# Source code for filterpy.discrete_bayes.discrete_bayes

# -*- coding: utf-8 -*-
"""Copyright 2015 Roger R Labbe Jr.

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

Documentation at:

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

"""

from __future__ import (absolute_import, division, print_function,
unicode_literals)

import numpy as np
from scipy.ndimage.filters import convolve
from scipy.ndimage.interpolation import shift

[docs]def normalize(pdf):
"""Normalize distribution pdf in-place so it sums to 1.0.

Returns pdf for convienence, so you can write things like:

>>> kernel = normalize(randn(7))

Parameters
----------

pdf : ndarray
discrete distribution that needs to be converted to a pdf. Converted
in-place, i.e., this is modified.

Returns
-------

pdf : ndarray
The converted pdf.
"""

pdf /= sum(np.asarray(pdf, dtype=float))
return pdf

[docs]def update(likelihood, prior):
""" Computes the posterior of a discrete random variable given a
discrete likelihood and prior. In a typical application the likelihood
will be the likelihood of a measurement matching your current environment,
and the prior comes from discrete_bayes.predict().

Parameters
----------

likelihood : ndarray, dtype=flaot
array of likelihood values

prior : ndarray, dtype=flaot
prior pdf.

Returns
-------

posterior : ndarray, dtype=float
Returns array representing the posterior.

Examples
--------
.. code-block:: Python

# self driving car. Sensor returns values that can be equated to positions
# on the road. A real likelihood compuation would be much more complicated
# than this example.

prior = predict(posterior, velocity, kernel)
posterior = update(likelihood, prior)
"""

posterior = prior * likelihood
return normalize(posterior)

[docs]def predict(pdf, offset, kernel, mode='wrap', cval=0.):
""" Performs the discrete Bayes filter prediction step, generating
the prior.

pdf is a discrete probability distribution expressing our initial
belief.

offset is an integer specifying how much we want to move to the right
(negative values means move to the left)

We assume there is some noise in that offset, which we express in kernel.
For example, if offset=3 and kernel=[.1, .7., .2], that means we think
there is a 70% chance of moving right by 3, a 10% chance of moving 2
spaces, and a 20% chance of moving by 4.

It returns the resulting distribution.

If mode='wrap', then the probability distribution is wrapped around
the array.

If mode='constant', or any other value the pdf is shifted, with cval
used to fill in missing elements.

Examples
--------
.. code-block:: Python

belief = [.05, .05, .05, .05, .55, .05, .05, .05, .05, .05]
prior = predict(belief, offset=2, kernel=[.1, .8, .1])
"""

if mode == 'wrap':
return convolve(np.roll(pdf, offset), kernel, mode='wrap')

return convolve(shift(pdf, offset, cval=cval), kernel,
cval=cval, mode='constant')