__(pdf, temperature)
@property
def protocol(self):
return self._protocol
@protocol.setter
def protocol(self, value):
self._protocol = value
@property
def reverse_protocol(self):
return self._reverse_protocol
@reverse_protocol.setter
def reverse_protocol(self, value):
self._reverse_protocol = value
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