In [6]:
import numpy as np
import math
import matplotlib.pyplot as plt
%matplotlib inline
import random
from numpy.random import rand
from copy import copy
from __future__ import division
import time
def read_text_whole(filename):
with open(filename, 'r') as f:
X = ''.join(f.readlines()).replace('\n', '')
return X
def read_text_words(filename, wordsnumber):
with open(filename) as f:
X = f.readlines()
X = X[:wordsnumber]
X = ''.join(X)
X = X.replace('\n', '')
return X
def read_text_filesize(filename, size):
with open(filename) as f:
X = f.read(1024*1024*size)
X = X.replace('\n', '')
return X
def get_unicount(text):
length = len(text)
counts = np.zeros(26)
for i in xrange(length):
c = ord(text[i])
counts[c-97]+=1
#97-122
return counts
def get_bigram_stats_dic(text):
length = len(text)
dic = {}
for i in 'abcdefghijklmnopqrstuvwxyz':
for j in 'abcdefghijklmnopqrstuvwxyz':
dic[(i,j)]=0
for i in xrange(length-1):
if (text[i], text[i+1]) in dic:
dic[(text[i], text[i+1])] += 1
for k,v in dic.items():
dic[k] = v/(counts[ord(k[0])-97])
return dic
def quality(decrypted, original):
l = len(decrypted)
zipped = zip(decrypted, original)
return sum(1.0 for x,y in zipped if x == y)/l
def crypt(text):
p = range(26)
random.shuffle(p)
output=''
for ch in text:
try:
x = ord(ch) - ord('a')
output+=(chr(p[x] + ord('a')))
except:
pass
return output, p
def get_desiredPDF_bigram(permutation):
logp = 0
for i in xrange(len(encrypted)-1):
pr = stats[chr(permutation[ord(encrypted[i])-97]+97),
chr(permutation[ord(encrypted[i+1])-97]+97)]
if pr>0:
logp += math.log(pr)
else:
logp += -9 #penalty for non existant pairs
return logp
def metropolis( desiredPDF, initValue, computableRVS, skipIterations = 1000):
random_variable = initValue
random_variableDensityValue = desiredPDF( random_variable )
for i in xrange( skipIterations ):
candidate = computableRVS( random_variable )
candidateDensityValue = desiredPDF( candidate )
acceptanceProb = min(0, candidateDensityValue - random_variableDensityValue )
if math.log(random.random()) < acceptanceProb:
random_variable = candidate
random_variableDensityValue = candidateDensityValue
while True:
candidate = computableRVS( random_variable )
candidateDensityValue = desiredPDF( candidate )
acceptanceProb = min( 0, candidateDensityValue - random_variableDensityValue )
if math.log(random.random()) < acceptanceProb:
random_variable = candidate
random_variableDensityValue = candidateDensityValue
yield random_variable, random_variableDensityValue
def uniform( n ):
#initialize permutation with identical
permutation = [ i for i in xrange( n ) ]
#swap ith object with random onject from i to n - 1 enclusively
for i in xrange( n ):
j = random.randint( i, n - 1 )
permutation[ i ], permutation[ j ] = permutation[ j ], permutation[ i ]
return permutation
def applyTransposition( basePermutation ):
n = len( basePermutation )
permutation = copy( basePermutation )
#apply n random transpositions (including identical) to base permutation
# for i in xrange( n ):
k, l = random.randint( 0, n - 1 ), random.randint( 0, n - 1 )
permutation[ k ], permutation[ l ] = permutation[ l ], permutation[ k ]
return permutation
def decrypt(permutation, encrypted):
decrypted = []
for i in encrypted:
decrypted.append(chr(permutation[ord(i)-97]+97))
return ''.join(decrypted)
crypt with given permutation:
In [7]:
def crypt_given(permutation, text):
output=''
# p.append(26)
for ch in text:
try:
x = ord(ch) - ord('a')
output+=(chr(permutation[x] + ord('a')))
except:
pass
return output
fixed training text (War and Peace):
In [9]:
train_text = read_text_whole('main/war_and_peace.txt')
counts = get_unicount(train_text)
stats = get_bigram_stats_dic(train_text)
vary size of train text (used War and Peace, total 3Mb)
In [12]:
sizes = [1000,2000,4000,8000,16000,32000,64000,128000]
qs = list()
fixed_permutation = uniform(26)
for s in sizes:
print 'size of encrypted text: ',s
original = read_text_words('main/oliver_twist.txt', s)[3:]
encrypted = crypt_given(fixed_permutation, original)
init_p = uniform(26)
#Metropolis here
st = time.time()
computableGen = lambda t: applyTransposition(t)
metropolisgenerator = \
metropolis(get_desiredPDF_bigram, init_p, computableGen, 1500)
y = float('-inf')
for i in xrange( 1000 ):
cand = metropolisgenerator.next()
if (cand[1] > y):
y = cand[1]
x = cand[0]
et = time.time() - st
print 'metropolis time: ', et
print 'best density among 1000 last iterations: ', y
print 'corresponding permutation: ', x
decrypted = decrypt(x, encrypted)
qs.append(quality(decrypted, original))
plt.plot(sizes[:len(qs)], qs)
Out[12]:
compare war and peace and shakespeare as training sets
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