# 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._minkowski.
Minkowski distance & similarity
"""
from deprecation import deprecated
from ._token_distance import _TokenDistance
from .. import __version__
__all__ = ['Minkowski', 'dist_minkowski', 'minkowski', 'sim_minkowski']
[docs]class Minkowski(_TokenDistance):
"""Minkowski distance.
The Minkowski distance :cite:`Minkowski:1910` is a distance metric in
:math:`L^p-space`.
.. versionadded:: 0.3.6
"""
def __init__(
self,
pval=1,
alphabet=0,
tokenizer=None,
intersection_type='crisp',
**kwargs
):
"""Initialize Euclidean instance.
Parameters
----------
pval : int
The :math:`p`-value of the :math:`L^p`-space
alphabet : collection or int
The values or size of the alphabet
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(Minkowski, self).__init__(
tokenizer=tokenizer,
alphabet=alphabet,
intersection_type=intersection_type,
**kwargs
)
self.set_params(pval=pval)
[docs] def dist_abs(self, src, tar, normalized=False):
"""Return the Minkowski distance (:math:`L^p`-norm) of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
normalized : bool
Normalizes to [0, 1] if True
Returns
-------
float
The Minkowski distance
Examples
--------
>>> cmp = Minkowski()
>>> cmp.dist_abs('cat', 'hat')
4.0
>>> cmp.dist_abs('Niall', 'Neil')
7.0
>>> cmp.dist_abs('Colin', 'Cuilen')
9.0
>>> cmp.dist_abs('ATCG', 'TAGC')
10.0
.. versionadded:: 0.3.0
.. versionchanged:: 0.3.6
Encapsulated in class
"""
self._tokenize(src, tar)
diffs = self._symmetric_difference().values()
normalizer = 1
if normalized:
totals = self._total().values()
if self.params['alphabet']:
normalizer = self.params['alphabet']
elif self.params['pval'] == 0:
normalizer = len(totals)
else:
normalizer = sum(_ ** self.params['pval'] for _ in totals) ** (
1 / self.params['pval']
)
if len(diffs) == 0:
return 0.0
if self.params['pval'] == float('inf'):
# Chebyshev distance
return max(diffs) / normalizer
if self.params['pval'] == 0:
# This is the l_0 "norm" as developed by David Donoho
return sum(_ != 0 for _ in diffs) / normalizer
return (
sum(_ ** self.params['pval'] for _ in diffs)
** (1 / self.params['pval'])
/ normalizer
)
[docs] def dist(self, src, tar):
"""Return normalized Minkowski distance of two strings.
The normalized Minkowski distance :cite:`Minkowski:1910` is a distance
metric in :math:`L^p`-space, normalized to [0, 1].
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
The normalized Minkowski distance
Examples
--------
>>> cmp = Minkowski()
>>> cmp.dist('cat', 'hat')
0.5
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.636363636364
>>> round(cmp.dist('Colin', 'Cuilen'), 12)
0.692307692308
>>> cmp.dist('ATCG', 'TAGC')
1.0
.. versionadded:: 0.3.0
.. versionchanged:: 0.3.6
Encapsulated in class
"""
return self.dist_abs(src, tar, normalized=True)
[docs]@deprecated(
deprecated_in='0.4.0',
removed_in='0.6.0',
current_version=__version__,
details='Use the Minkowski.dist_abs method instead.',
)
def minkowski(src, tar, qval=2, pval=1, normalized=False, alphabet=0):
"""Return the Minkowski distance (:math:`L^p`-norm) of two strings.
This is a wrapper for :py:meth:`Minkowski.dist_abs`.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
qval : int
The length of each q-gram
pval : int or float
The :math:`p`-value of the :math:`L^p`-space
normalized : bool
Normalizes to [0, 1] if True
alphabet : collection or int
The values or size of the alphabet
Returns
-------
float
The Minkowski distance
Examples
--------
>>> minkowski('cat', 'hat')
4.0
>>> minkowski('Niall', 'Neil')
7.0
>>> minkowski('Colin', 'Cuilen')
9.0
>>> minkowski('ATCG', 'TAGC')
10.0
.. versionadded:: 0.3.0
"""
return Minkowski(pval=pval, alphabet=alphabet, qval=qval).dist_abs(
src, tar, normalized=normalized
)
[docs]@deprecated(
deprecated_in='0.4.0',
removed_in='0.6.0',
current_version=__version__,
details='Use the Minkowski.dist method instead.',
)
def dist_minkowski(src, tar, qval=2, pval=1, alphabet=0):
"""Return normalized Minkowski distance of two strings.
This is a wrapper for :py:meth:`Minkowski.dist`.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
qval : int
The length of each q-gram
pval : int or float
The :math:`p`-value of the :math:`L^p`-space
alphabet : collection or int
The values or size of the alphabet
Returns
-------
float
The normalized Minkowski distance
Examples
--------
>>> dist_minkowski('cat', 'hat')
0.5
>>> round(dist_minkowski('Niall', 'Neil'), 12)
0.636363636364
>>> round(dist_minkowski('Colin', 'Cuilen'), 12)
0.692307692308
>>> dist_minkowski('ATCG', 'TAGC')
1.0
.. versionadded:: 0.3.0
"""
return Minkowski(pval=pval, alphabet=alphabet, qval=qval).dist_abs(
src, tar, normalized=True
)
[docs]@deprecated(
deprecated_in='0.4.0',
removed_in='0.6.0',
current_version=__version__,
details='Use the Minkowski.sim method instead.',
)
def sim_minkowski(src, tar, qval=2, pval=1, alphabet=0):
"""Return normalized Minkowski similarity of two strings.
This is a wrapper for :py:meth:`Minkowski.sim`.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
qval : int
The length of each q-gram
pval : int or float
The :math:`p`-value of the :math:`L^p`-space
alphabet : collection or int
The values or size of the alphabet
Returns
-------
float
The normalized Minkowski similarity
Examples
--------
>>> sim_minkowski('cat', 'hat')
0.5
>>> round(sim_minkowski('Niall', 'Neil'), 12)
0.363636363636
>>> round(sim_minkowski('Colin', 'Cuilen'), 12)
0.307692307692
>>> sim_minkowski('ATCG', 'TAGC')
0.0
.. versionadded:: 0.3.0
"""
return Minkowski(pval=pval, alphabet=alphabet, qval=qval).sim(src, tar)
if __name__ == '__main__':
import doctest
doctest.testmod()