Source code for abydos.distance._minkowski

# 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.
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# 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 typing import (
    Any,
    Counter as TCounter,
    Optional,
    Sequence,
    Set,
    Union,
    cast,
)

from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer

__all__ = ['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: float = 1, alphabet: Optional[ Union[TCounter[str], Sequence[str], Set[str], int] ] = 0, tokenizer: Optional[_Tokenizer] = None, intersection_type: str = 'crisp', **kwargs: Any ) -> None: """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: str, tar: str, normalized: bool = False) -> float: """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 cast( float, sum(_ ** self.params['pval'] for _ in diffs) ** (1 / self.params['pval']) / normalizer, )
[docs] def dist(self, src: str, tar: str) -> float: """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)
if __name__ == '__main__': import doctest doctest.testmod()