# Source code for abydos.distance._gilbert_wells

# 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.
#
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# 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._gilbert_wells.

Gilbert & Wells similarity
"""

from math import factorial, log, pi
from sys import float_info

from ._token_distance import _TokenDistance

__all__ = ['GilbertWells']

_epsilon = float_info.epsilon

[docs]class GilbertWells(_TokenDistance):
r"""Gilbert & Wells similarity.

For two sets X and Y and a population N, the Gilbert & Wells
similarity :cite:Gilbert:1966 is

.. math::

sim_{GilbertWells}(X, Y) =
ln \frac{|N|^3}{2\pi |X| \cdot |Y| \cdot
|N \setminus Y| \cdot |N \setminus X|} + 2ln
\frac{|N|! \cdot |X \cap Y|! \cdot |X \setminus Y|! \cdot
|Y \setminus X|! \cdot |(N \setminus X) \setminus Y|!}
{|X|! \cdot |Y|! \cdot |N \setminus Y|! \cdot |N \setminus X|!}

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

.. math::

sim_{GilbertWells} =
ln \frac{n^3}{2\pi (a+b)(a+c)(b+d)(c+d)} +
2ln \frac{n!a!b!c!d!}{(a+b)!(a+c)!(b+d)!(c+d)!}

Notes
-----
Most lists of similarity & distance measures, including
:cite:Hubalek:1982,Choi:2010,Morris:2012 have a quite different formula,
which would be :math:ln~a - ln~b - ln \frac{a+b}{n} - ln \frac{a+c}{n} =
ln\frac{an}{(a+b)(a+c)}. However, neither this formula nor anything
similar or equivalent to it appears anywhere within the cited work,
:cite:Gilbert:1966. See :class:UnknownF for this, alternative,
measure.

"""

def __init__(self, alphabet=None, tokenizer=None, **kwargs):
"""Initialize GilbertWells 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
**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.

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

[docs]    def sim_score(self, src, tar):
"""Return the Gilbert & Wells 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
Gilbert & Wells similarity

Examples
--------
>>> cmp = GilbertWells()
>>> cmp.sim_score('cat', 'hat')
20.17617447734673
>>> cmp.sim_score('Niall', 'Neil')
16.717742356982733
>>> cmp.sim_score('aluminum', 'Catalan')
5.495096667524002
>>> cmp.sim_score('ATCG', 'TAGC')
1.6845961909440712

"""
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()

return log(
max(
_epsilon,
n ** 3
/ (
2
* pi
* max(_epsilon, a + b)
* max(_epsilon, a + c)
* max(_epsilon, b + d)
* max(_epsilon, c + d)
),
)
) + 2 * (
log(factorial(n))
+ log(factorial(a))
+ log(factorial(b))
+ log(factorial(c))
+ log(factorial(d))
- log(factorial(a + b))
- log(factorial(a + c))
- log(factorial(b + d))
- log(factorial(c + d))
)

[docs]    def sim(self, src, tar):
"""Return the normalized Gilbert & Wells 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
Normalized Gilbert & Wells similarity

Examples
--------
>>> cmp = GilbertWells()
>>> cmp.sim('cat', 'hat')
0.4116913723876516
>>> cmp.sim('Niall', 'Neil')
0.2457247406857589
>>> cmp.sim('aluminum', 'Catalan')
0.05800001636414742
>>> cmp.sim('ATCG', 'TAGC')
0.028716013247135602

"""
if src == tar:
return 1.0
if not src or not tar:
return 0.0
norm = max(self.sim_score(src, src), self.sim_score(tar, tar))
return self.sim_score(src, tar) / norm

if __name__ == '__main__':
import doctest

doctest.testmod()