# Source code for abydos.distance._dunning

# Copyright 2018-2020 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._dunning.

Dunning similarity
"""

from math import log

from ._token_distance import _TokenDistance

__all__ = ['Dunning']

[docs]class Dunning(_TokenDistance):
r"""Dunning similarity.

For two sets X and Y and a population N, Dunning log-likelihood
:cite:Dunning:1993, following :cite:Church:1991, is

.. math::

sim_{Dunning}(X, Y) = \lambda =
|X \cap Y| \cdot log_2(|X \cap Y|) +\\
|X \setminus Y| \cdot log_2(|X \setminus Y|) +
|Y \setminus X| \cdot log_2(|Y \setminus X|) +\\
|(N \setminus X) \setminus Y| \cdot
log_2(|(N \setminus X) \setminus Y|) -\\
(|X| \cdot log_2(|X|) +
|Y| \cdot log_2(|Y|) +\\
|N \setminus Y| \cdot log_2(|N \setminus Y|) +
|N \setminus X| \cdot log_2(|N \setminus X|))

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

.. math::

sim_{Dunning} = \lambda =
a \cdot log_2(a) +\\
b \cdot log_2(b) + c \cdot log_2(c) +
d \cdot log_2(d) - \\
((a+b) \cdot log_2(a+b) + (a+c) \cdot log_2(a+c) +\\
(b+d) \cdot log_2(b+d) + (c+d) log_2(c+d))

Notes
-----
To avoid NaNs, every logarithm is calculated as the logarithm of 1 greater
than the value in question. (Python's math.log1p function is used.)

"""

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

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

Examples
--------
>>> cmp = Dunning()
>>> cmp.sim('cat', 'hat')
0.33462839191969423
>>> cmp.sim('Niall', 'Neil')
0.19229445539929793
>>> cmp.sim('aluminum', 'Catalan')
0.03220862737070572
>>> cmp.sim('ATCG', 'TAGC')
0.0010606026735052122

"""
self._tokenize(src, tar)

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

# a should not equal n, because 0 will result
# As a workaround, we set d to 1 and add one to n.
if a == n:
d = 1
n += 1

a /= n
b /= n
c /= n
d /= n

score = 0.0
for i in [a, b, c, d]:
if i > 0:
score += i * log(i)
for i in [a, d]:
for j in [b, c]:
ij = i + j
if ij > 0:
score -= ij * log(ij)
score *= 2
score /= log(2)

return abs(round(score, 15))

[docs]    def sim(self, src, tar):
"""Return the normalized Dunning 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 Dunning similarity

Examples
--------
>>> cmp = Dunning()
>>> cmp.sim('cat', 'hat')
0.33462839191969423
>>> cmp.sim('Niall', 'Neil')
0.19229445539929793
>>> cmp.sim('aluminum', 'Catalan')
0.03220862737070572
>>> cmp.sim('ATCG', 'TAGC')
0.0010606026735052122

"""
if src == tar:
return 1.0

score = self.sim_score(src, tar)
if not score:
return 0.0

norm = max(self.sim_score(src, src), self.sim_score(tar, tar))
return score / norm

if __name__ == '__main__':
import doctest

doctest.testmod()