# Source code for abydos.distance._gilbert

# 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,
# 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._gilbert.

Gilbert correlation
"""

from ._token_distance import _TokenDistance

__all__ = ['Gilbert']

[docs]class Gilbert(_TokenDistance):
r"""Gilbert correlation.

For two sets X and Y and a population N, the Gilbert correlation
:cite:Gilbert:1884 is

.. math::

corr_{Gilbert}(X, Y) =
\frac{2(|X \cap Y| \cdot |(N \setminus X) \setminus Y| -
|X \setminus Y| \cdot |Y \setminus X|)}
{|N|^2 - |X \cap Y|^2 + |X \setminus Y|^2 + |Y \setminus X|^2 -
|(N \setminus X) \setminus Y|^2}

For lack of access to the original, this formula is based on the concurring
formulae presented in :cite:Peirce:1884 and :cite:Doolittle:1884.

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

.. math::

corr_{Gilbert} =

"""

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

[docs]    def corr(self, src, tar):
"""Return the Gilbert correlation 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 correlation

Examples
--------
>>> cmp = Gilbert()
>>> cmp.corr('cat', 'hat')
0.3310580204778157
>>> cmp.corr('Niall', 'Neil')
0.21890122402504983
>>> cmp.corr('aluminum', 'Catalan')
0.057094811018577836
>>> cmp.corr('ATCG', 'TAGC')
-0.003198976327575176

"""
if src == tar:
return 1.0

self._tokenize(src, tar)

a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
n = self._population_unique_card()

num = a * n - (a + b) * (a + c)
if num:
return num / (n * (a + b + c) - (a + b) * (a + c))
return 0.0

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

Examples
--------
>>> cmp = Gilbert()
>>> cmp.sim('cat', 'hat')
0.6655290102389079
>>> cmp.sim('Niall', 'Neil')
0.6094506120125249
>>> cmp.sim('aluminum', 'Catalan')
0.5285474055092889
>>> cmp.sim('ATCG', 'TAGC')
0.4984005118362124