abydos/distance/_bhattacharyya.py
# Copyright 2019-2020 by Christopher C. Little.
# This file is part of Abydos.
#
# Abydos is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Abydos is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Abydos. If not, see <http://www.gnu.org/licenses/>.
"""abydos.distance._bhattacharyya.
Bhattacharyya distance
"""
from math import log
from typing import Any, Optional
from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer
__all__ = ['Bhattacharyya']
class Bhattacharyya(_TokenDistance):
r"""Bhattacharyya distance.
For two multisets X and Y drawn from an alphabet S, Bhattacharyya distance
:cite:`Bhattacharyya:1946` is
.. math::
dist_{Bhattacharyya}(X, Y) =
-log(\sum_{i \in S} \sqrt{X_iY_i})
.. versionadded:: 0.4.0
"""
def __init__(
self, tokenizer: Optional[_Tokenizer] = None, **kwargs: Any
) -> None:
"""Initialize Bhattacharyya instance.
Parameters
----------
tokenizer : _Tokenizer
A tokenizer instance from the :py:mod:`abydos.tokenizer` package
**kwargs
Arbitrary keyword arguments
Other Parameters
----------------
qval : int
The length of each q-gram. Using this parameter and tokenizer=None
will cause the instance to use the QGram tokenizer with this
q value.
.. versionadded:: 0.4.0
"""
super(Bhattacharyya, self).__init__(tokenizer=tokenizer, **kwargs)
def dist_abs(self, src: str, tar: str) -> float:
"""Return the Bhattacharyya distance of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Bhattacharyya distance
Examples
--------
>>> cmp = Bhattacharyya()
>>> cmp.dist_abs('cat', 'hat')
0.6931471805599453
>>> cmp.dist_abs('Niall', 'Neil')
1.0074515102711326
>>> cmp.dist_abs('aluminum', 'Catalan')
2.1383330595080277
>>> cmp.dist_abs('ATCG', 'TAGC')
-inf
.. versionadded:: 0.4.0
"""
bc = self.dist(src, tar)
if bc == 0:
return float('-inf')
elif bc == 1:
return 0.0
else:
return -log(bc)
def dist(self, src: str, tar: str) -> float:
"""Return the Bhattacharyya coefficient of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Bhattacharyya distance
Examples
--------
>>> cmp = Bhattacharyya()
>>> cmp.dist('cat', 'hat')
0.5
>>> cmp.dist('Niall', 'Neil')
0.3651483716701107
>>> cmp.dist('aluminum', 'Catalan')
0.11785113019775792
>>> cmp.dist('ATCG', 'TAGC')
0.0
.. versionadded:: 0.4.0
"""
self._tokenize(src, tar)
alphabet = self._intersection().keys()
src_pop = sum(self._src_tokens.values())
tar_pop = sum(self._tar_tokens.values())
return float(
sum(
(
self._src_tokens[tok]
/ src_pop
* self._tar_tokens[tok]
/ tar_pop
)
** 0.5
for tok in alphabet
)
)
if __name__ == '__main__':
import doctest
doctest.testmod()