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# -*- coding: utf-8 -*- |
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# Copyright 2019 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._cao. |
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Cao's CY dissimilarity. |
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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 math import log10 |
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from ._token_distance import _TokenDistance |
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__all__ = ['Cao'] |
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class Cao(_TokenDistance): |
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r"""Cao's CY dissimilarity. |
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Given :math:`X_{ij}` (the number of individuals of speecies :math:`j` in |
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sample :math:`i`), :math:`X_{kj}` (the number of individuals of speecies |
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:math:`j` in sample :math:`k`), and :math:`N` (the total number of speecies |
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present in both samples), Cao dissimilarity (CYd) :cite:`Cao:1997` is: |
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.. math:: |
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dist_{Cao}(X, Y) = |
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CYd = \frac{1}{N}\sum\Bigg(\frac{(X_{ij} + X_{kj})log_{10}\big( |
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\frac{X_{ij}+X_{kj}}{2}\big)-X_{ij}log_{10}X_{kj}-X_{kj}log_{10}X_{ij}} |
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{X_{ij}+X_{kj}}\Bigg) |
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In the above formula, whenever :math:`X_{ij} = 0` or :math:`X_{kj} = 0`, |
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the value 0.1 is substituted. |
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Since this measure ranges from 0 to :math:`\infty`, a similarity measure, |
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CYs, ranging from 0 to 1 was also developed. |
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.. math:: |
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sim_{Cao}(X, Y) = CYs = 1 - \frac{Observed~CYd}{Maximum~CYd} |
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where |
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.. math:: |
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Observed~CYd = \sum\Bigg(\frac{(X_{ij} + X_{kj})log_{10}\big( |
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\frac{X_{ij}+X_{kj}}{2}\big)-X_{ij}log_{10}X_{kj}-X_{kj}log_{10}X_{ij}} |
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{X_{ij}+X_{kj}}\Bigg) |
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and with :math:`a` (the number of species present in both samples), |
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:math:`b` (the number of species present in sample :math:`i` only), and |
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:math:`c` (the number of species present in sample :math:`j` only), |
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.. math:: |
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Maximum~CYd = D_1 + D_2 + D_3 |
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with |
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.. math:: |
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D_1 = \sum_{j=1}^b \Bigg(\frac{(X_{ij} + 0.1) log_{10} \big( |
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\frac{X_{ij}+0.1}{2}\big)-X_{ij}log_{10}0.1-0.1log_{10}X_{ij}} |
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{X_{ij}+0.1}\Bigg) |
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D_2 = \sum_{j=1}^c \Bigg(\frac{(X_{kj} + 0.1) log_{10} \big( |
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\frac{X_{kj}+0.1}{2}\big)-X_{kj}log_{10}0.1-0.1log_{10}X_{kj}} |
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{X_{kj}+0.1}\Bigg) |
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D_1 = \sum_{j=1}^a \frac{a}{2} \Bigg(\frac{(D_i + 1) log_{10} |
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\big(\frac{D_i+1}{2}\big)-log_{10}D_i}{D_i+1} + \frac{(D_k + 1) log_{10} |
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\big(\frac{D_k+1}{2}\big)-log_{10}D_k}{D_k+1}\Bigg) |
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with |
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.. math:: |
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D_i = \frac{\sum X_{ij} - \frac{a}{2}}{\frac{a}{2}} |
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D_k = \frac{\sum X_{kj} - \frac{a}{2}}{\frac{a}{2}} |
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for |
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.. math:: |
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X_{ij} \geq 1 |
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X_{kj} \geq 1 |
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.. versionadded:: 0.4.1 |
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""" |
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def __init__(self, **kwargs): |
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"""Initialize Cao instance. |
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Parameters |
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---------- |
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**kwargs |
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Arbitrary keyword arguments |
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.. versionadded:: 0.4.1 |
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""" |
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super(Cao, self).__init__(**kwargs) |
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def sim(self, src, tar): |
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"""Return Cao's CY similarity (CYs) 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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Cao's CY similarity |
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Examples |
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-------- |
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>>> cmp = Cao() |
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>>> cmp.sim('cat', 'hat') |
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0.0 |
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>>> cmp.sim('Niall', 'Neil') |
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0.0 |
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>>> cmp.sim('aluminum', 'Catalan') |
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0.0 |
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>>> cmp.sim('ATCG', 'TAGC') |
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0.0 |
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.. versionadded:: 0.4.1 |
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""" |
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if src == tar: |
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return 1.0 |
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if not src or not tar: |
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return 0.0 |
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self._tokenize(src, tar) |
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alphabet = self._total().keys() |
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in_both_samples_half = len(self._intersection().keys()) / 2 |
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if not in_both_samples_half: |
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return 0.0 |
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observed_cyd = 0 |
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maximum_cyd = 0 |
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for symbol in alphabet: |
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src_tok = max(0.1, self._src_tokens[symbol]) |
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tar_tok = max(0.1, self._tar_tokens[symbol]) |
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tok_sum = src_tok + tar_tok |
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observed_cyd += ( |
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tok_sum * log10(tok_sum / 2) |
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- src_tok * log10(tar_tok) |
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- tar_tok * log10(src_tok) |
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) / tok_sum |
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if self._tar_tokens[symbol] == 0: |
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maximum_cyd += ( |
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(self._src_tokens[symbol] + 0.1) |
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* log10((self._src_tokens[symbol] + 0.1) / 2) |
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- self._src_tokens[symbol] * log10(0.1) |
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- 0.1 * log10(self._src_tokens[symbol]) |
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) / (self._src_tokens[symbol] + 0.1) |
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elif self._src_tokens[symbol] == 0: |
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maximum_cyd += ( |
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(self._tar_tokens[symbol] + 0.1) |
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* log10((self._tar_tokens[symbol] + 0.1) / 2) |
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- self._tar_tokens[symbol] * log10(0.1) |
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- 0.1 * log10(self._tar_tokens[symbol]) |
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) / (self._tar_tokens[symbol] + 0.1) |
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d_i = 0 |
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d_k = 0 |
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for symbol in self._intersection().keys(): |
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d_i += self._src_tokens[symbol] |
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d_k += self._tar_tokens[symbol] |
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d_i = (d_i - in_both_samples_half) / in_both_samples_half |
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d_k = (d_k - in_both_samples_half) / in_both_samples_half |
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maximum_cyd += in_both_samples_half * ( |
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((d_i + 1) * log10((d_i + 1) / 2) - log10(d_i)) / (d_i + 1) |
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+ ((d_k + 1) * log10((d_k + 1) / 2) - log10(d_k)) / (d_k + 1) |
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) |
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return max(0.0, min(1.0, 1 - (observed_cyd / maximum_cyd))) |
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def dist_abs(self, src, tar): |
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"""Return Cao's CY dissimilarity (CYd) 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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Cao's CY dissimilarity |
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Examples |
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-------- |
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>>> cmp = Cao() |
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>>> cmp.dist_abs('cat', 'hat') |
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0.3247267992925765 |
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>>> cmp.dist_abs('Niall', 'Neil') |
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0.4132886536450973 |
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>>> cmp.dist_abs('aluminum', 'Catalan') |
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0.5530666041976232 |
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>>> cmp.dist_abs('ATCG', 'TAGC') |
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0.6494535985851531 |
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.. versionadded:: 0.4.1 |
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""" |
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if src == tar: |
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return 0.0 |
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self._tokenize(src, tar) |
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alphabet = self._total().keys() |
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score = 0 |
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for symbol in alphabet: |
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src_tok = max(0.1, self._src_tokens[symbol]) |
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tar_tok = max(0.1, self._tar_tokens[symbol]) |
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tok_sum = src_tok + tar_tok |
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score += ( |
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tok_sum * log10(tok_sum / 2) |
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- src_tok * log10(tar_tok) |
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- tar_tok * log10(src_tok) |
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) / tok_sum |
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return score / sum(self._total().values()) |
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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
