# Source code for abydos.distance._fleiss

# 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._fleiss.

Fleiss correlation
"""

from ._token_distance import _TokenDistance

__all__ = ['Fleiss']

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

For two sets X and Y and a population N, Fleiss correlation
:cite:Fleiss:1975 is

.. math::

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

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

.. math::

corr_{Fleiss} =

This is Fleiss' :math:M(A_1), :math:ad-bc divided by the harmonic mean
of the marginals :math:p_1q_1 = (a+b)(c+d) and
:math:p_2q_2 = (a+c)(b+d).

"""

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

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

Examples
--------
>>> cmp = Fleiss()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.3621712520061204
>>> cmp.corr('aluminum', 'Catalan')
0.10839724112919989
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

"""
self._tokenize(src, tar)

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

num = (a * d - b * c) * ((a + b) * (c + d) + (a + c) * (b + d))

if num == 0.0:
return 0.0
return num / (2.0 * (a + b) * (c + d) * (a + c) * (b + d))

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

Examples
--------
>>> cmp = Fleiss()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6810856260030602
>>> cmp.sim('aluminum', 'Catalan')
0.5541986205645999
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

"""
return (1.0 + self.corr(src, tar)) / 2.0

if __name__ == '__main__':
import doctest

doctest.testmod()