# Source code for abydos.distance._goodman_kruskal_lambda

# Copyright 2018-2020 by Christopher C. Little.
# This file is part of Abydos.
#
# Abydos is free software: you can redistribute it and/or modify
# 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,
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
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# 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._goodman_kruskal_lambda.

Goodman & Kruskal's Lambda similarity
"""

from ._token_distance import _TokenDistance

__all__ = ['GoodmanKruskalLambda']

[docs]class GoodmanKruskalLambda(_TokenDistance):
r"""Goodman & Kruskal's Lambda similarity.

For two sets X and Y and a population N, Goodman & Kruskal's lambda
:cite:Goodman:1954 is

.. math::

sim_{GK_\lambda}(X, Y) =
\frac{\frac{1}{2}(max(|X \cap Y|, |X \setminus Y|)+
max(|Y \setminus X|, |(N \setminus X) \setminus Y|)+
max(|X \cap Y|, |Y \setminus X|)+
max(|X \setminus Y|, |(N \setminus X) \setminus Y|))-
(max(|X|, |N \setminus X|)+max(|Y|, |N \setminus Y|))}
{|N|-\frac{1}{2}(max(|X|, |N \setminus X|)+
max(|Y|, |N \setminus Y|))}

In :ref:2x2 confusion table terms <confusion_table>, where a+b+c+d=n,
this is

.. math::

sim_{GK_\lambda} =
\frac{\frac{1}{2}((max(a,b)+max(c,d)+max(a,c)+max(b,d))-
(max(a+b,c+d)+max(a+c,b+d)))}
{n-\frac{1}{2}(max(a+b,c+d)+max(a+c,b+d))}

"""

def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
**kwargs
):
"""Initialize GoodmanKruskalLambda 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.

"""
super(GoodmanKruskalLambda, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)

[docs]    def sim(self, src, tar):
"""Return   Goodman & Kruskal's Lambda similarity 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
Goodman & Kruskal's Lambda similarity

Examples
--------
>>> cmp = GoodmanKruskalLambda()
>>> cmp.sim('cat', 'hat')
0.0
>>> cmp.sim('Niall', 'Neil')
0.0
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

"""
if src == tar:
return 1.0

self._tokenize(src, tar)

a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
d = self._total_complement_card()

sigma = max(a, b) + max(c, d) + max(a, c) + max(b, d)
sigma_prime = max(a + c, b + d) + max(a + b, c + d)
num = sigma - sigma_prime

if num:
return num / (2 * (a + b + c + d) - sigma_prime)
return 0.0

if __name__ == '__main__':
import doctest

doctest.testmod()