# 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._lorentzian.
Lorentzian distance
"""
from math import log1p
from ._token_distance import _TokenDistance
__all__ = ['Lorentzian']
[docs]class Lorentzian(_TokenDistance):
r"""Lorentzian distance.
For two multisets X and Y drawn from an alphabet S, Lorentzian distance is
.. math::
dist_{Lorentzian}(X, Y) =
\sum_{i \in S} log(1 + |A_i - B_i|)
Notes
-----
No primary source for this measure could be located, but it is included
in surveys and catalogues, such as :cite:`Deza:2016` and :cite:`Cha:2008`.
.. versionadded:: 0.4.0
"""
def __init__(self, tokenizer=None, **kwargs):
"""Initialize Lorentzian instance.
Parameters
----------
tokenizer : _Tokenizer
A tokenizer instance from the :py:mod:`abydos.tokenizer` package
**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.
.. versionadded:: 0.4.0
"""
super(Lorentzian, self).__init__(tokenizer=tokenizer, **kwargs)
[docs] def dist_abs(self, src, tar):
"""Return the Lorentzian distance 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
Lorentzian distance
Examples
--------
>>> cmp = Lorentzian()
>>> cmp.dist_abs('cat', 'hat')
2.772588722239781
>>> cmp.dist_abs('Niall', 'Neil')
4.852030263919617
>>> cmp.dist_abs('aluminum', 'Catalan')
10.1095256359474
>>> cmp.dist_abs('ATCG', 'TAGC')
6.931471805599453
.. versionadded:: 0.4.0
"""
self._tokenize(src, tar)
alphabet = self._total().keys()
return sum(
log1p(abs(self._src_tokens[tok] - self._tar_tokens[tok]))
for tok in alphabet
)
[docs] def dist(self, src, tar):
"""Return the normalized Lorentzian distance 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
Normalized Lorentzian distance
Examples
--------
>>> cmp = Lorentzian()
>>> cmp.dist('cat', 'hat')
0.6666666666666667
>>> cmp.dist('Niall', 'Neil')
0.7777777777777778
>>> cmp.dist('aluminum', 'Catalan')
0.9358355851062377
>>> cmp.dist('ATCG', 'TAGC')
1.0
.. versionadded:: 0.4.0
"""
if src == tar:
return 0.0
elif not src or not tar:
return 1.0
score = self.dist_abs(src, tar)
alphabet = self._total().keys()
return score / sum(
log1p(max(self._src_tokens[tok], self._tar_tokens[tok]))
for tok in alphabet
)
if __name__ == '__main__':
import doctest
doctest.testmod()