abydos/distance/_baulieu_iii.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_iii.
Baulieu III distance
"""
from typing import Any, Counter as TCounter, Optional, Sequence, Set, Union
from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer
__all__ = ['BaulieuIII']
class BaulieuIII(_TokenDistance):
r"""Baulieu III distance.
For two sets X and Y and a population N, Baulieu III distance
:cite:`Baulieu:1989` is
.. math::
sim_{BaulieuIII}(X, Y) =
\frac{|N|^2 - 4(|X \cap Y| \cdot |(N \setminus X) \setminus Y| -
|X \setminus Y| \cdot |Y \setminus X|)}{2 \cdot |N|^2}
This is based on Baulieu's 20th dissimilarity coefficient.
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{BaulieuIII} =
\frac{n^2 - 4(ad-bc)}{2n^2}
Notes
-----
It should be noted that this is *based on* Baulieu's 20th dissimilarity
coefficient. This distance is exactly half Baulieu's 20th dissimilarity.
According to :cite:`Baulieu:1989`, the 20th dissimilarity should be a
value in the range [0.0, 1.0], meeting the article's (P1) property, but the
formula given ranges [0.0, 2.0], so dividing by 2 corrects the formula to
meet the article's expectations.
.. 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',
**kwargs: Any
) -> None:
"""Initialize BaulieuIII 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(BaulieuIII, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
def dist(self, src: str, tar: str) -> float:
"""Return the Baulieu III 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 III distance
Examples
--------
>>> cmp = BaulieuIII()
>>> cmp.dist('cat', 'hat')
0.4949500208246564
>>> cmp.dist('Niall', 'Neil')
0.4949955747605165
>>> cmp.dist('aluminum', 'Catalan')
0.49768591017891195
>>> cmp.dist('ATCG', 'TAGC')
0.5000813463140358
.. 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()
num = n * n - 4 * (a * d - b * c)
if num == 0:
return 0.0
return num / (2 * n * n)
if __name__ == '__main__':
import doctest
doctest.testmod()