# Source code for nltk.translate.gale_church

```# -*- coding: utf-8 -*-

# Natural Language Toolkit: Gale-Church Aligner
#
# Copyright (C) 2001-2019 NLTK Project
# Author: Torsten Marek <marek@ifi.uzh.ch>
# Contributor: Cassidy Laidlaw, Liling Tan
# URL: <http://nltk.org/>

"""

A port of the Gale-Church Aligner.

Gale & Church (1993), A Program for Aligning Sentences in Bilingual Corpora.
http://aclweb.org/anthology/J93-1004.pdf

"""

from __future__ import division
import math

try:
from scipy.stats import norm
from norm import logsf as norm_logsf
except ImportError:

[docs]    def erfcc(x):
"""Complementary error function."""
z = abs(x)
t = 1 / (1 + 0.5 * z)
r = t * math.exp(
-z * z
- 1.26551223
+ t
* (
1.00002368
+ t
* (
0.37409196
+ t
* (
0.09678418
+ t
* (
-0.18628806
+ t
* (
0.27886807
+ t
* (
-1.13520398
+ t
* (1.48851587 + t * (-0.82215223 + t * 0.17087277))
)
)
)
)
)
)
)
if x >= 0.0:
return r
else:
return 2.0 - r

[docs]    def norm_cdf(x):
"""Return the area under the normal distribution from M{-∞..x}."""
return 1 - 0.5 * erfcc(x / math.sqrt(2))

[docs]    def norm_logsf(x):
try:
return math.log(1 - norm_cdf(x))
except ValueError:
return float('-inf')

LOG2 = math.log(2)

[docs]class LanguageIndependent(object):
# These are the language-independent probabilities and parameters
# given in Gale & Church

# for the computation, l_1 is always the language with less characters
PRIORS = {
(1, 0): 0.0099,
(0, 1): 0.0099,
(1, 1): 0.89,
(2, 1): 0.089,
(1, 2): 0.089,
(2, 2): 0.011,
}

AVERAGE_CHARACTERS = 1
VARIANCE_CHARACTERS = 6.8

[docs]def trace(backlinks, source_sents_lens, target_sents_lens):
"""
Traverse the alignment cost from the tracebacks and retrieves
appropriate sentence pairs.

:param backlinks: A dictionary where the key is the alignment points and value is the cost (referencing the LanguageIndependent.PRIORS)
:param source_sents_lens: A list of target sentences' lengths
:type source_sents_lens: list(int)
:param target_sents_lens: A list of target sentences' lengths
:type target_sents_lens: list(int)
"""
position = (len(source_sents_lens), len(target_sents_lens))
while position != (0, 0) and all(p >= 0 for p in position):
try:
s, t = backlinks[position]
except TypeError:
position = (position - 1, position - 1)
continue
for i in range(s):
for j in range(t):
links.append((position - i - 1, position - j - 1))
position = (position - s, position - t)

[docs]def align_log_prob(i, j, source_sents, target_sents, alignment, params):
"""Returns the log probability of the two sentences C{source_sents[i]}, C{target_sents[j]}
being aligned with a specific C{alignment}.

@param i: The offset of the source sentence.
@param j: The offset of the target sentence.
@param source_sents: The list of source sentence lengths.
@param target_sents: The list of target sentence lengths.
@param alignment: The alignment type, a tuple of two integers.
@param params: The sentence alignment parameters.

@returns: The log probability of a specific alignment between the two sentences, given the parameters.
"""
l_s = sum(source_sents[i - offset - 1] for offset in range(alignment))
l_t = sum(target_sents[j - offset - 1] for offset in range(alignment))
try:
# actually, the paper says l_s * params.VARIANCE_CHARACTERS, this is based on the C
# reference implementation. With l_s in the denominator, insertions are impossible.
m = (l_s + l_t / params.AVERAGE_CHARACTERS) / 2
delta = (l_s * params.AVERAGE_CHARACTERS - l_t) / math.sqrt(
m * params.VARIANCE_CHARACTERS
)
except ZeroDivisionError:
return float('-inf')

return -(LOG2 + norm_logsf(abs(delta)) + math.log(params.PRIORS[alignment]))

[docs]def align_blocks(source_sents_lens, target_sents_lens, params=LanguageIndependent):
"""Return the sentence alignment of two text blocks (usually paragraphs).

>>> align_blocks([5,5,5], [7,7,7])
[(0, 0), (1, 1), (2, 2)]
>>> align_blocks([10,5,5], [12,20])
[(0, 0), (1, 1), (2, 1)]
>>> align_blocks([12,20], [10,5,5])
[(0, 0), (1, 1), (1, 2)]
>>> align_blocks([10,2,10,10,2,10], [12,3,20,3,12])
[(0, 0), (1, 1), (2, 2), (3, 2), (4, 3), (5, 4)]

@param source_sents_lens: The list of source sentence lengths.
@param target_sents_lens: The list of target sentence lengths.
@param params: the sentence alignment parameters.
@return: The sentence alignments, a list of index pairs.
"""

alignment_types = list(params.PRIORS.keys())

# there are always three rows in the history (with the last of them being filled)
D = [[]]

for i in range(len(source_sents_lens) + 1):
for j in range(len(target_sents_lens) + 1):
min_dist = float('inf')
min_align = None
for a in alignment_types:
prev_i = -1 - a
prev_j = j - a
if prev_i < -len(D) or prev_j < 0:
continue
p = D[prev_i][prev_j] + align_log_prob(
i, j, source_sents_lens, target_sents_lens, a, params
)
if p < min_dist:
min_dist = p
min_align = a

if min_dist == float('inf'):
min_dist = 0

backlinks[(i, j)] = min_align
D[-1].append(min_dist)

if len(D) > 2:
D.pop(0)
D.append([])

return trace(backlinks, source_sents_lens, target_sents_lens)

[docs]def align_texts(source_blocks, target_blocks, params=LanguageIndependent):
"""Creates the sentence alignment of two texts.

Texts can consist of several blocks. Block boundaries cannot be crossed by sentence

Each block consists of a list that contains the lengths (in characters) of the sentences
in this block.

@param source_blocks: The list of blocks in the source text.
@param target_blocks: The list of blocks in the target text.
@param params: the sentence alignment parameters.

@returns: A list of sentence alignment lists
"""
if len(source_blocks) != len(target_blocks):
raise ValueError(
"Source and target texts do not have the same number of blocks."
)

return [
align_blocks(source_block, target_block, params)
for source_block, target_block in zip(source_blocks, target_blocks)
]

# File I/O functions; may belong in a corpus reader

[docs]def split_at(it, split_value):
"""Splits an iterator C{it} at values of C{split_value}.

Each instance of C{split_value} is swallowed. The iterator produces
subiterators which need to be consumed fully before the next subiterator
can be used.
"""

def _chunk_iterator(first):
v = first
while v != split_value:
yield v
v = it.next()

while True:
yield _chunk_iterator(it.next())

[docs]def parse_token_stream(stream, soft_delimiter, hard_delimiter):
"""Parses a stream of tokens and splits it into sentences (using C{soft_delimiter} tokens)
and blocks (using C{hard_delimiter} tokens) for use with the L{align_texts} function.
"""
return [
[
sum(len(token) for token in sentence_it)
for sentence_it in split_at(block_it, soft_delimiter)
]
for block_it in split_at(stream, hard_delimiter)
]

#    Code for test files in nltk_contrib/align/data/*.tok
#    import sys
#    from contextlib import nested
#    with nested(open(sys.argv, "r"), open(sys.argv, "r")) as (s, t):
#        source = parse_token_stream((l.strip() for l in s), ".EOS", ".EOP")
#        target = parse_token_stream((l.strip() for l in t), ".EOS", ".EOP")
#        print align_texts(source, target)
```