# 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._horn_morisita.
Horn-Morisita index of overlap
"""
from ._token_distance import _TokenDistance
__all__ = ['HornMorisita']
[docs]class HornMorisita(_TokenDistance):
r"""Horn-Morisita index of overlap.
Horn-Morisita index of overlap :cite:`Horn:1966`, given two populations X
and Y drawn from S species, is:
.. math::
sim_{Horn-Morisita}(X, Y) =
C_{\lambda} = \frac{2\sum_{i=1}^S x_i y_i}
{(\hat{\lambda}_x + \hat{\lambda}_y)XY}
where
.. math::
X = \sum_{i=1}^S x_i ~~;~~ Y = \sum_{i=1}^S y_i
.. math::
\hat{\lambda}_x = \frac{\sum_{i=1}^S x_i^2}{X^2} ~~;~~
\hat{\lambda}_y = \frac{\sum_{i=1}^S y_i^2}{Y^2}
Observe that this is identical to Morisita similarity, except for the
definition of the :math:`\lambda` values in the denominator.
.. versionadded:: 0.4.1
"""
def __init__(self, **kwargs):
"""Initialize HornMorisita instance.
Parameters
----------
**kwargs
Arbitrary keyword arguments
.. versionadded:: 0.4.1
"""
super(HornMorisita, self).__init__(**kwargs)
[docs] def sim(self, src, tar):
"""Return the Horn-Morisita similarity of two strings.
Parameters
----------
src : str
Source string for comparison
tar : str
Target string for comparison
Returns
-------
float
Horn-Morisita similarity
Examples
--------
>>> cmp = HornMorisita()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3636363636363636
>>> cmp.sim('aluminum', 'Catalan')
0.10650887573964497
>>> cmp.sim('ATCG', 'TAGC')
0.0
.. versionadded:: 0.4.1
"""
self._tokenize(src, tar)
intersection = self._intersection()
src_card = self._src_card()
tar_card = self._tar_card()
src_lambda = 0
tar_lambda = 0
for val in self._src_tokens.values():
src_lambda += val * val
if src_lambda:
src_lambda /= src_card * src_card
for val in self._tar_tokens.values():
tar_lambda += val * val
if tar_lambda:
tar_lambda /= tar_card * tar_card
sim = 0
for symbol in intersection.keys():
sim += self._src_tokens[symbol] * self._tar_tokens[symbol]
sim *= 2
if src_card:
sim /= src_card
if tar_card:
sim /= tar_card
if src_lambda + tar_lambda:
sim /= src_lambda + tar_lambda
return sim
if __name__ == '__main__':
import doctest
doctest.testmod()