Source code for filterpy.monte_carlo.resampling

# -*- coding: utf-8 -*-
# pylint: disable=C0103, R0913, R0902, C0326, R0914
# disable snake_case warning, too many arguments, too many attributes,
# one space before assignment, too many local variables



"""Copyright 2015 Roger R Labbe Jr.

FilterPy library.
http://github.com/rlabbe/filterpy

Documentation at:
https://filterpy.readthedocs.org

Supporting book at:
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python

This is licensed under an MIT license. See the readme.MD file
for more information.
"""

import numpy as np
from numpy.random import random


def residual_resample(weights):
    """ Performs the residual resampling algorithm used by particle filters.

    Based on observation that we don't need to use random numbers to select
    most of the weights. Take int(N*w^i) samples of each particle i, and then
    resample any remaining using a standard resampling algorithm [1]


    Parameters
    ----------

    weights : list-like of float
        list of weights as floats

    Returns
    -------

    indexes : ndarray of ints
        array of indexes into the weights defining the resample. i.e. the
        index of the zeroth resample is indexes[0], etc.

    References
    ----------

    .. [1] J. S. Liu and R. Chen. Sequential Monte Carlo methods for dynamic
       systems. Journal of the American Statistical Association,
       93(443):1032–1044, 1998.
    """

    N = len(weights)
    indexes = np.zeros(N, 'i')

    # take int(N*w) copies of each weight, which ensures particles with the
    # same weight are drawn uniformly
    num_copies = (np.floor(N*np.asarray(weights))).astype(int)
    k = 0
    for i in range(N):
        for _ in range(num_copies[i]): # make n copies
            indexes[k] = i
            k += 1

    # use multinormal resample on the residual to fill up the rest. This
    # maximizes the variance of the samples
    residual = weights - num_copies     # get fractional part
    residual /= sum(residual)           # normalize
    cumulative_sum = np.cumsum(residual)
    cumulative_sum[-1] = 1. # avoid round-off errors: ensures sum is exactly one
    indexes[k:N] = np.searchsorted(cumulative_sum, random(N-k))

    return indexes



def stratified_resample(weights):
    """ Performs the stratified resampling algorithm used by particle filters.

    This algorithms aims to make selections relatively uniformly across the
    particles. It divides the cumulative sum of the weights into N equal
    divisions, and then selects one particle randomly from each division. This
    guarantees that each sample is between 0 and 2/N apart.

    Parameters
    ----------
    weights : list-like of float
        list of weights as floats

    Returns
    -------

    indexes : ndarray of ints
        array of indexes into the weights defining the resample. i.e. the
        index of the zeroth resample is indexes[0], etc.
    """

    N = len(weights)
    # make N subdivisions, and chose a random position within each one
    positions = (random(N) + range(N)) / N

    indexes = np.zeros(N, 'i')
    cumulative_sum = np.cumsum(weights)
    i, j = 0, 0
    while i < N:
        if positions[i] < cumulative_sum[j]:
            indexes[i] = j
            i += 1
        else:
            j += 1
    return indexes


def systematic_resample(weights):
    """ Performs the systemic resampling algorithm used by particle filters.

    This algorithm separates the sample space into N divisions. A single random
    offset is used to to choose where to sample from for all divisions. This
    guarantees that every sample is exactly 1/N apart.

    Parameters
    ----------
    weights : list-like of float
        list of weights as floats

    Returns
    -------

    indexes : ndarray of ints
        array of indexes into the weights defining the resample. i.e. the
        index of the zeroth resample is indexes[0], etc.
    """
    N = len(weights)

    # make N subdivisions, and choose positions with a consistent random offset
    positions = (random() + np.arange(N)) / N

    indexes = np.zeros(N, 'i')
    cumulative_sum = np.cumsum(weights)
    i, j = 0, 0
    while i < N:
        if positions[i] < cumulative_sum[j]:
            indexes[i] = j
            i += 1
        else:
            j += 1
    return indexes


def multinomial_resample(weights):
    """ This is the naive form of roulette sampling where we compute the
    cumulative sum of the weights and then use binary search to select the
    resampled point based on a uniformly distributed random number. Run time
    is O(n log n). You do not want to use this algorithm in practice; for some
    reason it is popular in blogs and online courses so I included it for
    reference.

   Parameters
   ----------

    weights : list-like of float
        list of weights as floats

    Returns
    -------

    indexes : ndarray of ints
        array of indexes into the weights defining the resample. i.e. the
        index of the zeroth resample is indexes[0], etc.
    """
    cumulative_sum = np.cumsum(weights)
    cumulative_sum[-1] = 1.  # avoid round-off errors: ensures sum is exactly one
    return np.searchsorted(cumulative_sum, random(len(weights)))