import numpy as np
from .base import Resampler
from ..base import Property
from ..types.state import ParticleState
[docs]class SystematicResampler(Resampler):
[docs] def resample(self, particles, nparts=None):
"""Resample the particles
Parameters
----------
particles : :class:`~.ParticleState` or list of :class:`~.Particle`
The particles or particle state to be resampled according to their weights
nparts : int
The number of particles to be returned from resampling
Returns
-------
particle state: :class:`~.ParticleState`
The particle state after resampling
"""
if not isinstance(particles, ParticleState):
particles = ParticleState(None, particle_list=particles)
if nparts is None:
nparts = len(particles)
log_weights = particles.log_weight
weight_order = np.argsort(log_weights, kind='stable')
max_log_value = log_weights[weight_order[-1]]
with np.errstate(divide='ignore'):
cdf = np.log(np.cumsum(np.exp(log_weights[weight_order] - max_log_value)))
cdf += max_log_value
# Pick random starting point
u_i = np.random.uniform(0, 1 / nparts)
# Cycle through the cumulative distribution and copy the particle
# that pushed the score over the current value
u_j = u_i + (1 / nparts) * np.arange(nparts)
index = weight_order[np.searchsorted(cdf, np.log(u_j))]
new_particles = particles[index]
new_particles.log_weight = np.full((nparts, ), np.log(1/nparts))
return new_particles
[docs]class ESSResampler(Resampler):
""" This wrapper uses a :class:`~.Resampler` to resample the particles inside
an instant of :class:`~.Particles`, but only after checking if this is necessary
by comparing Effective Sample Size (ESS) with a supplied threshold (numeric).
Kish's ESS is used, as recommended in Section 3.5 of this tutorial [1]_.
References
----------
.. [1] Doucet A., Johansen A.M., 2009, Tutorial on Particle Filtering \
and Smoothing: Fifteen years later, Handbook of Nonlinear Filtering, Vol. 12.
"""
threshold: float = Property(default=None,
doc='Threshold compared with ESS to decide whether to resample. \
Default is number of particles divided by 2, \
set in resample method')
resampler: Resampler = Property(default=SystematicResampler,
doc='Resampler to wrap, which is called \
when ESS below threshold')
[docs] def resample(self, particles):
"""
Parameters
----------
particles : list of :class:`~.Particle`
The particles to be resampled according to their weight
Returns
-------
particles : list of :class:`~.Particle`
The particles, either unchanged or resampled, depending on weight degeneracy
"""
if not isinstance(particles, ParticleState):
particles = ParticleState(None, particle_list=particles)
if self.threshold is None:
self.threshold = len(particles) / 2
# If ESS too small, resample
if 1 / np.sum(np.exp(2*particles.log_weight)) < self.threshold:
return self.resampler.resample(self.resampler, particles)
else:
return particles