abydos/distance/_baulieu_iv.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._baulieu_iv.
Baulieu IV distance
"""
from math import e
from typing import Any, Counter as TCounter, Optional, Sequence, Set, Union
from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer
__all__ = ['BaulieuIV']
class BaulieuIV(_TokenDistance):
r"""Baulieu IV distance.
For two sets X and Y, a population N, and a positive irractional number k,
Baulieu IV distance :cite:`Baulieu:1997` is
.. math::
dist_{BaulieuIV}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X| -
(|X \cap Y| + \frac{1}{2}) \cdot (|(N \setminus X) \setminus Y| +
\frac{1}{2}) \cdot |(N \setminus X) \setminus Y| \cdot k}{|N|}
This is Baulieu's 22nd dissimilarity coefficient.
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
dist_{BaulieuIV} = \frac{b+c-(a+\frac{1}{2})(d+\frac{1}{2})dk}{n}
Notes
-----
The default value of k is Euler's number :math:`e`, but other irrationals
such as :math:`\pi` or :math:`\sqrt{2}` could be substituted at
initialization.
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet: Optional[
Union[TCounter[str], Sequence[str], Set[str], int]
] = None,
tokenizer: Optional[_Tokenizer] = None,
intersection_type: str = 'crisp',
positive_irrational: float = e,
**kwargs: Any
) -> None:
"""Initialize BaulieuIV instance.
Parameters
----------
alphabet : Counter, collection, int, or None
This represents the alphabet of possible tokens.
See :ref:`alphabet <alphabet>` description in
:py:class:`_TokenDistance` for details.
tokenizer : _Tokenizer
A tokenizer instance from the :py:mod:`abydos.tokenizer` package
intersection_type : str
Specifies the intersection type, and set type as a result:
See :ref:`intersection_type <intersection_type>` description in
:py:class:`_TokenDistance` for details.
**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.
metric : _Distance
A string distance measure class for use in the ``soft`` and
``fuzzy`` variants.
threshold : float
A threshold value, similarities above which are counted as
members of the intersection for the ``fuzzy`` variant.
.. versionadded:: 0.4.0
"""
super(BaulieuIV, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
self._positive_irrational = positive_irrational
def dist_abs(self, src: str, tar: str) -> float:
"""Return the Baulieu IV 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
Baulieu IV distance
Examples
--------
>>> cmp = BaulieuIV()
>>> cmp.dist_abs('cat', 'hat')
-5249.96272285802
>>> cmp.dist_abs('Niall', 'Neil')
-5209.561726488335
>>> cmp.dist_abs('aluminum', 'Catalan')
-3073.6070822721244
>>> cmp.dist_abs('ATCG', 'TAGC')
-1039.2151656463932
.. versionadded:: 0.4.0
"""
self._tokenize(src, tar)
a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
d = self._total_complement_card()
n = self._population_unique_card()
k = self._positive_irrational
num = (b + c) - (a + 0.5) * (d + 0.5) * d * k
if num == 0.0:
return 0.0
return num / n
def dist(self, src: str, tar: str) -> float:
"""Return the normalized Baulieu IV 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
Normalized Baulieu IV distance
Examples
--------
>>> cmp = BaulieuIV()
>>> cmp.dist('cat', 'hat')
0.49999799606535283
>>> cmp.dist('Niall', 'Neil')
0.49999801148659684
>>> cmp.dist('aluminum', 'Catalan')
0.49999883126809364
>>> cmp.dist('ATCG', 'TAGC')
0.4999996033268451
.. versionadded:: 0.4.0
"""
distance = self.dist_abs(src, tar)
n3 = self._population_unique_card() ** 3
k = self._positive_irrational
num = distance + n3 * k
if num == 0.0:
return 0.0
return (distance + n3 * k) / (2 * n3 * k)
if __name__ == '__main__':
import doctest
doctest.testmod()