# Source code for abydos.distance._gini_i

# 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._gini_i.

Gini I correlation
"""

from sys import float_info

from ._token_distance import _TokenDistance

__all__ = ['GiniI']

_epsilon = float_info.epsilon

[docs]class GiniI(_TokenDistance):
r"""Gini I correlation.

For two sets X and Y and a population N, Gini I correlation
:cite:Gini:1912, using the formula from :cite:Goodman:1959, is

.. math::

corr_{GiniI}(X, Y) =
\frac{\frac{|X \cap Y|+|(N \setminus X) \setminus Y|}{|N|} -
\frac{|X| \cdot |Y|}{|N|} +
\frac{|N \setminus Y| \cdot |N \setminus X|}{|N|}}
{\sqrt{(1-(\frac{|X|}{|N|}^2+\frac{|Y|}{|N|}^2)) \cdot
(1-(\frac{|N \setminus Y|}{|N|}^2 +
\frac{|N \setminus X|}{|N|}^2))}}

In :ref:2x2 confusion table terms <confusion_table>, where a+b+c+d=n,
after each term has been converted to a proportion by dividing by n, this
is

.. math::

corr_{GiniI} =
\frac{(a+d)-(a+b)(a+c) + (b+d)(c+d)}
{\sqrt{(1-((a+b)^2+(c+d)^2))\cdot(1-((a+c)^2+(b+d)^2))}}

"""

def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
normalizer='proportional',
**kwargs
):
"""Initialize GiniI 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.
normalizer : str
Specifies the normalization type. See :ref:normalizer <alphabet>
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(GiniI, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
normalizer=normalizer,
**kwargs
)

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

Examples
--------
>>> cmp = GiniI()
>>> cmp.corr('cat', 'hat')
0.49722814498933254
>>> cmp.corr('Niall', 'Neil')
0.39649090262533215
>>> cmp.corr('aluminum', 'Catalan')
0.14887105223941113
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237489576

"""
self._tokenize(src, tar)

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

return ((a + d) - ((a + b) * (a + c) + (c + d) * (b + d))) / (
(1 + _epsilon - ((a + b) ** 2 + (c + d) ** 2))
* (1 + _epsilon - ((a + c) ** 2 + (b + d) ** 2))
) ** 0.5

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

Examples
--------
>>> cmp = GiniI()
>>> cmp.sim('cat', 'hat')
0.7486140724946663
>>> cmp.sim('Niall', 'Neil')
0.6982454513126661
>>> cmp.sim('aluminum', 'Catalan')
0.5744355261197056
>>> cmp.sim('ATCG', 'TAGC')
0.4967907573812552