# Copyright 2016-2019 Douglas G. Moore. All rights reserved.
# Use of this source code is governed by a MIT
# license that can be found in the LICENSE file.
"""
Block entropy, also known as N-gram entropy [Shannon1948]_, is the the standard
Shannon entropy applied to the time series (or sequence) of :math:`k`-histories
of a time series (or sequence):
.. math::
H(X^{(k)}) = -\\sum_{x^{(k)}_i} p(x^{(k)}_i) \\log_2 p(x^{(k)}_i)
which of course reduces to the traditional Shannon entropy for ``k == 1``. Much
as with :ref:`active-information`, the ideal usage is to take
:math:`k \\rightarrow \\infty`.
Examples
--------
A Single Initial Condition
^^^^^^^^^^^^^^^^^^^^^^^^^^
The typical usage is to provide the time series as a sequence (or
``numpy.ndarray``) and the block size as an integer and let the
:py:func:`block_entropy` sort out the rest:
.. doctest:: block_entropy
>>> block_entropy([0,0,1,1,1,1,0,0,0], k=1)
0.9910760598382222
>>> block_entropy([0,0,1,1,1,1,0,0,0], k=1, local=True)
array([[0.84799691, 0.84799691, 1.169925 , 1.169925 , 1.169925 ,
1.169925 , 0.84799691, 0.84799691, 0.84799691]])
.. doctest:: block_entropy
>>> block_entropy([0,0,1,1,1,1,0,0,0], k=2)
1.811278124459133
>>> block_entropy([0,0,1,1,1,1,0,0,0], k=2, local=True)
array([[1.4150375, 3. , 1.4150375, 1.4150375, 1.4150375, 3. ,
1.4150375, 1.4150375]])
Multiple Initial Conditions
^^^^^^^^^^^^^^^^^^^^^^^^^^^
Do we support multiple initial conditions? Of course we do!
.. doctest:: block_entropy
>>> series = [[0,0,1,1,1,1,0,0,0], [1,0,0,1,0,0,1,0,0]]
>>> block_entropy(series, k=2)
1.936278124459133
>>> block_entropy(series, k=2, local=True)
array([[1.4150375, 2.4150375, 2.4150375, 2.4150375, 2.4150375, 2. ,
1.4150375, 1.4150375],
[2. , 1.4150375, 2.4150375, 2. , 1.4150375, 2.4150375,
2. , 1.4150375]])
Or you can compute the block entropy on each initial condition and average:
.. doctest:: block_entropy
>>> import numpy as np
>>> np.apply_along_axis(block_entropy, 1, series, 2).mean()
1.686278124459133
"""
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 block_entropy(series, k, local=False):
"""
Compute the (local) block entropy of a time series with block size *k*.
:param series: the time series
:type series: sequence or `numpy.ndarray`
:param int k: the block size
:param bool local: compute the local block entropy
:returns: the average or local block entropy
:rtype: float or `numpy.ndarray`
:raises ValueError: if the time series has no initial conditions
:raises ValueError: if the time series is greater than 2-D
:raises InformError: if an error occurs within the ``inform`` C call
"""
xs = np.ascontiguousarray(series, np.int32)
if xs.ndim == 0:
raise ValueError("empty timeseries")
elif xs.ndim > 2:
raise ValueError("dimension greater than 2")
b = max(2, np.amax(xs) + 1)
data = xs.ctypes.data_as(POINTER(c_int))
if xs.ndim == 1:
n, m = 1, xs.shape[0]
else:
n, m = xs.shape
e = ErrorCode(0)
if local is True:
q = max(0, m - k + 1)
ai = np.empty((n, q), dtype=np.float64)
out = ai.ctypes.data_as(POINTER(c_double))
_local_block_entropy(data, c_ulong(n), c_ulong(m), c_int(b), c_ulong(k), out, byref(e))
else:
ai = _block_entropy(data, c_ulong(n), c_ulong(m), c_int(b), c_ulong(k), byref(e))
error_guard(e)
return ai
_block_entropy = _inform.inform_block_entropy
_block_entropy.argtypes = [POINTER(c_int), c_ulong, c_ulong, c_int, c_ulong, POINTER(c_int)]
_block_entropy.restype = c_double
_local_block_entropy = _inform.inform_local_block_entropy
_local_block_entropy.argtypes = [POINTER(c_int), c_ulong, c_ulong, c_int, c_ulong, POINTER(c_double), POINTER(c_int)]
_local_block_entropy.restype = POINTER(c_double)