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# -*- coding: utf-8 -*- |
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# Copyright 2018 by Christopher C. Little. |
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# This file is part of Abydos. |
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# |
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# Abydos is free software: you can redistribute it and/or modify |
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# it under the terms of the GNU General Public License as published by |
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# the Free Software Foundation, either version 3 of the License, or |
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# (at your option) any later version. |
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# |
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# Abydos is distributed in the hope that it will be useful, |
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# but WITHOUT ANY WARRANTY; without even the implied warranty of |
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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# GNU General Public License for more details. |
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# |
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# You should have received a copy of the GNU General Public License |
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# along with Abydos. If not, see <http://www.gnu.org/licenses/>. |
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"""abydos.distance._minkowski. |
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Minkowski distance & similarity |
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""" |
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from __future__ import ( |
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absolute_import, |
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division, |
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print_function, |
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unicode_literals, |
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) |
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from numbers import Number |
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from ._token_distance import _TokenDistance |
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__all__ = ['Minkowski', 'dist_minkowski', 'minkowski', 'sim_minkowski'] |
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class Minkowski(_TokenDistance): |
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"""Minkowski distance. |
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The Minkowski distance :cite:`Minkowski:1910` is a distance metric in |
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:math:`L^p-space`. |
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""" |
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def dist_abs( |
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self, src, tar, qval=2, pval=1, normalized=False, alphabet=None |
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): |
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"""Return the Minkowski distance (:math:`L^p`-norm) of two strings. |
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Parameters |
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---------- |
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src : str |
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Source string (or QGrams/Counter objects) for comparison |
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tar : str |
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Target string (or QGrams/Counter objects) for comparison |
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qval : int |
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The length of each q-gram; 0 for non-q-gram version |
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pval : int or float |
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The :math:`p`-value of the :math:`L^p`-space |
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normalized : bool |
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Normalizes to [0, 1] if True |
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alphabet : collection or int |
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The values or size of the alphabet |
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Returns |
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------- |
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float |
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The Minkowski distance |
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Examples |
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-------- |
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>>> cmp = Minkowski() |
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>>> cmp.dist_abs('cat', 'hat') |
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4.0 |
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>>> cmp.dist_abs('Niall', 'Neil') |
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7.0 |
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>>> cmp.dist_abs('Colin', 'Cuilen') |
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9.0 |
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>>> cmp.dist_abs('ATCG', 'TAGC') |
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10.0 |
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""" |
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q_src, q_tar = self._get_qgrams(src, tar, qval) |
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diffs = ((q_src - q_tar) + (q_tar - q_src)).values() |
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normalizer = 1 |
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if normalized: |
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totals = (q_src + q_tar).values() |
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if alphabet is not None: |
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# noinspection PyTypeChecker |
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normalizer = ( |
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alphabet if isinstance(alphabet, Number) else len(alphabet) |
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) |
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elif pval == 0: |
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normalizer = len(totals) |
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else: |
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normalizer = sum(_ ** pval for _ in totals) ** (1 / pval) |
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if len(diffs) == 0: |
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return 0.0 |
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if pval == float('inf'): |
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# Chebyshev distance |
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return max(diffs) / normalizer |
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if pval == 0: |
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# This is the l_0 "norm" as developed by David Donoho |
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return len(diffs) / normalizer |
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return sum(_ ** pval for _ in diffs) ** (1 / pval) / normalizer |
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def dist(self, src, tar, qval=2, pval=1, alphabet=None): |
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"""Return normalized Minkowski distance of two strings. |
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The normalized Minkowski distance :cite:`Minkowski:1910` is a distance |
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metric in :math:`L^p`-space, normalized to [0, 1]. |
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Parameters |
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---------- |
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src : str |
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Source string (or QGrams/Counter objects) for comparison |
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tar : str |
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Target string (or QGrams/Counter objects) for comparison |
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qval : int |
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The length of each q-gram; 0 for non-q-gram version |
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pval : int or float |
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The :math:`p`-value of the :math:`L^p`-space |
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alphabet : collection or int |
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The values or size of the alphabet |
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Returns |
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------- |
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float |
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The normalized Minkowski distance |
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Examples |
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-------- |
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>>> cmp = Minkowski() |
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>>> cmp.dist('cat', 'hat') |
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0.5 |
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>>> round(cmp.dist('Niall', 'Neil'), 12) |
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0.636363636364 |
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>>> round(cmp.dist('Colin', 'Cuilen'), 12) |
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0.692307692308 |
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>>> cmp.dist('ATCG', 'TAGC') |
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1.0 |
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""" |
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return self.dist_abs(src, tar, qval, pval, True, alphabet) |
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def minkowski(src, tar, qval=2, pval=1, normalized=False, alphabet=None): |
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"""Return the Minkowski distance (:math:`L^p`-norm) of two strings. |
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This is a wrapper for :py:meth:`Minkowski.dist_abs`. |
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Parameters |
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---------- |
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src : str |
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Source string (or QGrams/Counter objects) for comparison |
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tar : str |
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Target string (or QGrams/Counter objects) for comparison |
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qval : int |
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The length of each q-gram; 0 for non-q-gram version |
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pval : int or float |
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The :math:`p`-value of the :math:`L^p`-space |
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normalized : bool |
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Normalizes to [0, 1] if True |
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alphabet : collection or int |
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The values or size of the alphabet |
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Returns |
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------- |
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float |
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The Minkowski distance |
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Examples |
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-------- |
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>>> minkowski('cat', 'hat') |
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4.0 |
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>>> minkowski('Niall', 'Neil') |
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7.0 |
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>>> minkowski('Colin', 'Cuilen') |
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9.0 |
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>>> minkowski('ATCG', 'TAGC') |
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10.0 |
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""" |
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return Minkowski().dist_abs(src, tar, qval, pval, normalized, alphabet) |
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def dist_minkowski(src, tar, qval=2, pval=1, alphabet=None): |
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"""Return normalized Minkowski distance of two strings. |
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This is a wrapper for :py:meth:`Minkowski.dist`. |
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Parameters |
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---------- |
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src : str |
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Source string (or QGrams/Counter objects) for comparison |
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tar : str |
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Target string (or QGrams/Counter objects) for comparison |
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qval : int |
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The length of each q-gram; 0 for non-q-gram version |
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pval : int or float |
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The :math:`p`-value of the :math:`L^p`-space |
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alphabet : collection or int |
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The values or size of the alphabet |
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Returns |
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------- |
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float |
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The normalized Minkowski distance |
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Examples |
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-------- |
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>>> dist_minkowski('cat', 'hat') |
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0.5 |
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>>> round(dist_minkowski('Niall', 'Neil'), 12) |
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0.636363636364 |
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>>> round(dist_minkowski('Colin', 'Cuilen'), 12) |
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0.692307692308 |
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>>> dist_minkowski('ATCG', 'TAGC') |
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1.0 |
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""" |
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return Minkowski().dist(src, tar, qval, pval, alphabet) |
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def sim_minkowski(src, tar, qval=2, pval=1, alphabet=None): |
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"""Return normalized Minkowski similarity of two strings. |
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This is a wrapper for :py:meth:`Minkowski.sim`. |
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Parameters |
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---------- |
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src : str |
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Source string (or QGrams/Counter objects) for comparison |
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tar : str |
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Target string (or QGrams/Counter objects) for comparison |
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qval : int |
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The length of each q-gram; 0 for non-q-gram version |
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pval : int or float |
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The :math:`p`-value of the :math:`L^p`-space |
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alphabet : collection or int |
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The values or size of the alphabet |
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Returns |
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------- |
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float |
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The normalized Minkowski similarity |
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Examples |
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-------- |
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>>> sim_minkowski('cat', 'hat') |
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0.5 |
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>>> round(sim_minkowski('Niall', 'Neil'), 12) |
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0.363636363636 |
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>>> round(sim_minkowski('Colin', 'Cuilen'), 12) |
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0.307692307692 |
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>>> sim_minkowski('ATCG', 'TAGC') |
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0.0 |
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""" |
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return Minkowski().sim(src, tar, qval, pval, alphabet) |
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if __name__ == '__main__': |
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import doctest |
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doctest.testmod() |
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