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# Copyright 2019-2020 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._meta_levenshtein. |
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Meta-Levenshtein distance |
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""" |
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from collections import defaultdict |
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from math import log1p |
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from typing import ( |
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Any, |
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Callable, |
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DefaultDict, |
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List, |
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Optional, |
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Tuple, |
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cast, |
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) |
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from numpy import float_ as np_float |
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from numpy import zeros as np_zeros |
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from ._distance import _Distance |
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from ._jaro_winkler import JaroWinkler |
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from ..corpus import UnigramCorpus |
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from ..tokenizer import QGrams, WhitespaceTokenizer, _Tokenizer |
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__all__ = ['MetaLevenshtein'] |
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class MetaLevenshtein(_Distance): |
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r"""Meta-Levenshtein distance. |
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Meta-Levenshtein distance :cite:`Moreau:2008` combines Soft-TFIDF with |
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Levenshtein alignment. |
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.. versionadded:: 0.4.0 |
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""" |
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def __init__( |
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self, |
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tokenizer: Optional[_Tokenizer] = None, |
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corpus: Optional[UnigramCorpus] = None, |
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metric: Optional[_Distance] = None, |
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normalizer: Callable[[List[float]], float] = max, |
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**kwargs: Any |
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) -> None: |
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"""Initialize MetaLevenshtein instance. |
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Parameters |
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---------- |
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tokenizer : _Tokenizer |
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A tokenizer instance from the :py:mod:`abydos.tokenizer` package |
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corpus : UnigramCorpus |
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A unigram corpus :py:class:`UnigramCorpus`. If None, a corpus will |
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be created from the two words when a similarity function is called. |
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metric : _Distance |
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A string distance measure class for making soft matches, by default |
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Jaro-Winkler. |
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normalizer : function |
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A function that takes an list and computes a normalization term |
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by which the edit distance is divided (max by default). Another |
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good option is the sum function. |
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**kwargs |
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Arbitrary keyword arguments |
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Other Parameters |
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---------------- |
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qval : int |
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The length of each q-gram. Using this parameter and tokenizer=None |
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will cause the instance to use the QGram tokenizer with this |
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q value. |
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.. versionadded:: 0.4.0 |
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""" |
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super(MetaLevenshtein, self).__init__(**kwargs) |
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self._corpus = corpus |
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self._metric = JaroWinkler() if metric is None else metric |
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self._normalizer = normalizer |
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qval = 2 if 'qval' not in self.params else self.params['qval'] |
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self.params['tokenizer'] = ( |
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tokenizer |
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if tokenizer is not None |
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else WhitespaceTokenizer() |
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if qval == 0 |
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else QGrams(qval=qval, start_stop='$#', skip=0, scaler=None) |
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) |
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def dist_abs(self, src: str, tar: str) -> float: |
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"""Return the Meta-Levenshtein distance of two strings. |
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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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Returns |
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------- |
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float |
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Meta-Levenshtein distance |
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Examples |
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-------- |
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>>> cmp = MetaLevenshtein() |
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>>> cmp.dist_abs('cat', 'hat') |
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0.6155602628882225 |
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>>> cmp.dist_abs('Niall', 'Neil') |
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2.538900657220556 |
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>>> cmp.dist_abs('aluminum', 'Catalan') |
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6.940747163450747 |
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>>> cmp.dist_abs('ATCG', 'TAGC') |
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3.2311205257764453 |
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.. versionadded:: 0.4.0 |
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""" |
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if src == tar: |
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return 0.0 |
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if not src: |
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return float(len(tar)) |
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if not tar: |
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return float(len(src)) |
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src_tok = self.params['tokenizer'].tokenize(src) |
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src_ordered = src_tok.get_list() |
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src_tok = src_tok.get_counter() |
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tar_tok = self.params['tokenizer'].tokenize(tar) |
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tar_ordered = tar_tok.get_list() |
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tar_tok = tar_tok.get_counter() |
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if self._corpus is None: |
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corpus = UnigramCorpus(word_tokenizer=self.params['tokenizer']) |
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corpus.add_document(src) |
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corpus.add_document(tar) |
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else: |
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corpus = self._corpus |
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dists = defaultdict(float) # type: DefaultDict[Tuple[str, str], float] |
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s_toks = set(src_tok.keys()) |
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t_toks = set(tar_tok.keys()) |
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for s_tok in s_toks: |
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for t_tok in t_toks: |
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dists[(s_tok, t_tok)] = ( |
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self._metric.dist(s_tok, t_tok) if s_tok != t_tok else 0 |
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) |
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vws_dict = {} |
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vwt_dict = {} |
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for token in src_tok.keys(): |
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vws_dict[token] = log1p(src_tok[token]) * corpus.idf(token) |
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for token in tar_tok.keys(): |
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vwt_dict[token] = log1p(tar_tok[token]) * corpus.idf(token) |
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def _dist(s_tok: str, t_tok: str) -> float: |
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return dists[(s_tok, t_tok)] * vws_dict[s_tok] * vwt_dict[t_tok] |
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d_mat = np_zeros( |
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(len(src_ordered) + 1, len(tar_ordered) + 1), dtype=np_float |
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) |
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for i in range(len(src_ordered) + 1): |
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d_mat[i, 0] = i |
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for j in range(len(tar_ordered) + 1): |
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d_mat[0, j] = j |
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for i in range(len(src_ordered)): |
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for j in range(len(tar_ordered)): |
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d_mat[i + 1, j + 1] = min( |
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d_mat[i + 1, j] + 1, # ins |
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d_mat[i, j + 1] + 1, # del |
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d_mat[i, j] |
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+ _dist(src_ordered[i], tar_ordered[j]), # sub/== |
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) |
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return cast(float, d_mat[len(src_ordered), len(tar_ordered)]) |
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def dist(self, src: str, tar: str) -> float: |
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"""Return the normalized Levenshtein distance between two strings. |
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The Levenshtein distance is normalized by dividing the Levenshtein |
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distance (calculated by any of the three supported methods) by the |
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greater of the number of characters in src times the cost of a delete |
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and the number of characters in tar times the cost of an insert. |
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For the case in which all operations have :math:`cost = 1`, this is |
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equivalent to the greater of the length of the two strings src & tar. |
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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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Returns |
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------- |
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float |
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The normalized Levenshtein distance between src & tar |
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Examples |
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-------- |
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>>> cmp = MetaLevenshtein() |
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>>> round(cmp.dist('cat', 'hat'), 12) |
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0.205186754296 |
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>>> round(cmp.dist('Niall', 'Neil'), 12) |
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0.507780131444 |
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>>> cmp.dist('aluminum', 'Catalan') |
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0.8675933954313434 |
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>>> cmp.dist('ATCG', 'TAGC') |
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0.8077801314441113 |
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.. versionadded:: 0.1.0 |
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.. versionchanged:: 0.3.6 |
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Encapsulated in class |
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""" |
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if src == tar: |
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return 0.0 |
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return self.dist_abs(src, tar) / ( |
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self._normalizer( |
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[ |
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self.dist_abs(src, ' ' * len(tar)), |
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self.dist_abs(src, ' ' * len(src)), |
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] |
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) |
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if self._corpus |
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else self._normalizer([len(src), len(tar)]) |
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) |
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if __name__ == '__main__': |
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import doctest |
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doctest.testmod() |
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chrislit /
abydos
