abydos/distance/_pearson_heron_ii.py
# 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._pearson_heron_ii.
Pearson & Heron II correlation
"""
from math import cos, pi
from typing import Any, Counter as TCounter, Optional, Sequence, Set, Union
from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer
__all__ = ['PearsonHeronII']
class PearsonHeronII(_TokenDistance):
r"""Pearson & Heron II correlation.
For two sets X and Y and a population N, Pearson & Heron II correlation
:cite:`Pearson:1913` is
.. math::
corr_{PearsonHeronII}(X, Y) =
\cos \Big(\frac{\pi\sqrt{|X \setminus Y| \cdot |Y \setminus X|}}
{\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} +
\sqrt{|X \setminus Y| \cdot |Y \setminus X|}}\Big)
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
corr_{PearsonHeronII} =
\cos \Big(\frac{\pi\sqrt{bc}}{\sqrt{ad}+\sqrt{bc}}\Big)
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet: Optional[
Union[TCounter[str], Sequence[str], Set[str], int]
] = None,
tokenizer: Optional[_Tokenizer] = None,
intersection_type: str = 'crisp',
**kwargs: Any
) -> None:
"""Initialize PearsonHeronII 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.
.. versionadded:: 0.4.0
"""
super(PearsonHeronII, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
def corr(self, src: str, tar: str) -> float:
"""Return the Pearson & Heron II 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
Pearson & Heron II correlation
Examples
--------
>>> cmp = PearsonHeronII()
>>> cmp.corr('cat', 'hat')
0.9885309061036239
>>> cmp.corr('Niall', 'Neil')
0.9678978997263907
>>> cmp.corr('aluminum', 'Catalan')
0.7853000893691571
>>> cmp.corr('ATCG', 'TAGC')
-1.0
.. versionadded:: 0.4.0
"""
if src == tar:
return 1.0
if not src or not tar:
return -1.0
self._tokenize(src, tar)
root_ad = (
self._intersection_card() * self._total_complement_card()
) ** 0.5
root_bc = (self._src_only_card() * self._tar_only_card()) ** 0.5
num = pi * root_bc
return cos((num / (root_ad + root_bc)) if num else 0.0)
def sim(self, src: str, tar: str) -> float:
"""Return the Pearson & Heron II 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
Pearson & Heron II similarity
Examples
--------
>>> cmp = PearsonHeronII()
>>> cmp.sim('cat', 'hat')
0.994265453051812
>>> cmp.sim('Niall', 'Neil')
0.9839489498631954
>>> cmp.sim('aluminum', 'Catalan')
0.8926500446845785
>>> cmp.sim('ATCG', 'TAGC')
0.0
.. versionadded:: 0.4.0
"""
return (1.0 + self.corr(src, tar)) / 2.0
if __name__ == '__main__':
import doctest
doctest.testmod()