/usr/lib/python3/dist-packages/csb/statistics/samplers/mc/multichain.py is in python3-csb 1.2.3+dfsg-3.
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Implements several extended-ensemble Monte Carlo sampling algorithms.
Here is a short example which shows how to sample from a PDF using the replica
exchange with non-equilibrium switches (RENS) method. It draws 5000 samples from
a 1D normal distribution using the RENS algorithm working on three Markov chains
being generated by the HMC algorithm:
>>> import numpy
>>> from numpy import sqrt
>>> from csb.io.plots import Chart
>>> from csb.statistics.pdf import Normal
>>> from csb.statistics.samplers import State
>>> from csb.statistics.samplers.mc.multichain import ThermostattedMDRENSSwapParameterInfo
>>> from csb.statistics.samplers.mc.multichain import ThermostattedMDRENS, AlternatingAdjacentSwapScheme
>>> from csb.statistics.samplers.mc.singlechain import HMCSampler
>>> # Pick some initial state for the different Markov chains:
>>> initial_state = State(numpy.array([1.]))
>>> # Set standard deviations:
>>> std_devs = [1./sqrt(5), 1. / sqrt(3), 1.]
>>> # Set HMC timesteps and trajectory length:
>>> hmc_timesteps = [0.6, 0.7, 0.6]
>>> hmc_trajectory_length = 20
>>> hmc_gradients = [lambda q, t: 1 / (std_dev ** 2) * q for std_dev in std_devs]
>>> # Set parameters for the thermostatted RENS algorithm:
>>> rens_trajectory_length = 30
>>> rens_timesteps = [0.3, 0.5]
>>> # Set interpolation gradients as a function of the work parameter l:
>>> rens_gradients = [lambda q, l, i=i: (l / (std_devs[i + 1] ** 2) + (1 - l) / (std_devs[i] ** 2)) * q
for i in range(len(std_devs)-1)]
>>> # Initialize HMC samplers:
>>> samplers = [HMCSampler(Normal(sigma=std_devs[i]), initial_state, hmc_gradients[i], hmc_timesteps[i],
hmc_trajectory_length) for i in range(len(std_devs))]
>>> # Create swap parameter objects:
params = [ThermostattedMDRENSSwapParameterInfo(samplers[0], samplers[1], rens_timesteps[0],
rens_trajectory_length, rens_gradients[0]),
ThermostattedMDRENSSwapParameterInfo(samplers[1], samplers[2], rens_timesteps[1],
rens_trajectory_length, rens_gradients[1])]
>>> # Initialize thermostatted RENS algorithm:
>>> algorithm = ThermostattedMDRENS(samplers, params)
>>> # Initialize swapping scheme:
>>> swapper = AlternatingAdjacentSwapScheme(algorithm)
>>> # Initialize empty list which will store the samples:
>>> states = []
>>> for i in range(5000):
if i % 5 == 0:
swapper.swap_all()
states.append(algorithm.sample())
>>> # Print acceptance rates:
>>> print('HMC acceptance rates:', [s.acceptance_rate for s in samplers])
>>> print('swap acceptance rates:', algorithm.acceptance_rates)
>>> # Create and plot histogram for first sampler and numpy.random.normal reference:
>>> chart = Chart()
>>> rawstates = [state[0].position[0] for state in states]
>>> chart.plot.hist([numpy.random.normal(size=5000, scale=std_devs[0]), rawstates], bins=30, normed=True)
>>> chart.plot.legend(['numpy.random.normal', 'RENS + HMC'])
>>> chart.show()
For L{ReplicaExchangeMC} (RE), the procedure is easier because apart from the
two sampler instances the corresponding L{RESwapParameterInfo} objects take
no arguments.
Every replica exchange algorithm in this module (L{ReplicaExchangeMC}, L{MDRENS},
L{ThermostattedMDRENS}) is used in a similar way. A simulation is always
initialized with a list of samplers (instances of classes derived from
L{AbstractSingleChainMC}) and a list of L{AbstractSwapParameterInfo} objects
suited for the algorithm under consideration. Every L{AbstractSwapParameterInfo}
object holds all the information needed to perform a swap between two samplers.
The usual scheme is to swap only adjacent replicae in a scheme::
1 <--> 2, 3 <--> 4, ...
2 <--> 3, 4 <--> 5, ...
1 <--> 2, 3 <--> 4, ...
This swapping scheme is implemented in the L{AlternatingAdjacentSwapScheme} class,
but different schemes can be easily implemented by deriving from L{AbstractSwapScheme}.
Then the simulation is run by looping over the number of samples to be drawn
and calling the L{AbstractExchangeMC.sample} method of the algorithm. By calling
the L{AbstractSwapScheme.swap_all} method of the specific L{AbstractSwapScheme}
implementation, all swaps defined in the list of L{AbstractSwapParameterInfo}
objects are performed according to the swapping scheme. The
L{AbstractSwapScheme.swap_all} method may be called for example after sampling
intervals of a fixed length or randomly.
"""
import numpy
import csb.numeric
from abc import ABCMeta, abstractmethod
from csb.statistics.samplers import EnsembleState
from csb.statistics.samplers.mc import AbstractMC, Trajectory, MCCollection, augment_state
from csb.statistics.samplers.mc.propagators import MDPropagator, ThermostattedMDPropagator
from csb.statistics.samplers.mc.neqsteppropagator import NonequilibriumStepPropagator
from csb.statistics.samplers.mc.neqsteppropagator import Protocol, Step, ReducedHamiltonian
from csb.statistics.samplers.mc.neqsteppropagator import ReducedHamiltonianPerturbation
from csb.statistics.samplers.mc.neqsteppropagator import HMCPropagation, HMCPropagationParam
from csb.statistics.samplers.mc.neqsteppropagator import HamiltonianSysInfo, NonequilibriumTrajectory
from csb.numeric.integrators import AbstractGradient, FastLeapFrog
class AbstractEnsembleMC(AbstractMC):
"""
Abstract class for Monte Carlo sampling algorithms simulating several ensembles.
@param samplers: samplers which sample from their respective equilibrium distributions
@type samplers: list of L{AbstractSingleChainMC}
"""
__metaclass__ = ABCMeta
def __init__(self, samplers):
self._samplers = MCCollection(samplers)
state = EnsembleState([x.state for x in self._samplers])
super(AbstractEnsembleMC, self).__init__(state)
def sample(self):
"""
Draw an ensemble sample.
@rtype: L{EnsembleState}
"""
sample = EnsembleState([sampler.sample() for sampler in self._samplers])
self.state = sample
return sample
@property
def energy(self):
"""
Total ensemble energy.
"""
return sum([x.energy for x in self._samplers])
class AbstractExchangeMC(AbstractEnsembleMC):
"""
Abstract class for Monte Carlo sampling algorithms employing some replica exchange method.
@param samplers: samplers which sample from their respective equilibrium distributions
@type samplers: list of L{AbstractSingleChainMC}
@param param_infos: list of ParameterInfo instances providing information needed
for performing swaps
@type param_infos: list of L{AbstractSwapParameterInfo}
"""
__metaclass__ = ABCMeta
def __init__(self, samplers, param_infos):
super(AbstractExchangeMC, self).__init__(samplers)
self._swaplist1 = []
self._swaplist2 = []
self._currentswaplist = self._swaplist1
self._param_infos = param_infos
self._statistics = SwapStatistics(self._param_infos)
def _checkstate(self, state):
if not isinstance(state, EnsembleState):
raise TypeError(state)
def swap(self, index):
"""
Perform swap between sampler pair described by param_infos[index]
and return outcome (true = accepted, false = rejected).
@param index: index of swap pair in param_infos
@type index: int
@rtype: boolean
"""
param_info = self._param_infos[index]
swapcom = self._propose_swap(param_info)
swapcom = self._calc_pacc_swap(swapcom)
result = self._accept_swap(swapcom)
self.state = EnsembleState([x.state for x in self._samplers])
self.statistics.stats[index].update(result)
return result
@abstractmethod
def _propose_swap(self, param_info):
"""
Calculate proposal states for a swap between two samplers.
@param param_info: ParameterInfo instance holding swap parameters
@type param_info: L{AbstractSwapParameterInfo}
@rtype: L{AbstractSwapCommunicator}
"""
pass
@abstractmethod
def _calc_pacc_swap(self, swapcom):
"""
Calculate probability to accept a swap given initial and proposal states.
@param swapcom: SwapCommunicator instance holding information to be communicated
between distinct swap substeps
@type swapcom: L{AbstractSwapCommunicator}
@rtype: L{AbstractSwapCommunicator}
"""
pass
def _accept_swap(self, swapcom):
"""
Accept / reject an exchange between two samplers given proposal states and
the acceptance probability and returns the outcome (true = accepted, false = rejected).
@param swapcom: SwapCommunicator instance holding information to be communicated
between distinct swap substeps
@type swapcom: L{AbstractSwapCommunicator}
@rtype: boolean
"""
if numpy.random.random() < swapcom.acceptance_probability:
if swapcom.sampler1.state.momentum is None and swapcom.sampler2.state.momentum is None:
swapcom.traj12.final.momentum = None
swapcom.traj21.final.momentum = None
swapcom.sampler1.state = swapcom.traj21.final
swapcom.sampler2.state = swapcom.traj12.final
return True
else:
return False
@property
def acceptance_rates(self):
"""
Return swap acceptance rates.
@rtype: list of floats
"""
return self.statistics.acceptance_rates
@property
def param_infos(self):
"""
List of SwapParameterInfo instances holding all necessary parameters.
@rtype: list of L{AbstractSwapParameterInfo}
"""
return self._param_infos
@property
def statistics(self):
return self._statistics
def _update_statistics(self, index, accepted):
"""
Update statistics of a given swap process.
@param index: position of swap statistics to be updated
@type index: int
@param accepted: outcome of the swap
@type accepted: boolean
"""
self._stats[index][0] += 1
self._stats[index][1] += int(accepted)
class AbstractSwapParameterInfo(object):
"""
Subclass instances hold all parameters necessary for performing a swap
between two given samplers.
"""
__metaclass__ = ABCMeta
def __init__(self, sampler1, sampler2):
"""
@param sampler1: First sampler
@type sampler1: L{AbstractSingleChainMC}
@param sampler2: Second sampler
@type sampler2: L{AbstractSingleChainMC}
"""
self._sampler1 = sampler1
self._sampler2 = sampler2
@property
def sampler1(self):
return self._sampler1
@property
def sampler2(self):
return self._sampler2
class AbstractSwapCommunicator(object):
"""
Holds all the information which needs to be communicated between
distinct swap substeps.
@param param_info: ParameterInfo instance holding swap parameters
@type param_info: L{AbstractSwapParameterInfo}
@param traj12: Forward trajectory
@type traj12: L{Trajectory}
@param traj21: Reverse trajectory
@type traj21: L{Trajectory}
"""
__metaclass__ = ABCMeta
def __init__(self, param_info, traj12, traj21):
self._sampler1 = param_info.sampler1
self._sampler2 = param_info.sampler2
self._traj12 = traj12
self._traj21 = traj21
self._param_info = param_info
self._acceptance_probability = None
self._accepted = False
@property
def sampler1(self):
return self._sampler1
@property
def sampler2(self):
return self._sampler2
@property
def traj12(self):
return self._traj12
@property
def traj21(self):
return self._traj21
@property
def acceptance_probability(self):
return self._acceptance_probability
@acceptance_probability.setter
def acceptance_probability(self, value):
self._acceptance_probability = value
@property
def accepted(self):
return self._accepted
@accepted.setter
def accepted(self, value):
self._accepted = value
@property
def param_info(self):
return self._param_info
class ReplicaExchangeMC(AbstractExchangeMC):
"""
Replica Exchange (RE, Swendsen & Yang 1986) implementation.
"""
def _propose_swap(self, param_info):
return RESwapCommunicator(param_info, Trajectory([param_info.sampler1.state,
param_info.sampler1.state]),
Trajectory([param_info.sampler2.state,
param_info.sampler2.state]))
def _calc_pacc_swap(self, swapcom):
E1 = lambda x:-swapcom.sampler1._pdf.log_prob(x)
E2 = lambda x:-swapcom.sampler2._pdf.log_prob(x)
T1 = swapcom.sampler1.temperature
T2 = swapcom.sampler2.temperature
state1 = swapcom.traj12.initial
state2 = swapcom.traj21.initial
proposal1 = swapcom.traj21.final
proposal2 = swapcom.traj12.final
swapcom.acceptance_probability = csb.numeric.exp(-E1(proposal1.position) / T1
+ E1(state1.position) / T1
- E2(proposal2.position) / T2
+ E2(state2.position) / T2)
return swapcom
class RESwapParameterInfo(AbstractSwapParameterInfo):
"""
Holds parameters for a standard Replica Exchange swap.
"""
pass
class RESwapCommunicator(AbstractSwapCommunicator):
"""
Holds all the information which needs to be communicated between distinct
RE swap substeps.
See L{AbstractSwapCommunicator} for constructor signature.
"""
pass
class AbstractRENS(AbstractExchangeMC):
"""
Abstract Replica Exchange with Nonequilibrium Switches
(RENS, Ballard & Jarzynski 2009) class.
Subclasses implement various ways of generating trajectories
(deterministic or stochastic).
"""
__metaclass__ = ABCMeta
def _propose_swap(self, param_info):
init_state1 = param_info.sampler1.state
init_state2 = param_info.sampler2.state
trajinfo12 = RENSTrajInfo(param_info, init_state1, direction="fw")
trajinfo21 = RENSTrajInfo(param_info, init_state2, direction="bw")
traj12 = self._run_traj_generator(trajinfo12)
traj21 = self._run_traj_generator(trajinfo21)
return RENSSwapCommunicator(param_info, traj12, traj21)
def _setup_protocol(self, traj_info):
"""
Sets the protocol lambda(t) to either the forward or the reverse protocol.
@param traj_info: TrajectoryInfo object holding information neccessary to
calculate the rens trajectories.
@type traj_info: L{RENSTrajInfo}
"""
if traj_info.direction == "fw":
return traj_info.param_info.protocol
else:
return lambda t, tau: traj_info.param_info.protocol(tau - t, tau)
return protocol
def _get_init_temperature(self, traj_info):
"""
Determine the initial temperature of a RENS trajectory.
@param traj_info: TrajectoryInfo object holding information neccessary to
calculate the RENS trajectory.
@type traj_info: L{RENSTrajInfo}
"""
if traj_info.direction == "fw":
return traj_info.param_info.sampler1.temperature
else:
return traj_info.param_info.sampler2.temperature
@abstractmethod
def _calc_works(self, swapcom):
"""
Calculates the works expended during the nonequilibrium
trajectories.
@param swapcom: Swap communicator object holding all the
neccessary information.
@type swapcom: L{RENSSwapCommunicator}
@return: The expended during the forward and the backward
trajectory.
@rtype: 2-tuple of floats
"""
pass
def _calc_pacc_swap(self, swapcom):
work12, work21 = self._calc_works(swapcom)
swapcom.acceptance_probability = csb.numeric.exp(-work12 - work21)
return swapcom
@abstractmethod
def _propagator_factory(self, traj_info):
"""
Factory method which produces the propagator object used to calculate
the RENS trajectories.
@param traj_info: TrajectoryInfo object holding information neccessary to
calculate the rens trajectories.
@type traj_info: L{RENSTrajInfo}
@rtype: L{AbstractPropagator}
"""
pass
def _run_traj_generator(self, traj_info):
"""
Run the trajectory generator which generates a trajectory
of a given length between the states of two samplers.
@param traj_info: TrajectoryInfo instance holding information
needed to generate a nonequilibrium trajectory
@type traj_info: L{RENSTrajInfo}
@rtype: L{Trajectory}
"""
init_temperature = self._get_init_temperature(traj_info)
init_state = traj_info.init_state.clone()
if init_state.momentum is None:
init_state = augment_state(init_state,
init_temperature,
traj_info.param_info.mass_matrix)
gen = self._propagator_factory(traj_info)
traj = gen.generate(init_state, int(traj_info.param_info.traj_length))
return traj
class AbstractRENSSwapParameterInfo(RESwapParameterInfo):
"""
Holds parameters for a RENS swap.
"""
__metaclass__ = ABCMeta
def __init__(self, sampler1, sampler2, protocol):
super(AbstractRENSSwapParameterInfo, self).__init__(sampler1, sampler2)
## Can't pass the linear protocol as a default argument because of a reported bug
## in epydoc parsing which makes it fail building the docs.
self._protocol = None
if protocol is None:
self._protocol = lambda t, tau: t / tau
else:
self._protocol = protocol
@property
def protocol(self):
"""
Switching protocol determining the time dependence
of the switching parameter.
"""
return self._protocol
@protocol.setter
def protocol(self, value):
self._protocol = value
class RENSSwapCommunicator(AbstractSwapCommunicator):
"""
Holds all the information which needs to be communicated between distinct
RENS swap substeps.
See L{AbstractSwapCommunicator} for constructor signature.
"""
pass
class RENSTrajInfo(object):
"""
Holds information necessary for calculating a RENS trajectory.
@param param_info: ParameterInfo instance holding swap parameters
@type param_info: L{AbstractSwapParameterInfo}
@param init_state: state from which the trajectory is supposed to start
@type init_state: L{State}
@param direction: Either "fw" or "bw", indicating a forward or backward
trajectory. This is neccessary to pick the protocol or
the reversed protocol, respectively.
@type direction: string, either "fw" or "bw"
"""
def __init__(self, param_info, init_state, direction):
self._param_info = param_info
self._init_state = init_state
self._direction = direction
@property
def param_info(self):
return self._param_info
@property
def init_state(self):
return self._init_state
@property
def direction(self):
return self._direction
class MDRENS(AbstractRENS):
"""
Replica Exchange with Nonequilibrium Switches (RENS, Ballard & Jarzynski 2009)
with Molecular Dynamics (MD) trajectories.
@param samplers: Samplers which sample their
respective equilibrium distributions
@type samplers: list of L{AbstractSingleChainMC}
@param param_infos: ParameterInfo instance holding
information required to perform a MDRENS swap
@type param_infos: list of L{MDRENSSwapParameterInfo}
@param integrator: Subclass of L{AbstractIntegrator} to be used to
calculate the non-equilibrium trajectories
@type integrator: type
"""
def __init__(self, samplers, param_infos,
integrator=csb.numeric.integrators.FastLeapFrog):
super(MDRENS, self).__init__(samplers, param_infos)
self._integrator = integrator
def _propagator_factory(self, traj_info):
protocol = self._setup_protocol(traj_info)
tau = traj_info.param_info.traj_length * traj_info.param_info.timestep
factory = InterpolationFactory(protocol, tau)
gen = MDPropagator(factory.build_gradient(traj_info.param_info.gradient),
traj_info.param_info.timestep,
mass_matrix=traj_info.param_info.mass_matrix,
integrator=self._integrator)
return gen
def _calc_works(self, swapcom):
T1 = swapcom.param_info.sampler1.temperature
T2 = swapcom.param_info.sampler2.temperature
heat12 = swapcom.traj12.heat
heat21 = swapcom.traj21.heat
proposal1 = swapcom.traj21.final
proposal2 = swapcom.traj12.final
state1 = swapcom.traj12.initial
state2 = swapcom.traj21.initial
if swapcom.param_info.mass_matrix.is_unity_multiple:
inverse_mass_matrix = 1.0 / swapcom.param_info.mass_matrix[0][0]
else:
inverse_mass_matrix = swapcom.param_info.mass_matrix.inverse
E1 = lambda x:-swapcom.sampler1._pdf.log_prob(x)
E2 = lambda x:-swapcom.sampler2._pdf.log_prob(x)
K = lambda x: 0.5 * numpy.dot(x.T, numpy.dot(inverse_mass_matrix, x))
w12 = (K(proposal2.momentum) + E2(proposal2.position)) / T2 - \
(K(state1.momentum) + E1(state1.position)) / T1 - heat12
w21 = (K(proposal1.momentum) + E1(proposal1.position)) / T1 - \
(K(state2.momentum) + E2(state2.position)) / T2 - heat21
return w12, w21
class MDRENSSwapParameterInfo(RESwapParameterInfo):
"""
Holds parameters for a MDRENS swap.
@param sampler1: First sampler
@type sampler1: L{AbstractSingleChainMC}
@param sampler2: Second sampler
@type sampler2: L{AbstractSingleChainMC}
@param timestep: Integration timestep
@type timestep: float
@param traj_length: Trajectory length in number of timesteps
@type traj_length: int
@param gradient: Gradient which determines the dynamics during a trajectory
@type gradient: L{AbstractGradient}
@param protocol: Switching protocol determining the time dependence of the
switching parameter. It is a function M{f} taking the running
time t and the switching time tau to yield a value in M{[0, 1]}
with M{f(0, tau) = 0} and M{f(tau, tau) = 1}. Default is a linear
protocol, which is being set manually due to an epydoc bug
@type protocol: callable
@param mass_matrix: Mass matrix
@type mass_matrix: n-dimensional matrix of type L{InvertibleMatrix} with n being the dimension
of the configuration space, that is, the dimension of
the position / momentum vectors
"""
def __init__(self, sampler1, sampler2, timestep, traj_length, gradient,
protocol=None, mass_matrix=None):
super(MDRENSSwapParameterInfo, self).__init__(sampler1, sampler2)
self._mass_matrix = mass_matrix
if self.mass_matrix is None:
d = len(sampler1.state.position)
self.mass_matrix = csb.numeric.InvertibleMatrix(numpy.eye(d), numpy.eye(d))
self._traj_length = traj_length
self._gradient = gradient
self._timestep = timestep
## Can't pass the linear protocol as a default argument because of a reported bug
## in epydoc parsing which makes it fail building the docs.
self._protocol = None
if protocol is None:
self._protocol = lambda t, tau: t / tau
else:
self._protocol = protocol
@property
def timestep(self):
"""
Integration timestep.
"""
return self._timestep
@timestep.setter
def timestep(self, value):
self._timestep = float(value)
@property
def traj_length(self):
"""
Trajectory length in number of integration steps.
"""
return self._traj_length
@traj_length.setter
def traj_length(self, value):
self._traj_length = int(value)
@property
def gradient(self):
"""
Gradient which governs the equations of motion.
"""
return self._gradient
@property
def mass_matrix(self):
return self._mass_matrix
@mass_matrix.setter
def mass_matrix(self, value):
self._mass_matrix = value
@property
def protocol(self):
"""
Switching protocol determining the time dependence
of the switching parameter.
"""
return self._protocol
@protocol.setter
def protocol(self, value):
self._protocol = value
class ThermostattedMDRENS(MDRENS):
"""
Replica Exchange with Nonequilibrium Switches (RENS, Ballard & Jarzynski, 2009)
with Andersen-thermostatted Molecular Dynamics (MD) trajectories.
@param samplers: Samplers which sample their
respective equilibrium distributions
@type samplers: list of L{AbstractSingleChainMC}
@param param_infos: ParameterInfo instance holding
information required to perform a MDRENS swap
@type param_infos: list of L{ThermostattedMDRENSSwapParameterInfo}
@param integrator: Subclass of L{AbstractIntegrator} to be used to
calculate the non-equilibrium trajectories
@type integrator: type
"""
def __init__(self, samplers, param_infos, integrator=csb.numeric.integrators.LeapFrog):
super(ThermostattedMDRENS, self).__init__(samplers, param_infos, integrator)
def _propagator_factory(self, traj_info):
protocol = self._setup_protocol(traj_info)
tau = traj_info.param_info.traj_length * traj_info.param_info.timestep
factory = InterpolationFactory(protocol, tau)
grad = factory.build_gradient(traj_info.param_info.gradient)
temp = factory.build_temperature(traj_info.param_info.temperature)
gen = ThermostattedMDPropagator(grad,
traj_info.param_info.timestep, temperature=temp,
collision_probability=traj_info.param_info.collision_probability,
update_interval=traj_info.param_info.collision_interval,
mass_matrix=traj_info.param_info.mass_matrix,
integrator=self._integrator)
return gen
class ThermostattedMDRENSSwapParameterInfo(MDRENSSwapParameterInfo):
"""
@param sampler1: First sampler
@type sampler1: subclass instance of L{AbstractSingleChainMC}
@param sampler2: Second sampler
@type sampler2: subclass instance of L{AbstractSingleChainMC}
@param timestep: Integration timestep
@type timestep: float
@param traj_length: Trajectory length in number of timesteps
@type traj_length: int
@param gradient: Gradient which determines the dynamics during a trajectory
@type gradient: subclass instance of L{AbstractGradient}
@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 protocol: Switching protocol determining the time dependence of the
switching parameter. It is a function f taking the running
time t and the switching time tau to yield a value in [0, 1]
with f(0, tau) = 0 and f(tau, tau) = 1
@type protocol: callable
@param temperature: Temperature interpolation function.
@type temperature: Real-valued function mapping from [0,1] to R.
T(0) = temperature of the ensemble sampler1 samples from, T(1) = temperature
of the ensemble sampler2 samples from
@param collision_probability: Probability for a collision with the heatbath during one timestep
@type collision_probability: float
@param collision_interval: Interval during which collision may occur with probability
collision_probability
@type collision_interval: int
"""
def __init__(self, sampler1, sampler2, timestep, traj_length, gradient, mass_matrix=None,
protocol=None, temperature=lambda l: 1.0,
collision_probability=0.1, collision_interval=1):
super(ThermostattedMDRENSSwapParameterInfo, self).__init__(sampler1, sampler2, timestep,
traj_length, gradient,
mass_matrix=mass_matrix,
protocol=protocol)
self._collision_probability = None
self._collision_interval = None
self._temperature = temperature
self.collision_probability = collision_probability
self.collision_interval = collision_interval
@property
def collision_probability(self):
"""
Probability for a collision with the heatbath during one timestep.
"""
return self._collision_probability
@collision_probability.setter
def collision_probability(self, value):
self._collision_probability = float(value)
@property
def collision_interval(self):
"""
Interval during which collision may occur with probability
C{collision_probability}.
"""
return self._collision_interval
@collision_interval.setter
def collision_interval(self, value):
self._collision_interval = int(value)
@property
def temperature(self):
return self._temperature
class AbstractStepRENS(AbstractRENS):
"""
Replica Exchange with Nonequilibrium Switches (RENS, Ballard & Jarzynski 2009)
with stepwise trajectories as described in Nilmeier et al., "Nonequilibrium candidate
Monte Carlo is an efficient tool for equilibrium simulation", PNAS 2011.
The switching parameter dependence of the Hamiltonian is a linear interpolation
between the PDFs of the sampler objects,
M{H(S{lambda}) = H_2 * S{lambda} + (1 - S{lambda}) * H_1}.
The perturbation kernel is a thermodynamic perturbation and the propagation is subclass
responsibility.
Note that due to the linear interpolations between the two Hamiltonians, the
log-probability has to be evaluated four times per perturbation step which can be
costly. In this case it is advisable to define the intermediate log probabilities
in _run_traj_generator differently.
@param samplers: Samplers which sample their respective equilibrium distributions
@type samplers: list of L{AbstractSingleChainMC}
@param param_infos: ParameterInfo instances holding
information required to perform a HMCStepRENS swaps
@type param_infos: list of L{AbstractSwapParameterInfo}
"""
__metaclass__ = ABCMeta
def __init__(self, samplers, param_infos):
super(AbstractStepRENS, self).__init__(samplers, param_infos)
self._evaluate_im_works = True
@abstractmethod
def _setup_propagations(self, im_sys_infos, param_info):
"""
Set up the propagation steps using the information about the current system
setup and parameters from the SwapParameterInfo object.
@param im_sys_infos: Information about the intermediate system setups
@type im_sys_infos: List of L{AbstractSystemInfo}
@param param_info: SwapParameterInfo object containing parameters for the
propagations like timesteps, trajectory lengths etc.
@type param_info: L{AbstractSwapParameterInfo}
"""
pass
@abstractmethod
def _add_gradients(self, im_sys_infos, param_info, t_prot):
"""
If needed, set im_sys_infos.hamiltonian.gradient.
@param im_sys_infos: Information about the intermediate system setups
@type im_sys_infos: List of L{AbstractSystemInfo}
@param param_info: SwapParameterInfo object containing parameters for the
propagations like timesteps, trajectory lengths etc.
@type param_info: L{AbstractSwapParameterInfo}
@param t_prot: Switching protocol defining the time dependence of the switching
parameter.
@type t_prot: callable
"""
pass
def _setup_stepwise_protocol(self, traj_info):
"""
Sets up the stepwise protocol consisting of perturbation and relaxation steps.
@param traj_info: TrajectoryInfo instance holding information
needed to generate a nonequilibrium trajectory
@type traj_info: L{RENSTrajInfo}
@rtype: L{Protocol}
"""
pdf1 = traj_info.param_info.sampler1._pdf
pdf2 = traj_info.param_info.sampler2._pdf
T1 = traj_info.param_info.sampler1.temperature
T2 = traj_info.param_info.sampler2.temperature
traj_length = traj_info.param_info.intermediate_steps
prot = self._setup_protocol(traj_info)
t_prot = lambda i: prot(float(i), float(traj_length))
im_log_probs = [lambda x, i=i: pdf2.log_prob(x) * t_prot(i) + \
(1 - t_prot(i)) * pdf1.log_prob(x)
for i in range(traj_length + 1)]
im_temperatures = [T2 * t_prot(i) + (1 - t_prot(i)) * T1
for i in range(traj_length + 1)]
im_reduced_hamiltonians = [ReducedHamiltonian(im_log_probs[i],
temperature=im_temperatures[i])
for i in range(traj_length + 1)]
im_sys_infos = [HamiltonianSysInfo(im_reduced_hamiltonians[i])
for i in range(traj_length + 1)]
perturbations = [ReducedHamiltonianPerturbation(im_sys_infos[i], im_sys_infos[i+1])
for i in range(traj_length)]
if self._evaluate_im_works == False:
for p in perturbations:
p.evaluate_work = False
im_sys_infos = self._add_gradients(im_sys_infos, traj_info.param_info, t_prot)
propagations = self._setup_propagations(im_sys_infos, traj_info.param_info)
steps = [Step(perturbations[i], propagations[i]) for i in range(traj_length)]
return Protocol(steps)
def _propagator_factory(self, traj_info):
protocol = self._setup_stepwise_protocol(traj_info)
gen = NonequilibriumStepPropagator(protocol)
return gen
def _run_traj_generator(self, traj_info):
init_temperature = self._get_init_temperature(traj_info)
gen = self._propagator_factory(traj_info)
traj = gen.generate(traj_info.init_state)
return NonequilibriumTrajectory([traj_info.init_state, traj.final], jacobian=1.0,
heat=traj.heat, work=traj.work, deltaH=traj.deltaH)
class HMCStepRENS(AbstractStepRENS):
"""
Replica Exchange with Nonequilibrium Switches (RENS, Ballard & Jarzynski 2009)
with stepwise trajectories as described in Nilmeier et al., "Nonequilibrium candidate
Monte Carlo is an efficient tool for equilibrium simulation", PNAS 2011.
The switching parameter dependence of the Hamiltonian is a linear interpolation
between the PDFs of the sampler objects,
M{H(S{lambda}) = H_2 * S{lambda} + (1 - S{lambda}) * H_1}.
The perturbation kernel is a thermodynamic perturbation and the propagation is done using HMC.
Note that due to the linear interpolations between the two Hamiltonians, the
log-probability and its gradient has to be evaluated four times per perturbation step which
can be costly. In this case it is advisable to define the intermediate log probabilities
in _run_traj_generator differently.
@param samplers: Samplers which sample their respective equilibrium distributions
@type samplers: list of L{AbstractSingleChainMC}
@param param_infos: ParameterInfo instances holding
information required to perform a HMCStepRENS swaps
@type param_infos: list of L{HMCStepRENSSwapParameterInfo}
"""
def __init__(self, samplers, param_infos):
super(HMCStepRENS, self).__init__(samplers, param_infos)
def _add_gradients(self, im_sys_infos, param_info, t_prot):
im_gradients = [lambda x, t, i=i: param_info.gradient(x, t_prot(i))
for i in range(param_info.intermediate_steps + 1)]
for i, s in enumerate(im_sys_infos):
s.hamiltonian.gradient = im_gradients[i]
return im_sys_infos
def _setup_propagations(self, im_sys_infos, param_info):
propagation_params = [HMCPropagationParam(param_info.timestep,
param_info.hmc_traj_length,
im_sys_infos[i+1].hamiltonian.gradient,
param_info.hmc_iterations,
mass_matrix=param_info.mass_matrix,
integrator=param_info.integrator)
for i in range(param_info.intermediate_steps)]
propagations = [HMCPropagation(im_sys_infos[i+1], propagation_params[i], evaluate_heat=False)
for i in range(param_info.intermediate_steps)]
return propagations
def _calc_works(self, swapcom):
return swapcom.traj12.work, swapcom.traj21.work
class HMCStepRENSSwapParameterInfo(AbstractRENSSwapParameterInfo):
"""
Holds all required information for performing HMCStepRENS swaps.
@param sampler1: First sampler
@type sampler1: subclass instance of L{AbstractSingleChainMC}
@param sampler2: Second sampler
@type sampler2: subclass instance of L{AbstractSingleChainMC}
@param timestep: integration timestep
@type timestep: float
@param hmc_traj_length: HMC trajectory length
@type hmc_traj_length: int
@param hmc_iterations: number of HMC iterations in the propagation step
@type hmc_iterations: int
@param gradient: gradient governing the equations of motion, function of
position array and switching protocol
@type gradient: callable
@param intermediate_steps: number of steps in the protocol; this is a discrete version
of the switching time in "continuous" RENS implementations
@type intermediate_steps: int
@param protocol: Switching protocol determining the time dependence of the
switching parameter. It is a function f taking the running
time t and the switching time tau to yield a value in [0, 1]
with f(0, tau) = 0 and f(tau, tau) = 1
@type protocol: callable
@param mass_matrix: mass matrix for kinetic energy definition
@type mass_matrix: L{InvertibleMatrix}
@param integrator: Integration scheme to be utilized
@type integrator: l{AbstractIntegrator}
"""
def __init__(self, sampler1, sampler2, timestep, hmc_traj_length, hmc_iterations,
gradient, intermediate_steps, parametrization=None, protocol=None,
mass_matrix=None, integrator=FastLeapFrog):
super(HMCStepRENSSwapParameterInfo, self).__init__(sampler1, sampler2, protocol)
self._mass_matrix = None
self.mass_matrix = mass_matrix
if self.mass_matrix is None:
d = len(sampler1.state.position)
self.mass_matrix = csb.numeric.InvertibleMatrix(numpy.eye(d), numpy.eye(d))
self._hmc_traj_length = None
self.hmc_traj_length = hmc_traj_length
self._gradient = None
self.gradient = gradient
self._timestep = None
self.timestep = timestep
self._hmc_iterations = None
self.hmc_iterations = hmc_iterations
self._intermediate_steps = None
self.intermediate_steps = intermediate_steps
self._integrator = None
self.integrator = integrator
@property
def timestep(self):
"""
Integration timestep.
"""
return self._timestep
@timestep.setter
def timestep(self, value):
self._timestep = float(value)
@property
def hmc_traj_length(self):
"""
HMC trajectory length in number of integration steps.
"""
return self._hmc_traj_length
@hmc_traj_length.setter
def hmc_traj_length(self, value):
self._hmc_traj_length = int(value)
@property
def gradient(self):
"""
Gradient which governs the equations of motion.
"""
return self._gradient
@gradient.setter
def gradient(self, value):
self._gradient = value
@property
def mass_matrix(self):
return self._mass_matrix
@mass_matrix.setter
def mass_matrix(self, value):
self._mass_matrix = value
@property
def hmc_iterations(self):
return self._hmc_iterations
@hmc_iterations.setter
def hmc_iterations(self, value):
self._hmc_iterations = value
@property
def intermediate_steps(self):
return self._intermediate_steps
@intermediate_steps.setter
def intermediate_steps(self, value):
self._intermediate_steps = value
@property
def integrator(self):
return self._integrator
@integrator.setter
def integrator(self, value):
self._integrator = value
class AbstractSwapScheme(object):
"""
Provides the interface for classes defining schemes according to which swaps in
Replica Exchange-like simulations are performed.
@param algorithm: Exchange algorithm that performs the swaps
@type algorithm: L{AbstractExchangeMC}
"""
__metaclass__ = ABCMeta
def __init__(self, algorithm):
self._algorithm = algorithm
@abstractmethod
def swap_all(self):
"""
Advises the Replica Exchange-like algorithm to perform swaps according to
the schedule defined here.
"""
pass
class AlternatingAdjacentSwapScheme(AbstractSwapScheme):
"""
Provides a swapping scheme in which tries exchanges between neighbours only
following the scheme 1 <-> 2, 3 <-> 4, ... and after a sampling period 2 <-> 3, 4 <-> 5, ...
@param algorithm: Exchange algorithm that performs the swaps
@type algorithm: L{AbstractExchangeMC}
"""
def __init__(self, algorithm):
super(AlternatingAdjacentSwapScheme, self).__init__(algorithm)
self._current_swap_list = None
self._swap_list1 = []
self._swap_list2 = []
self._create_swap_lists()
def _create_swap_lists(self):
if len(self._algorithm.param_infos) == 1:
self._swap_list1.append(0)
self._swap_list2.append(0)
else:
i = 0
while i < len(self._algorithm.param_infos):
self._swap_list1.append(i)
i += 2
i = 1
while i < len(self._algorithm.param_infos):
self._swap_list2.append(i)
i += 2
self._current_swap_list = self._swap_list1
def swap_all(self):
for x in self._current_swap_list:
self._algorithm.swap(x)
if self._current_swap_list == self._swap_list1:
self._current_swap_list = self._swap_list2
else:
self._current_swap_list = self._swap_list1
class SingleSwapStatistics(object):
"""
Tracks swap statistics of a single sampler pair.
@param param_info: ParameterInfo instance holding swap parameters
@type param_info: L{AbstractSwapParameterInfo}
"""
def __init__(self, param_info):
self._total_swaps = 0
self._accepted_swaps = 0
@property
def total_swaps(self):
return self._total_swaps
@property
def accepted_swaps(self):
return self._accepted_swaps
@property
def acceptance_rate(self):
"""
Acceptance rate of the sampler pair.
"""
if self.total_swaps > 0:
return float(self.accepted_swaps) / float(self.total_swaps)
else:
return 0.
def update(self, accepted):
"""
Updates swap statistics.
"""
self._total_swaps += 1
self._accepted_swaps += int(accepted)
class SwapStatistics(object):
"""
Tracks swap statistics for an AbstractExchangeMC subclass instance.
@param param_infos: list of ParameterInfo instances providing information
needed for performing swaps
@type param_infos: list of L{AbstractSwapParameterInfo}
"""
def __init__(self, param_infos):
self._stats = [SingleSwapStatistics(x) for x in param_infos]
@property
def stats(self):
return tuple(self._stats)
@property
def acceptance_rates(self):
"""
Returns acceptance rates for all swaps.
"""
return [x.acceptance_rate for x in self._stats]
class InterpolationFactory(object):
"""
Produces interpolations for functions changed during non-equilibrium
trajectories.
@param protocol: protocol to be used to generate non-equilibrium trajectories
@type protocol: function mapping t to [0...1] for fixed tau
@param tau: switching time
@type tau: float
"""
def __init__(self, protocol, tau):
self._protocol = None
self._tau = None
self.protocol = protocol
self.tau = tau
@property
def protocol(self):
return self._protocol
@protocol.setter
def protocol(self, value):
if not hasattr(value, '__call__'):
raise TypeError(value)
self._protocol = value
@property
def tau(self):
return self._tau
@tau.setter
def tau(self, value):
self._tau = float(value)
def build_gradient(self, gradient):
"""
Create a gradient instance with according to given protocol
and switching time.
@param gradient: gradient with G(0) = G_1 and G(1) = G_2
@type gradient: callable
"""
return Gradient(gradient, self._protocol, self._tau)
def build_temperature(self, temperature):
"""
Create a temperature function according to given protocol and
switching time.
@param temperature: temperature with T(0) = T_1 and T(1) = T_2
@type temperature: callable
"""
return lambda t: temperature(self.protocol(t, self.tau))
class Gradient(AbstractGradient):
def __init__(self, gradient, protocol, tau):
self._protocol = protocol
self._gradient = gradient
self._tau = tau
def evaluate(self, q, t):
return self._gradient(q, self._protocol(t, self._tau))
class ReplicaHistory(object):
'''
Replica history object, works with both RE and RENS for
the AlternatingAdjacentSwapScheme.
@param samples: list holding ensemble states
@type samples: list
@param swap_interval: interval with which swaps were attempted, e.g.,
5 means that every 5th regular MC step is replaced
by a swap
@type swap_interval: int
@param first_swap: sample index of the first sample generated by a swap attempt.
If None, the first RE sampled is assumed to have sample index
swap_interval. If specified, it has to be greater than zero
@type first_swap: int
'''
def __init__(self, samples, swap_interval, first_swap=None):
self.samples = samples
self.swap_interval = swap_interval
if first_swap == None:
self.first_swap = swap_interval - 1
elif first_swap > 0:
self.first_swap = first_swap - 1
else:
raise(ValueError("Sample index of first swap has to be greater than zero!"))
self.n_replicas = len(samples[0])
@staticmethod
def _change_direction(x):
if x == 1:
return -1
if x == -1:
return 1
def calculate_history(self, start_ensemble):
'''
Calculates the replica history of the first state of ensemble #start_ensemble.
@param start_ensemble: index of the ensemble to start at, zero-indexed
@type start_ensemble: int
@return: replica history as a list of ensemble indices
@rtype: list of ints
'''
sample_counter = 0
# determine the direction (up = 1, down = -1) in the "temperature ladder" of
# the first swap attempt. Remember: first swap series is always 0 <-> 1, 2 <-> 3, ...
if start_ensemble % 2 == 0:
direction = +1
else:
direction = -1
# if number of replicas is not even and the start ensemble is the highest-temperature-
# ensemble, the first swap will be attempted "downwards"
if start_ensemble % 2 == 0 and start_ensemble == self.n_replicas - 1:
direction = -1
# will store the indices of the ensembles the state will visit in chronological order
history = []
# the ensemble the state is currently in
ens = start_ensemble
while sample_counter < len(self.samples):
if self.n_replicas == 2:
if (sample_counter - self.first_swap - 1) % self.swap_interval == 0 and \
sample_counter >= self.first_swap:
## swap attempt: determine whether it was successfull or not
# state after swap attempt
current_sample = self.samples[sample_counter][ens]
# state before swap attempt
previous_sample = self.samples[sample_counter - 1][history[-1]]
# swap was accepted when position of the current state doesn't equal
# the position of the state before the swap attempt, that is, the last
# state in the history
swap_accepted = not numpy.all(current_sample.position ==
previous_sample.position)
if swap_accepted:
if ens == 0:
ens = 1
else:
ens = 0
history.append(ens)
else:
history.append(ens)
else:
if (sample_counter - self.first_swap - 1) % self.swap_interval == 0 and \
sample_counter >= self.first_swap:
# state after swap attempt
current_sample = self.samples[sample_counter][ens]
# state before swap attempt
previous_sample = self.samples[sample_counter - 1][ens]
# swap was accepted when position of the current state doesn't equal
# the position of the state before the swap attempt, that is, the last
# state in the history
swap_accepted = not numpy.all(current_sample.position == previous_sample.position)
if swap_accepted:
ens += direction
else:
if ens == self.n_replicas - 1:
# if at the top of the ladder, go downwards again
direction = -1
elif ens == 0:
# if at the bottom of the ladder, go upwards
direction = +1
else:
# in between, reverse the direction of the trajectory
# in temperature space
direction = self._change_direction(direction)
history.append(ens)
sample_counter += 1
return history
def calculate_projected_trajectories(self, ensemble):
'''
Calculates sequentially correlated trajectories projected on a specific ensemble.
@param ensemble: ensemble index of ensemble of interest, zero-indexed
@type ensemble: int
@return: list of Trajectory objects containg sequentially correlated trajectories
@rtype: list of L{Trajectory} objects.
'''
trajectories = []
for i in range(self.n_replicas):
history = self.calculate_history(i)
traj = [x[ensemble] for k, x in enumerate(self.samples) if history[k] == ensemble]
trajectories.append(Trajectory(traj))
return trajectories
def calculate_trajectories(self):
'''
Calculates sequentially correlated trajectories.
@return: list of Trajectory objects containg sequentially correlated trajectories
@rtype: list of L{Trajectory} objects.
'''
trajectories = []
for i in range(self.n_replicas):
history = self.calculate_history(i)
traj = [x[history[k]] for k, x in enumerate(self.samples)]
trajectories.append(Trajectory(traj))
return trajectories
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