abydos/distance/_baulieu_vi.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_vi.
Baulieu VI distance
"""
from typing import Any, Counter as TCounter, Optional, Sequence, Set, Union
from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer
__all__ = ['BaulieuVI']
class BaulieuVI(_TokenDistance):
r"""Baulieu VI distance.
For two sets X and Y and a population N, Baulieu VI distance
:cite:`Baulieu:1997` is
.. math::
dist_{BaulieuVI}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X|}
{|X \cap Y| + |X \setminus Y| + |Y \setminus X| + 1}
This is Baulieu's 24th dissimilarity coefficient. This coefficient fails
Baulieu's (P3) property, that :math:`D(a,b,c,d) = 1` for some (a,b,c,d).
Rather, :math:`D(a,b,c,d) < 1`, but
:math:`\lim_{b \to \infty, c \to \infty} D(a,b,c,d) = 0` for :math:`a = 0`.
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
dist_{BaulieuVI} = \frac{b+c}{a+b+c+1}
.. 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 BaulieuVI 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(BaulieuVI, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
def dist(self, src: str, tar: str) -> float:
"""Return the Baulieu VI 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 VI distance
Examples
--------
>>> cmp = BaulieuVI()
>>> cmp.dist('cat', 'hat')
0.5714285714285714
>>> cmp.dist('Niall', 'Neil')
0.7
>>> cmp.dist('aluminum', 'Catalan')
0.8823529411764706
>>> cmp.dist('ATCG', 'TAGC')
0.9090909090909091
.. versionadded:: 0.4.0
"""
self._tokenize(src, tar)
a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
return (b + c) / (a + b + c + 1)
if __name__ == '__main__':
import doctest
doctest.testmod()