# Source code for pyinform.conditionalentropy

# Copyright 2016-2019 Douglas G. Moore. All rights reserved.
# Use of this source code is governed by a MIT
"""
Conditional entropy_ is a measure of the amount of information
required to describe a random variable :math:Y given knowledge of another
random variable :math:X. When applied to time series, two time series are used
to construct the empirical distributions and then
:py:func:~.shannon.conditional_entropy can be applied to yield

.. math::

H(Y|X) = -\\sum_{x_i, y_i} p(x_i, y_i) \\log_2 \\frac{p(x_i, y_i)}{p(x_i)}.

This can be viewed as the time-average of the local conditional entropy

.. math::

h_{i}(Y|X) = -\\log_2 \\frac{p(x_i, y_i)}{p(x_i)}.

.. _Conditional entropy: https://en.wikipedia.org/wiki/Conditional_entropy

Examples
--------

.. doctest:: conditional_entropy

>>> xs = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1]
>>> ys = [0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1]
>>> conditional_entropy(xs,ys)      # H(Y|X)
0.5971071794515037
>>> conditional_entropy(ys,xs)      # H(X|Y)
0.5077571498797332
>>> conditional_entropy(xs, ys, local=True)
array([3.        , 3.        , 0.19264508, 0.19264508, 0.19264508,
0.19264508, 0.19264508, 0.19264508, 0.19264508, 0.19264508,
0.19264508, 0.19264508, 0.19264508, 0.19264508, 0.19264508,
0.19264508, 0.4150375 , 0.4150375 , 0.4150375 , 2.        ])
>>> conditional_entropy(ys, xs, local=True)
array([1.32192809, 1.32192809, 0.09953567, 0.09953567, 0.09953567,
0.09953567, 0.09953567, 0.09953567, 0.09953567, 0.09953567,
0.09953567, 0.09953567, 0.09953567, 0.09953567, 0.09953567,
0.09953567, 0.73696559, 0.73696559, 0.73696559, 3.9068906 ])
"""
import numpy as np

from ctypes import byref, c_int, c_ulong, c_double, POINTER
from pyinform import _inform
from pyinform.error import ErrorCode, error_guard

[docs]def conditional_entropy(xs, ys, local=False):
"""
Compute the (local) conditional entropy between two time series.

This function expects the **condition** to be the first argument.

:param xs: the time series drawn from the conditional distribution
:type xs: a sequence or numpy.ndarray
:param ys: the time series drawn from the target distribution
:type ys: a sequence or numpy.ndarray
:param bool local: compute the local conditional entropy
:return: the local or average conditional entropy
:rtype: float or numpy.ndarray
:raises ValueError: if the time series have different shapes
:raises InformError: if an error occurs within the inform C call
"""
us = np.ascontiguousarray(xs, dtype=np.int32)
vs = np.ascontiguousarray(ys, dtype=np.int32)
if us.shape != vs.shape:
raise ValueError("timeseries lengths do not match")

bx = max(2, np.amax(us) + 1)
by = max(2, np.amax(vs) + 1)

xdata = us.ctypes.data_as(POINTER(c_int))
ydata = vs.ctypes.data_as(POINTER(c_int))
n = us.size

e = ErrorCode(0)

if local is True:
ce = np.empty(us.shape, dtype=np.float64)
out = ce.ctypes.data_as(POINTER(c_double))
_local_conditional_entropy(xdata, ydata, c_ulong(n), c_int(bx), c_int(by), out, byref(e))
else:
ce = _conditional_entropy(xdata, ydata, c_ulong(n), c_int(bx), c_int(by), byref(e))

error_guard(e)

return ce

_conditional_entropy = _inform.inform_conditional_entropy
_conditional_entropy.argtypes = [POINTER(c_int), POINTER(c_int), c_ulong, c_int, c_int, POINTER(c_int)]
_conditional_entropy.restype = c_double

_local_conditional_entropy = _inform.inform_local_conditional_entropy
_local_conditional_entropy.argtypes = [POINTER(c_int), POINTER(c_int), c_ulong, c_int, c_int, POINTER(c_double), POINTER(c_int)]
_local_conditional_entropy.restype = c_double