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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._eudex. |
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eudex distance functions |
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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 types import GeneratorType |
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from six.moves import range |
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from ._distance import _Distance |
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from ..phonetic import eudex |
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__all__ = ['Eudex', 'dist_eudex', 'eudex_hamming', 'sim_eudex'] |
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class Eudex(_Distance): |
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"""Distance between the Eudex hashes of two terms. |
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Cf. :cite:`Ticki:2016`. |
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""" |
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@staticmethod |
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def gen_fibonacci(): |
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"""Yield the next Fibonacci number. |
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Based on https://www.python-course.eu/generators.php |
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Starts at Fibonacci number 3 (the second 1) |
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Yields |
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------ |
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int |
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The next Fibonacci number |
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""" |
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num_a, num_b = 1, 2 |
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1 |
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while True: |
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yield num_a |
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num_a, num_b = num_b, num_a + num_b |
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@staticmethod |
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def gen_exponential(base=2): |
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"""Yield the next value in an exponential series of the base. |
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Starts at base**0 |
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Parameters |
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---------- |
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base : int |
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The base to exponentiate |
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Yields |
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------ |
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int |
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The next power of `base` |
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""" |
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exp = 0 |
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while True: |
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yield base ** exp |
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exp += 1 |
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def dist_abs( |
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self, src, tar, weights='exponential', max_length=8, normalized=False |
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): |
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"""Calculate the distance between the Eudex hashes of two terms. |
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Parameters |
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---------- |
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src : str |
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Source string for comparison |
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tar : str |
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Target string for comparison |
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weights : str, iterable, or generator function |
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The weights or weights generator function |
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- If set to ``None``, a simple Hamming distance is calculated. |
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- If set to ``exponential``, weight decays by powers of 2, as |
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proposed in the eudex specification: |
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https://github.com/ticki/eudex. |
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- If set to ``fibonacci``, weight decays through the Fibonacci |
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series, as in the eudex reference implementation. |
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- If set to a callable function, this assumes it creates a |
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generator and the generator is used to populate a series of |
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weights. |
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- If set to an iterable, the iterable's values should be |
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integers and will be used as the weights. |
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max_length : int |
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The number of characters to encode as a eudex hash |
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normalized : bool |
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Normalizes to [0, 1] if True |
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Returns |
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------- |
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int |
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The Eudex Hamming distance |
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Examples |
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-------- |
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>>> cmp = Eudex() |
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>>> cmp.dist_abs('cat', 'hat') |
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128 |
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>>> cmp.dist_abs('Niall', 'Neil') |
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2 |
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>>> cmp.dist_abs('Colin', 'Cuilen') |
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10 |
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>>> cmp.dist_abs('ATCG', 'TAGC') |
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403 |
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>>> cmp.dist_abs('cat', 'hat', weights='fibonacci') |
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34 |
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>>> cmp.dist_abs('Niall', 'Neil', weights='fibonacci') |
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2 |
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>>> cmp.dist_abs('Colin', 'Cuilen', weights='fibonacci') |
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7 |
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>>> cmp.dist_abs('ATCG', 'TAGC', weights='fibonacci') |
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>>> cmp.dist_abs('cat', 'hat', weights=None) |
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1 |
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>>> cmp.dist_abs('Niall', 'Neil', weights=None) |
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1 |
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>>> cmp.dist_abs('Colin', 'Cuilen', weights=None) |
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2 |
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>>> cmp.dist_abs('ATCG', 'TAGC', weights=None) |
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9 |
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>>> # Using the OEIS A000142: |
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>>> cmp.dist_abs('cat', 'hat', [1, 1, 2, 6, 24, 120, 720, 5040]) |
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1 |
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>>> cmp.dist_abs('Niall', 'Neil', [1, 1, 2, 6, 24, 120, 720, 5040]) |
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720 |
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>>> cmp.dist_abs('Colin', 'Cuilen', |
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... [1, 1, 2, 6, 24, 120, 720, 5040]) |
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744 |
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>>> cmp.dist_abs('ATCG', 'TAGC', [1, 1, 2, 6, 24, 120, 720, 5040]) |
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6243 |
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""" |
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# Calculate the eudex hashes and XOR them |
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xored = eudex(src, max_length=max_length) ^ eudex( |
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tar, max_length=max_length |
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) |
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# Simple hamming distance (all bits are equal) |
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if not weights: |
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binary = bin(xored) |
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distance = binary.count('1') |
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if normalized: |
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return distance / (len(binary) - 2) |
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return distance |
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# If weights is a function, it should create a generator, |
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# which we now use to populate a list |
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if callable(weights): |
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weights = weights() |
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elif weights == 'exponential': |
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weights = Eudex.gen_exponential() |
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elif weights == 'fibonacci': |
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weights = Eudex.gen_fibonacci() |
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if isinstance(weights, GeneratorType): |
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weights = [next(weights) for _ in range(max_length)][::-1] |
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# Sum the weighted hamming distance |
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distance = 0 |
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max_distance = 0 |
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while (xored or normalized) and weights: |
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max_distance += 8 * weights[-1] |
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distance += bin(xored & 0xFF).count('1') * weights.pop() |
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xored >>= 8 |
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if normalized: |
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distance /= max_distance |
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return distance |
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def dist(self, src, tar, weights='exponential', max_length=8): |
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"""Return normalized distance between the Eudex hashes of two terms. |
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This is Eudex distance 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 for comparison |
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tar : str |
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Target string for comparison |
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weights : str, iterable, or generator function |
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The weights or weights generator function |
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max_length : int |
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The number of characters to encode as a eudex hash |
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Returns |
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------- |
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int |
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The normalized Eudex Hamming distance |
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Examples |
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-------- |
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>>> cmp = Eudex() |
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>>> round(cmp.dist('cat', 'hat'), 12) |
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0.062745098039 |
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>>> round(cmp.dist('Niall', 'Neil'), 12) |
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0.000980392157 |
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>>> round(cmp.dist('Colin', 'Cuilen'), 12) |
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0.004901960784 |
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>>> round(cmp.dist('ATCG', 'TAGC'), 12) |
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0.197549019608 |
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""" |
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return self.dist_abs(src, tar, weights, max_length, True) |
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def eudex_hamming( |
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src, tar, weights='exponential', max_length=8, normalized=False |
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): |
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"""Calculate the Hamming distance between the Eudex hashes of two terms. |
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This is a wrapper for :py:meth:`Eudex.eudex_hamming`. |
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Parameters |
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---------- |
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src : str |
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Source string for comparison |
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tar : str |
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Target string for comparison |
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weights : str, iterable, or generator function |
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The weights or weights generator function |
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max_length : int |
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The number of characters to encode as a eudex hash |
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normalized : bool |
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Normalizes to [0, 1] if True |
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Returns |
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------- |
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int |
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The Eudex Hamming distance |
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Examples |
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-------- |
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>>> eudex_hamming('cat', 'hat') |
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128 |
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>>> eudex_hamming('Niall', 'Neil') |
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2 |
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>>> eudex_hamming('Colin', 'Cuilen') |
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10 |
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>>> eudex_hamming('ATCG', 'TAGC') |
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403 |
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>>> eudex_hamming('cat', 'hat', weights='fibonacci') |
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34 |
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>>> eudex_hamming('Niall', 'Neil', weights='fibonacci') |
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2 |
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>>> eudex_hamming('Colin', 'Cuilen', weights='fibonacci') |
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7 |
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>>> eudex_hamming('ATCG', 'TAGC', weights='fibonacci') |
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117 |
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>>> eudex_hamming('cat', 'hat', weights=None) |
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1 |
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>>> eudex_hamming('Niall', 'Neil', weights=None) |
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1 |
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>>> eudex_hamming('Colin', 'Cuilen', weights=None) |
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2 |
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>>> eudex_hamming('ATCG', 'TAGC', weights=None) |
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9 |
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>>> # Using the OEIS A000142: |
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>>> eudex_hamming('cat', 'hat', [1, 1, 2, 6, 24, 120, 720, 5040]) |
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1 |
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>>> eudex_hamming('Niall', 'Neil', [1, 1, 2, 6, 24, 120, 720, 5040]) |
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720 |
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>>> eudex_hamming('Colin', 'Cuilen', [1, 1, 2, 6, 24, 120, 720, 5040]) |
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744 |
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>>> eudex_hamming('ATCG', 'TAGC', [1, 1, 2, 6, 24, 120, 720, 5040]) |
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6243 |
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""" |
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return Eudex().dist_abs(src, tar, weights, max_length, normalized) |
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1 |
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def dist_eudex(src, tar, weights='exponential', max_length=8): |
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"""Return normalized Hamming distance between Eudex hashes of two terms. |
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This is a wrapper for :py:meth:`Eudex.dist`. |
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Parameters |
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---------- |
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src : str |
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Source string for comparison |
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tar : str |
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Target string for comparison |
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weights : str, iterable, or generator function |
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The weights or weights generator function |
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max_length : int |
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The number of characters to encode as a eudex hash |
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Returns |
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------- |
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|
int |
|
326
|
|
|
The normalized Eudex Hamming distance |
|
327
|
|
|
|
|
328
|
|
|
Examples |
|
329
|
|
|
-------- |
|
330
|
|
|
>>> round(dist_eudex('cat', 'hat'), 12) |
|
331
|
|
|
0.062745098039 |
|
332
|
|
|
>>> round(dist_eudex('Niall', 'Neil'), 12) |
|
333
|
|
|
0.000980392157 |
|
334
|
|
|
>>> round(dist_eudex('Colin', 'Cuilen'), 12) |
|
335
|
|
|
0.004901960784 |
|
336
|
|
|
>>> round(dist_eudex('ATCG', 'TAGC'), 12) |
|
337
|
|
|
0.197549019608 |
|
338
|
|
|
|
|
339
|
|
|
""" |
|
340
|
1 |
|
return Eudex().dist(src, tar, weights, max_length) |
|
341
|
|
|
|
|
342
|
|
|
|
|
343
|
1 |
|
def sim_eudex(src, tar, weights='exponential', max_length=8): |
|
344
|
|
|
"""Return normalized Hamming similarity between Eudex hashes of two terms. |
|
345
|
|
|
|
|
346
|
|
|
This is a wrapper for :py:meth:`Eudex.sim`. |
|
347
|
|
|
|
|
348
|
|
|
Parameters |
|
349
|
|
|
---------- |
|
350
|
|
|
src : str |
|
351
|
|
|
Source string for comparison |
|
352
|
|
|
tar : str |
|
353
|
|
|
Target string for comparison |
|
354
|
|
|
weights : str, iterable, or generator function |
|
355
|
|
|
The weights or weights generator function |
|
356
|
|
|
max_length : int |
|
357
|
|
|
The number of characters to encode as a eudex hash |
|
358
|
|
|
|
|
359
|
|
|
Returns |
|
360
|
|
|
------- |
|
361
|
|
|
int |
|
362
|
|
|
The normalized Eudex Hamming similarity |
|
363
|
|
|
|
|
364
|
|
|
Examples |
|
365
|
|
|
-------- |
|
366
|
|
|
>>> round(sim_eudex('cat', 'hat'), 12) |
|
367
|
|
|
0.937254901961 |
|
368
|
|
|
>>> round(sim_eudex('Niall', 'Neil'), 12) |
|
369
|
|
|
0.999019607843 |
|
370
|
|
|
>>> round(sim_eudex('Colin', 'Cuilen'), 12) |
|
371
|
|
|
0.995098039216 |
|
372
|
|
|
>>> round(sim_eudex('ATCG', 'TAGC'), 12) |
|
373
|
|
|
0.802450980392 |
|
374
|
|
|
|
|
375
|
|
|
""" |
|
376
|
1 |
|
return Eudex().sim(src, tar, weights, max_length) |
|
377
|
|
|
|
|
378
|
|
|
|
|
379
|
|
|
if __name__ == '__main__': |
|
380
|
|
|
import doctest |
|
381
|
|
|
|
|
382
|
|
|
doctest.testmod() |
|
383
|
|
|
|