Coverage for nltk.parse.viterbi: 47%

100

101

102

103

# Natural Language Toolkit: Viterbi Probabilistic Parser

# Author: Edward Loper <edloper@gradient.cis.upenn.edu>

# Steven Bird <sb@csse.unimelb.edu.au>

# URL: <http://www.nltk.org/>

# For license information, see LICENSE.TXT

from __future__ import print_function

from functools import reduce

from nltk.tree import Tree, ProbabilisticTree

from nltk.parse.api import ParserI

##//////////////////////////////////////////////////////

## Viterbi PCFG Parser

##//////////////////////////////////////////////////////

class ViterbiParser(ParserI):

"""

A bottom-up ``PCFG`` parser that uses dynamic programming to find

the single most likely parse for a text. The ``ViterbiParser`` parser

parses texts by filling in a "most likely constituent table".

This table records the most probable tree representation for any

given span and node value. In particular, it has an entry for

every start index, end index, and node value, recording the most

likely subtree that spans from the start index to the end index,

and has the given node value.

The ``ViterbiParser`` parser fills in this table incrementally. It starts

by filling in all entries for constituents that span one element

of text (i.e., entries where the end index is one greater than the

start index). After it has filled in all table entries for

constituents that span one element of text, it fills in the

entries for constitutants that span two elements of text. It

continues filling in the entries for constituents spanning larger

and larger portions of the text, until the entire table has been

filled. Finally, it returns the table entry for a constituent

spanning the entire text, whose node value is the grammar's start

symbol.

In order to find the most likely constituent with a given span and

node value, the ``ViterbiParser`` parser considers all productions that

could produce that node value. For each production, it finds all

children that collectively cover the span and have the node values

specified by the production's right hand side. If the probability

of the tree formed by applying the production to the children is

greater than the probability of the current entry in the table,

then the table is updated with this new tree.

A pseudo-code description of the algorithm used by

``ViterbiParser`` is:

| Create an empty most likely constituent table, *MLC*.

| For width in 1...len(text):

| For start in 1...len(text)-width:

| For prod in grammar.productions:

| For each sequence of subtrees [t[1], t[2], ..., t[n]] in MLC,

| where t[i].node==prod.rhs[i],

| and the sequence covers [start:start+width]:

| old_p = MLC[start, start+width, prod.lhs]

| new_p = P(t[1])P(t[1])...P(t[n])P(prod)

| if new_p > old_p:

| new_tree = Tree(prod.lhs, t[1], t[2], ..., t[n])

| MLC[start, start+width, prod.lhs] = new_tree

| Return MLC[0, len(text), start_symbol]

:type _grammar: WeightedGrammar

:ivar _grammar: The grammar used to parse sentences.

:type _trace: int

:ivar _trace: The level of tracing output that should be generated

when parsing a text.

"""

def __init__(self, grammar, trace=0):

"""

Create a new ``ViterbiParser`` parser, that uses ``grammar`` to

parse texts.

:type grammar: WeightedGrammar

:param grammar: The grammar used to parse texts.

:type trace: int

:param trace: The level of tracing that should be used when

parsing a text. ``0`` will generate no tracing output;

and higher numbers will produce more verbose tracing

output.

"""

self._grammar = grammar

self._trace = trace

def grammar(self):

return self._grammar

def trace(self, trace=2):

"""

Set the level of tracing output that should be generated when

parsing a text.

:type trace: int

:param trace: The trace level. A trace level of ``0`` will

generate no tracing output; and higher trace levels will

produce more verbose tracing output.

:rtype: None

"""

self._trace = trace

def parse(self, tokens):

# Inherit docs from ParserI

tokens = list(tokens)

self._grammar.check_coverage(tokens)

# The most likely constituent table. This table specifies the

# most likely constituent for a given span and type.

# Constituents can be either Trees or tokens. For Trees,

# the "type" is the Nonterminal for the tree's root node

# value. For Tokens, the "type" is the token's type.

# The table is stored as a dictionary, since it is sparse.

constituents = {}

# Initialize the constituents dictionary with the words from

# the text.

if self._trace: print(('Inserting tokens into the most likely'+

' constituents table...'))

for index in range(len(tokens)):

token = tokens[index]

constituents[index,index+1,token] = token

if self._trace > 1:

self._trace_lexical_insertion(token, index, len(tokens))

# Consider each span of length 1, 2, ..., n; and add any trees

# that might cover that span to the constituents dictionary.

for length in range(1, len(tokens)+1):

if self._trace:

print(('Finding the most likely constituents'+

' spanning %d text elements...' % length))

for start in range(len(tokens)-length+1):

span = (start, start+length)

self._add_constituents_spanning(span, constituents,

tokens)

# Return the tree that spans the entire text & have the right cat

return constituents.get((0, len(tokens), self._grammar.start()))

def _add_constituents_spanning(self, span, constituents, tokens):

"""

Find any constituents that might cover ``span``, and add them

to the most likely constituents table.

:rtype: None

:type span: tuple(int, int)

:param span: The section of the text for which we are

trying to find possible constituents. The span is

specified as a pair of integers, where the first integer

is the index of the first token that should be included in

the constituent; and the second integer is the index of

the first token that should not be included in the

constituent. I.e., the constituent should cover

``text[span[0]:span[1]]``, where ``text`` is the text

that we are parsing.

:type constituents: dict(tuple(int,int,Nonterminal) -> ProbabilisticToken or ProbabilisticTree)

:param constituents: The most likely constituents table. This

table records the most probable tree representation for

any given span and node value. In particular,

``constituents(s,e,nv)`` is the most likely

``ProbabilisticTree`` that covers ``text[s:e]``

and has a node value ``nv.symbol()``, where ``text``

is the text that we are parsing. When

``_add_constituents_spanning`` is called, ``constituents``

should contain all possible constituents that are shorter

than ``span``.

:type tokens: list of tokens

:param tokens: The text we are parsing. This is only used for

trace output.

"""

# Since some of the grammar productions may be unary, we need to

# repeatedly try all of the productions until none of them add any

# new constituents.

changed = True

while changed:

changed = False

# Find all ways instantiations of the grammar productions that

# cover the span.

instantiations = self._find_instantiations(span, constituents)

# For each production instantiation, add a new

# ProbabilisticTree whose probability is the product

# of the childrens' probabilities and the production's

# probability.

for (production, children) in instantiations:

subtrees = [c for c in children if isinstance(c, Tree)]

p = reduce(lambda pr,t:pr*t.prob(),

subtrees, production.prob())

node = production.lhs().symbol()

tree = ProbabilisticTree(node, children, prob=p)

# If it's new a constituent, then add it to the

# constituents dictionary.

c = constituents.get((span[0], span[1], production.lhs()))

if self._trace > 1:

if c is None or c != tree:

if c is None or c.prob() < tree.prob():

print(' Insert:', end=' ')

else:

print(' Discard:', end=' ')

self._trace_production(production, p, span, len(tokens))

if c is None or c.prob() < tree.prob():

constituents[span[0], span[1], production.lhs()] = tree

changed = True

def _find_instantiations(self, span, constituents):

"""

:return: a list of the production instantiations that cover a

given span of the text. A "production instantiation" is

a tuple containing a production and a list of children,

where the production's right hand side matches the list of

children; and the children cover ``span``. :rtype: list

of ``pair`` of ``Production``, (list of

(``ProbabilisticTree`` or token.

:type span: tuple(int, int)

:param span: The section of the text for which we are

trying to find production instantiations. The span is

specified as a pair of integers, where the first integer

is the index of the first token that should be covered by

the production instantiation; and the second integer is

the index of the first token that should not be covered by

the production instantiation.

:type constituents: dict(tuple(int,int,Nonterminal) -> ProbabilisticToken or ProbabilisticTree)

:param constituents: The most likely constituents table. This

table records the most probable tree representation for

any given span and node value. See the module

documentation for more information.

"""

rv = []

for production in self._grammar.productions():

childlists = self._match_rhs(production.rhs(), span, constituents)

for childlist in childlists:

rv.append( (production, childlist) )

return rv

def _match_rhs(self, rhs, span, constituents):

"""

:return: a set of all the lists of children that cover ``span``

and that match ``rhs``.

:rtype: list(list(ProbabilisticTree or token)

:type rhs: list(Nonterminal or any)

:param rhs: The list specifying what kinds of children need to

cover ``span``. Each nonterminal in ``rhs`` specifies

that the corresponding child should be a tree whose node

value is that nonterminal's symbol. Each terminal in ``rhs``

specifies that the corresponding child should be a token

whose type is that terminal.

:type span: tuple(int, int)

:param span: The section of the text for which we are

trying to find child lists. The span is specified as a

pair of integers, where the first integer is the index of

the first token that should be covered by the child list;

and the second integer is the index of the first token

that should not be covered by the child list.

:type constituents: dict(tuple(int,int,Nonterminal) -> ProbabilisticToken or ProbabilisticTree)

:param constituents: The most likely constituents table. This

table records the most probable tree representation for

any given span and node value. See the module

documentation for more information.

"""

(start, end) = span

# Base case

if start >= end and rhs == (): return [[]]

if start >= end or rhs == (): return []

# Find everything that matches the 1st symbol of the RHS

childlists = []

for split in range(start, end+1):

l=constituents.get((start,split,rhs[0]))

if l is not None:

rights = self._match_rhs(rhs[1:], (split,end), constituents)

childlists += [[l]+r for r in rights]

return childlists

def _trace_production(self, production, p, span, width):

"""

Print trace output indicating that a given production has been

applied at a given location.

:param production: The production that has been applied

:type production: Production

:param p: The probability of the tree produced by the production.

:type p: float

:param span: The span of the production

:type span: tuple

:rtype: None

"""

str = '|' + '.' * span[0]

str += '=' * (span[1] - span[0])

str += '.' * (width - span[1]) + '| '

str += '%s' % production

if self._trace > 2: str = '%-40s %12.10f ' % (str, p)

print(str)

def _trace_lexical_insertion(self, token, index, width):

str = ' Insert: |' + '.' * index + '=' + '.' * (width-index-1) + '| '

str += '%s' % (token,)

print(str)

def __repr__(self):

return '<ViterbiParser for %r>' % self._grammar

##//////////////////////////////////////////////////////

## Test Code

##//////////////////////////////////////////////////////

def demo():

"""

A demonstration of the probabilistic parsers. The user is

prompted to select which demo to run, and how many parses should

be found; and then each parser is run on the same demo, and a

summary of the results are displayed.

"""

import sys, time

import nltk

from nltk import tokenize

from nltk.parse import ViterbiParser

# Define two demos. Each demo has a sentence and a grammar.

demos = [('I saw the man with my telescope', nltk.toy_pcfg1),

('the boy saw Jack with Bob under the table with a telescope', nltk.toy_pcfg2)]

# Ask the user which demo they want to use.

print()

for i in range(len(demos)):

print('%3s: %s' % (i+1, demos[i][0]))

print(' %r' % demos[i][1])

print()

print('Which demo (%d-%d)? ' % (1, len(demos)), end=' ')

try:

snum = int(sys.stdin.readline().strip())-1

sent, grammar = demos[snum]

except:

print('Bad sentence number')

return

# Tokenize the sentence.

tokens = sent.split()

parser = ViterbiParser(grammar)

all_parses = {}

print('\nsent: %s\nparser: %s\ngrammar: %s' % (sent,parser,grammar))

parser.trace(3)

t = time.time()

parses = parser.nbest_parse(tokens)

time = time.time()-t

if parses:

average = reduce(lambda a,b:a+b.prob(), parses, 0)/len(parses)

else:

average = 0

num_parses = len(parses)

for p in parses:

all_parses[p.freeze()] = 1

# Print some summary statistics

print()

print('Time (secs) # Parses Average P(parse)')

print('-----------------------------------------')

print('%11.4f%11d%19.14f' % (time, num_parses, average))

parses = all_parses.keys()

if parses:

p = reduce(lambda a,b:a+b.prob(), parses, 0)/len(parses)

else: p = 0

print('------------------------------------------')

print('%11s%11d%19.14f' % ('n/a', len(parses), p))

# Ask the user if we should draw the parses.

print()

print('Draw parses (y/n)? ', end=' ')

if sys.stdin.readline().strip().lower().startswith('y'):

from nltk.draw.tree import draw_trees

print(' please wait...')

draw_trees(*parses)

# Ask the user if we should print the parses.

print()

print('Print parses (y/n)? ', end=' ')

if sys.stdin.readline().strip().lower().startswith('y'):

for parse in parses:

print(parse)

if __name__ == '__main__':

demo()

Coverage for nltk.parse.viterbi : 47%

135 statements 63 run 72 missing 0 excluded