# 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._koppen_i.
Köppen I correlation
"""
from ._token_distance import _TokenDistance
__all__ = ['KoppenI']
[docs]class KoppenI(_TokenDistance):
r"""Köppen I correlation.
For two sets X and Y and an alphabet N, provided that :math:`|X| = |Y|`,
Köppen I correlation :cite:`Koppen:1870,Goodman:1959` is
.. math::
corr_{KoppenI}(X, Y) =
\frac{|X| \cdot |N \setminus X| - |X \setminus Y|}
{|X| \cdot |N \setminus X|}
To support cases where :math:`|X| \neq |Y|`, this class implements a slight
variation, while still providing the expected results when
:math:`|X| = |Y|`:
.. math::
corr_{KoppenI}(X, Y) =
\frac{\frac{|X|+|Y|}{2} \cdot
\frac{|N \setminus X|+|N \setminus Y|}{2}-
\frac{|X \triangle Y|}{2}}
{\frac{|X|+|Y|}{2} \cdot
\frac{|N \setminus X|+|N \setminus Y|}{2}}
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{KoppenI} =
\frac{\frac{2a+b+c}{2} \cdot \frac{2d+b+c}{2}-
\frac{b+c}{2}}
{\frac{2a+b+c}{2} \cdot \frac{2d+b+c}{2}}
Notes
-----
In the usual case all of the above values should be proportional to the
total number of samples n. I.e., a, b, c, d, & n should all be divided by
n prior to calculating the coefficient. This class's default normalizer
is, accordingly, 'proportional'.
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
normalizer='proportional',
**kwargs
):
"""Initialize KoppenI 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.
.. versionadded:: 0.4.0
"""
super(KoppenI, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
normalizer=normalizer,
**kwargs
)
[docs] def corr(self, src, tar):
"""Return the Köppen 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
Köppen I correlation
Examples
--------
>>> cmp = KoppenI()
>>> cmp.corr('cat', 'hat')
0.49615384615384617
>>> cmp.corr('Niall', 'Neil')
0.3575056927658083
>>> cmp.corr('aluminum', 'Catalan')
0.1068520131813188
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483896
.. versionadded:: 0.4.0
"""
if src == tar:
return 1.0
self._tokenize(src, tar)
a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
d = self._total_complement_card()
abac_dbdc_mean_prod = (2 * a + b + c) * (2 * d + b + c) / 4
num = abac_dbdc_mean_prod - (b + c) / 2
if num:
return num / abac_dbdc_mean_prod
return 0.0
[docs] def sim(self, src, tar):
"""Return the Köppen 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
Köppen I similarity
Examples
--------
>>> cmp = KoppenI()
>>> cmp.sim('cat', 'hat')
0.7480769230769231
>>> cmp.sim('Niall', 'Neil')
0.6787528463829041
>>> cmp.sim('aluminum', 'Catalan')
0.5534260065906594
>>> cmp.sim('ATCG', 'TAGC')
0.49679075738125805
.. versionadded:: 0.4.0
"""
return (1.0 + self.corr(src, tar)) / 2.0
if __name__ == '__main__':
import doctest
doctest.testmod()