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# -*- coding: utf-8 -*- |
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# Copyright 2014-2018 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.jaro. |
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The distance.jaro module implements distance metrics based on |
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:cite:`Jaro:1989` and subsequent works: |
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- Jaro distance |
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- Jaro-Winkler distance |
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- the strcmp95 algorithm variant of Jaro-Winkler distance |
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""" |
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from __future__ import division, unicode_literals |
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from collections import defaultdict |
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from six.moves import range |
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from ..tokenizer import QGrams |
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__all__ = [ |
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'dist_jaro_winkler', |
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'dist_strcmp95', |
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'sim_jaro_winkler', |
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'sim_strcmp95', |
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] |
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def sim_strcmp95(src, tar, long_strings=False): |
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"""Return the strcmp95 similarity of two strings. |
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This is a Python translation of the C code for strcmp95: |
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http://web.archive.org/web/20110629121242/http://www.census.gov/geo/msb/stand/strcmp.c |
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:cite:`Winkler:1994`. |
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The above file is a US Government publication and, accordingly, |
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in the public domain. |
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This is based on the Jaro-Winkler distance, but also attempts to correct |
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for some common typos and frequently confused characters. It is also |
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limited to uppercase ASCII characters, so it is appropriate to American |
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names, but not much else. |
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:param str src: source string for comparison |
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:param str tar: target string for comparison |
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:param bool long_strings: set to True to "Increase the probability of a |
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match when the number of matched characters is large. This option |
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allows for a little more tolerance when the strings are large. It is |
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not an appropriate test when comparing fixed length fields such as |
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phone and social security numbers." |
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:returns: strcmp95 similarity |
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:rtype: float |
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>>> sim_strcmp95('cat', 'hat') |
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0.7777777777777777 |
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>>> sim_strcmp95('Niall', 'Neil') |
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0.8454999999999999 |
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>>> sim_strcmp95('aluminum', 'Catalan') |
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0.6547619047619048 |
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>>> sim_strcmp95('ATCG', 'TAGC') |
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0.8333333333333334 |
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""" |
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def _in_range(char): |
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"""Return True if char is in the range (0, 91).""" |
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return 91 > ord(char) > 0 |
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ying = src.strip().upper() |
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yang = tar.strip().upper() |
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1 |
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if ying == yang: |
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return 1.0 |
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# If either string is blank - return - added in Version 2 |
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if not ying or not yang: |
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return 0.0 |
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1 |
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adjwt = defaultdict(int) |
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1 |
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sp_mx = ( |
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('A', 'E'), |
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('A', 'I'), |
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('A', 'O'), |
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('A', 'U'), |
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('B', 'V'), |
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('E', 'I'), |
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('E', 'O'), |
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('E', 'U'), |
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('I', 'O'), |
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('I', 'U'), |
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('O', 'U'), |
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('I', 'Y'), |
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('E', 'Y'), |
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('C', 'G'), |
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('E', 'F'), |
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('W', 'U'), |
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('W', 'V'), |
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('X', 'K'), |
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('S', 'Z'), |
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('X', 'S'), |
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('Q', 'C'), |
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('U', 'V'), |
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('M', 'N'), |
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('L', 'I'), |
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('Q', 'O'), |
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('P', 'R'), |
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('I', 'J'), |
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('2', 'Z'), |
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('5', 'S'), |
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('8', 'B'), |
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('1', 'I'), |
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('1', 'L'), |
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('0', 'O'), |
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('0', 'Q'), |
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('C', 'K'), |
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('G', 'J'), |
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) |
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# Initialize the adjwt array on the first call to the function only. |
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# The adjwt array is used to give partial credit for characters that |
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# may be errors due to known phonetic or character recognition errors. |
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# A typical example is to match the letter "O" with the number "0" |
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1 |
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for i in sp_mx: |
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adjwt[(i[0], i[1])] = 3 |
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1 |
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adjwt[(i[1], i[0])] = 3 |
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1 |
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if len(ying) > len(yang): |
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1 |
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search_range = len(ying) |
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1 |
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minv = len(yang) |
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else: |
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1 |
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search_range = len(yang) |
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1 |
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minv = len(ying) |
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# Blank out the flags |
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ying_flag = [0] * search_range |
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yang_flag = [0] * search_range |
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search_range = max(0, search_range // 2 - 1) |
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# Looking only within the search range, count and flag the matched pairs. |
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num_com = 0 |
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yl1 = len(yang) - 1 |
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for i in range(len(ying)): |
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low_lim = (i - search_range) if (i >= search_range) else 0 |
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hi_lim = (i + search_range) if ((i + search_range) <= yl1) else yl1 |
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for j in range(low_lim, hi_lim + 1): |
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if (yang_flag[j] == 0) and (yang[j] == ying[i]): |
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yang_flag[j] = 1 |
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ying_flag[i] = 1 |
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num_com += 1 |
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break |
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# If no characters in common - return |
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1 |
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if num_com == 0: |
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1 |
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return 0.0 |
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# Count the number of transpositions |
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k = n_trans = 0 |
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for i in range(len(ying)): |
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if ying_flag[i] != 0: |
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j = 0 |
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for j in range(k, len(yang)): # pragma: no branch |
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if yang_flag[j] != 0: |
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k = j + 1 |
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break |
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if ying[i] != yang[j]: |
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1 |
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n_trans += 1 |
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n_trans //= 2 |
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# Adjust for similarities in unmatched characters |
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n_simi = 0 |
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1 |
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if minv > num_com: |
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1 |
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for i in range(len(ying)): |
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if ying_flag[i] == 0 and _in_range(ying[i]): |
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1 |
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for j in range(len(yang)): |
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if yang_flag[j] == 0 and _in_range(yang[j]): |
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if (ying[i], yang[j]) in adjwt: |
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n_simi += adjwt[(ying[i], yang[j])] |
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yang_flag[j] = 2 |
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break |
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num_sim = n_simi / 10.0 + num_com |
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# Main weight computation |
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weight = ( |
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num_sim / len(ying) |
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+ num_sim / len(yang) |
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+ (num_com - n_trans) / num_com |
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) |
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1 |
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weight /= 3.0 |
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# Continue to boost the weight if the strings are similar |
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1 |
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if weight > 0.7: |
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# Adjust for having up to the first 4 characters in common |
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j = 4 if (minv >= 4) else minv |
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i = 0 |
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while (i < j) and (ying[i] == yang[i]) and (not ying[i].isdigit()): |
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1 |
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i += 1 |
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1 |
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if i: |
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1 |
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weight += i * 0.1 * (1.0 - weight) |
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# Optionally adjust for long strings. |
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# After agreeing beginning chars, at least two more must agree and |
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# the agreeing characters must be > .5 of remaining characters. |
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if ( |
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long_strings |
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and (minv > 4) |
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and (num_com > i + 1) |
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and (2 * num_com >= minv + i) |
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): |
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1 |
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if not ying[0].isdigit(): |
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1 |
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weight += (1.0 - weight) * ( |
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(num_com - i - 1) / (len(ying) + len(yang) - i * 2 + 2) |
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) |
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return weight |
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1 |
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def dist_strcmp95(src, tar, long_strings=False): |
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"""Return the strcmp95 distance between two strings. |
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strcmp95 distance is the complement of strcmp95 similarity: |
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:math:`dist_{strcmp95} = 1 - sim_{strcmp95}`. |
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:param str src: source string for comparison |
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:param str tar: target string for comparison |
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:param bool long_strings: set to True to "Increase the probability of a |
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match when the number of matched characters is large. This option |
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allows for a little more tolerance when the strings are large. It is |
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not an appropriate test when comparing fixed length fields such as |
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phone and social security numbers." |
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:returns: strcmp95 distance |
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:rtype: float |
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>>> round(dist_strcmp95('cat', 'hat'), 12) |
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0.222222222222 |
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>>> round(dist_strcmp95('Niall', 'Neil'), 12) |
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0.1545 |
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>>> round(dist_strcmp95('aluminum', 'Catalan'), 12) |
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0.345238095238 |
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>>> round(dist_strcmp95('ATCG', 'TAGC'), 12) |
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0.166666666667 |
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""" |
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return 1 - sim_strcmp95(src, tar, long_strings) |
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def sim_jaro_winkler( |
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src, |
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tar, |
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qval=1, |
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mode='winkler', |
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long_strings=False, |
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boost_threshold=0.7, |
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scaling_factor=0.1, |
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): |
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"""Return the Jaro or Jaro-Winkler similarity of two strings. |
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Jaro(-Winkler) distance is a string edit distance initially proposed by |
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Jaro and extended by Winkler :cite:`Jaro:1989,Winkler:1990`. |
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This is Python based on the C code for strcmp95: |
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http://web.archive.org/web/20110629121242/http://www.census.gov/geo/msb/stand/strcmp.c |
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:cite:`Winkler:1994`. The above file is a US Government publication and, |
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accordingly, in the public domain. |
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:param str src: source string for comparison |
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:param str tar: target string for comparison |
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:param int qval: the length of each q-gram (defaults to 1: character-wise |
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matching) |
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:param str mode: indicates which variant of this distance metric to |
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compute: |
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- 'winkler' -- computes the Jaro-Winkler distance (default) which |
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increases the score for matches near the start of the word |
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- 'jaro' -- computes the Jaro distance |
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The following arguments apply only when mode is 'winkler': |
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:param bool long_strings: set to True to "Increase the probability of a |
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match when the number of matched characters is large. This option |
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allows for a little more tolerance when the strings are large. It is |
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not an appropriate test when comparing fixed length fields such as |
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phone and social security numbers." |
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:param float boost_threshold: a value between 0 and 1, below which the |
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Winkler boost is not applied (defaults to 0.7) |
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:param float scaling_factor: a value between 0 and 0.25, indicating by how |
|
301
|
|
|
much to boost scores for matching prefixes (defaults to 0.1) |
|
302
|
|
|
|
|
303
|
|
|
:returns: Jaro or Jaro-Winkler similarity |
|
304
|
|
|
:rtype: float |
|
305
|
|
|
|
|
306
|
|
|
>>> round(sim_jaro_winkler('cat', 'hat'), 12) |
|
307
|
|
|
0.777777777778 |
|
308
|
|
|
>>> round(sim_jaro_winkler('Niall', 'Neil'), 12) |
|
309
|
|
|
0.805 |
|
310
|
|
|
>>> round(sim_jaro_winkler('aluminum', 'Catalan'), 12) |
|
311
|
|
|
0.60119047619 |
|
312
|
|
|
>>> round(sim_jaro_winkler('ATCG', 'TAGC'), 12) |
|
313
|
|
|
0.833333333333 |
|
314
|
|
|
|
|
315
|
|
|
>>> round(sim_jaro_winkler('cat', 'hat', mode='jaro'), 12) |
|
316
|
|
|
0.777777777778 |
|
317
|
|
|
>>> round(sim_jaro_winkler('Niall', 'Neil', mode='jaro'), 12) |
|
318
|
|
|
0.783333333333 |
|
319
|
|
|
>>> round(sim_jaro_winkler('aluminum', 'Catalan', mode='jaro'), 12) |
|
320
|
|
|
0.60119047619 |
|
321
|
|
|
>>> round(sim_jaro_winkler('ATCG', 'TAGC', mode='jaro'), 12) |
|
322
|
|
|
0.833333333333 |
|
323
|
|
|
""" |
|
324
|
1 |
|
if mode == 'winkler': |
|
325
|
1 |
|
if boost_threshold > 1 or boost_threshold < 0: |
|
326
|
1 |
|
raise ValueError( |
|
327
|
|
|
'Unsupported boost_threshold assignment; ' |
|
328
|
|
|
+ 'boost_threshold must be between 0 and 1.' |
|
329
|
|
|
) |
|
330
|
1 |
|
if scaling_factor > 0.25 or scaling_factor < 0: |
|
331
|
1 |
|
raise ValueError( |
|
332
|
|
|
'Unsupported scaling_factor assignment; ' |
|
333
|
|
|
+ 'scaling_factor must be between 0 and 0.25.' |
|
334
|
|
|
) |
|
335
|
|
|
|
|
336
|
1 |
|
if src == tar: |
|
337
|
1 |
|
return 1.0 |
|
338
|
|
|
|
|
339
|
1 |
|
src = QGrams(src.strip(), qval).ordered_list |
|
340
|
1 |
|
tar = QGrams(tar.strip(), qval).ordered_list |
|
341
|
|
|
|
|
342
|
1 |
|
lens = len(src) |
|
343
|
1 |
|
lent = len(tar) |
|
344
|
|
|
|
|
345
|
|
|
# If either string is blank - return - added in Version 2 |
|
346
|
1 |
|
if lens == 0 or lent == 0: |
|
347
|
1 |
|
return 0.0 |
|
348
|
|
|
|
|
349
|
1 |
|
if lens > lent: |
|
350
|
1 |
|
search_range = lens |
|
351
|
1 |
|
minv = lent |
|
352
|
|
|
else: |
|
353
|
1 |
|
search_range = lent |
|
354
|
1 |
|
minv = lens |
|
355
|
|
|
|
|
356
|
|
|
# Zero out the flags |
|
357
|
1 |
|
src_flag = [0] * search_range |
|
358
|
1 |
|
tar_flag = [0] * search_range |
|
359
|
1 |
|
search_range = max(0, search_range // 2 - 1) |
|
360
|
|
|
|
|
361
|
|
|
# Looking only within the search range, count and flag the matched pairs. |
|
362
|
1 |
|
num_com = 0 |
|
363
|
1 |
|
yl1 = lent - 1 |
|
364
|
1 |
|
for i in range(lens): |
|
365
|
1 |
|
low_lim = (i - search_range) if (i >= search_range) else 0 |
|
366
|
1 |
|
hi_lim = (i + search_range) if ((i + search_range) <= yl1) else yl1 |
|
367
|
1 |
|
for j in range(low_lim, hi_lim + 1): |
|
368
|
1 |
|
if (tar_flag[j] == 0) and (tar[j] == src[i]): |
|
369
|
1 |
|
tar_flag[j] = 1 |
|
370
|
1 |
|
src_flag[i] = 1 |
|
371
|
1 |
|
num_com += 1 |
|
372
|
1 |
|
break |
|
373
|
|
|
|
|
374
|
|
|
# If no characters in common - return |
|
375
|
1 |
|
if num_com == 0: |
|
376
|
1 |
|
return 0.0 |
|
377
|
|
|
|
|
378
|
|
|
# Count the number of transpositions |
|
379
|
1 |
|
k = n_trans = 0 |
|
380
|
1 |
|
for i in range(lens): |
|
381
|
1 |
|
if src_flag[i] != 0: |
|
382
|
1 |
|
j = 0 |
|
383
|
1 |
|
for j in range(k, lent): # pragma: no branch |
|
384
|
1 |
|
if tar_flag[j] != 0: |
|
385
|
1 |
|
k = j + 1 |
|
386
|
1 |
|
break |
|
387
|
1 |
|
if src[i] != tar[j]: |
|
388
|
1 |
|
n_trans += 1 |
|
389
|
1 |
|
n_trans //= 2 |
|
390
|
|
|
|
|
391
|
|
|
# Main weight computation for Jaro distance |
|
392
|
1 |
|
weight = num_com / lens + num_com / lent + (num_com - n_trans) / num_com |
|
393
|
1 |
|
weight /= 3.0 |
|
394
|
|
|
|
|
395
|
|
|
# Continue to boost the weight if the strings are similar |
|
396
|
|
|
# This is the Winkler portion of Jaro-Winkler distance |
|
397
|
1 |
|
if mode == 'winkler' and weight > boost_threshold: |
|
398
|
|
|
|
|
399
|
|
|
# Adjust for having up to the first 4 characters in common |
|
400
|
1 |
|
j = 4 if (minv >= 4) else minv |
|
401
|
1 |
|
i = 0 |
|
402
|
1 |
|
while (i < j) and (src[i] == tar[i]): |
|
403
|
1 |
|
i += 1 |
|
404
|
1 |
|
weight += i * scaling_factor * (1.0 - weight) |
|
405
|
|
|
|
|
406
|
|
|
# Optionally adjust for long strings. |
|
407
|
|
|
|
|
408
|
|
|
# After agreeing beginning chars, at least two more must agree and |
|
409
|
|
|
# the agreeing characters must be > .5 of remaining characters. |
|
410
|
1 |
|
if ( |
|
411
|
|
|
long_strings |
|
|
|
|
|
|
412
|
|
|
and (minv > 4) |
|
|
|
|
|
|
413
|
|
|
and (num_com > i + 1) |
|
|
|
|
|
|
414
|
|
|
and (2 * num_com >= minv + i) |
|
|
|
|
|
|
415
|
|
|
): |
|
416
|
1 |
|
weight += (1.0 - weight) * ( |
|
417
|
|
|
(num_com - i - 1) / (lens + lent - i * 2 + 2) |
|
418
|
|
|
) |
|
419
|
|
|
|
|
420
|
1 |
|
return weight |
|
421
|
|
|
|
|
422
|
|
|
|
|
423
|
1 |
|
def dist_jaro_winkler( |
|
|
|
|
|
|
424
|
|
|
src, |
|
|
|
|
|
|
425
|
|
|
tar, |
|
|
|
|
|
|
426
|
|
|
qval=1, |
|
|
|
|
|
|
427
|
|
|
mode='winkler', |
|
|
|
|
|
|
428
|
|
|
long_strings=False, |
|
|
|
|
|
|
429
|
|
|
boost_threshold=0.7, |
|
|
|
|
|
|
430
|
|
|
scaling_factor=0.1, |
|
|
|
|
|
|
431
|
|
|
): |
|
432
|
|
|
"""Return the Jaro or Jaro-Winkler distance between two strings. |
|
433
|
|
|
|
|
434
|
|
|
Jaro(-Winkler) similarity is the complement of Jaro(-Winkler) distance: |
|
435
|
|
|
:math:`sim_{Jaro(-Winkler)} = 1 - dist_{Jaro(-Winkler)}`. |
|
436
|
|
|
|
|
437
|
|
|
:param str src: source string for comparison |
|
438
|
|
|
:param str tar: target string for comparison |
|
439
|
|
|
:param int qval: the length of each q-gram (defaults to 1: character-wise |
|
440
|
|
|
matching) |
|
441
|
|
|
:param str mode: indicates which variant of this distance metric to |
|
442
|
|
|
compute: |
|
443
|
|
|
|
|
444
|
|
|
- 'winkler' -- computes the Jaro-Winkler distance (default) which |
|
445
|
|
|
increases the score for matches near the start of the word |
|
446
|
|
|
- 'jaro' -- computes the Jaro distance |
|
447
|
|
|
|
|
448
|
|
|
The following arguments apply only when mode is 'winkler': |
|
449
|
|
|
|
|
450
|
|
|
:param bool long_strings: set to True to "Increase the probability of a |
|
451
|
|
|
match when the number of matched characters is large. This option |
|
452
|
|
|
allows for a little more tolerance when the strings are large. It is |
|
453
|
|
|
not an appropriate test when comparing fixed length fields such as |
|
454
|
|
|
phone and social security numbers." |
|
455
|
|
|
:param float boost_threshold: a value between 0 and 1, below which the |
|
456
|
|
|
Winkler boost is not applied (defaults to 0.7) |
|
457
|
|
|
:param float scaling_factor: a value between 0 and 0.25, indicating by how |
|
458
|
|
|
much to boost scores for matching prefixes (defaults to 0.1) |
|
459
|
|
|
|
|
460
|
|
|
:returns: Jaro or Jaro-Winkler distance |
|
461
|
|
|
:rtype: float |
|
462
|
|
|
|
|
463
|
|
|
>>> round(dist_jaro_winkler('cat', 'hat'), 12) |
|
464
|
|
|
0.222222222222 |
|
465
|
|
|
>>> round(dist_jaro_winkler('Niall', 'Neil'), 12) |
|
466
|
|
|
0.195 |
|
467
|
|
|
>>> round(dist_jaro_winkler('aluminum', 'Catalan'), 12) |
|
468
|
|
|
0.39880952381 |
|
469
|
|
|
>>> round(dist_jaro_winkler('ATCG', 'TAGC'), 12) |
|
470
|
|
|
0.166666666667 |
|
471
|
|
|
|
|
472
|
|
|
>>> round(dist_jaro_winkler('cat', 'hat', mode='jaro'), 12) |
|
473
|
|
|
0.222222222222 |
|
474
|
|
|
>>> round(dist_jaro_winkler('Niall', 'Neil', mode='jaro'), 12) |
|
475
|
|
|
0.216666666667 |
|
476
|
|
|
>>> round(dist_jaro_winkler('aluminum', 'Catalan', mode='jaro'), 12) |
|
477
|
|
|
0.39880952381 |
|
478
|
|
|
>>> round(dist_jaro_winkler('ATCG', 'TAGC', mode='jaro'), 12) |
|
479
|
|
|
0.166666666667 |
|
480
|
|
|
""" |
|
481
|
1 |
|
return 1 - sim_jaro_winkler( |
|
482
|
|
|
src, tar, qval, mode, long_strings, boost_threshold, scaling_factor |
|
483
|
|
|
) |
|
484
|
|
|
|
|
485
|
|
|
|
|
486
|
|
|
if __name__ == '__main__': |
|
487
|
|
|
import doctest |
|
488
|
|
|
|
|
489
|
|
|
doctest.testmod() |
|
490
|
|
|
|