# Copyright 2019-2020 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._size_difference.
Penrose's size difference
"""
from ._token_distance import _TokenDistance
__all__ = ['Size']
[docs]class Size(_TokenDistance):
r"""Penrose's size difference.
For two sets X and Y and a population N, the Penrose's size difference
:cite:`Penrose:1952` is
.. math::
sim_{Size}(X, Y) =
\frac{(|X \triangle Y|)^2}{|N|^2}
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{Size} =
\frac{(b+c)^2}{n^2}
In :cite:`IBM:2017`, the formula is instead :math:`\frac{(b-c)^2}{n^2}`,
but it is clear from :cite:`Penrose:1952` that this should not be an
assymmetric value with respect two the ordering of the two sets. Meanwhile,
:cite:`Deza:2016` gives a formula that is equivalent to
:math:`\sqrt{n}\cdot(b+c)`.
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
**kwargs
):
"""Initialize Size 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(Size, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def dist(self, src, tar):
"""Return the Penrose's size difference 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
Size difference
Examples
--------
>>> cmp = Size()
>>> cmp.sim('cat', 'hat')
0.9999739691795085
>>> cmp.sim('Niall', 'Neil')
0.9999202806122449
>>> cmp.sim('aluminum', 'Catalan')
0.9996348736257049
>>> cmp.sim('ATCG', 'TAGC')
0.9998373073719283
.. versionadded:: 0.4.0
"""
if src == tar:
return 0.0
self._tokenize(src, tar)
return (
self._symmetric_difference_card()
) ** 2 / self._population_unique_card() ** 2
if __name__ == '__main__':
import doctest
doctest.testmod()