``````

In [5]:

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

with open(filename) as f:
X = X[:wordsnumber]
X = ''.join(X)
X = X.replace('\n', '')
return X

with open(filename) as f:
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)

``````
``````

In [6]:

fname = 'main/oliver_twist.txt'
encrypted,p = crypt(original)
print encrypted[:20]

``````
``````

dsfuzlafpdondfqwfzof

``````
``````

In [12]:

counts = get_unicount(train_text)
stats = get_bigram_stats_dic(train_text)

for k in xrange(5):
init_p = uniform(26)
#Metropolis here
st = time.time()
computableGen = lambda t: applyTransposition(t)
metropolisgenerator = \
metropolis(get_desiredPDF_bigram, init_p, computableGen, 2000)

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)
q = quality(decrypted, original)
print q

``````
``````

metropolis time:  153.507999897
best density among 1000 last iterations:  -56398.5046942
corresponding permutation:  [9, 16, 11, 19, 25, 4, 0, 3, 23, 12, 24, 14, 22, 20, 6, 2, 13, 5, 7, 21, 15, 18, 1, 8, 10, 17]
1.0
metropolis time:  152.47300005
best density among 1000 last iterations:  -56398.5046942
corresponding permutation:  [9, 16, 11, 19, 25, 4, 0, 3, 23, 12, 24, 14, 22, 20, 6, 2, 13, 5, 7, 21, 15, 18, 1, 8, 10, 17]
1.0
metropolis time:  161.621000051
best density among 1000 last iterations:  -56398.5046942
corresponding permutation:  [9, 16, 11, 19, 25, 4, 0, 3, 23, 12, 24, 14, 22, 20, 6, 2, 13, 5, 7, 21, 15, 18, 1, 8, 10, 17]
1.0
metropolis time:  156.662000179
best density among 1000 last iterations:  -56398.5046942
corresponding permutation:  [9, 16, 11, 19, 25, 4, 0, 3, 23, 12, 24, 14, 22, 20, 6, 2, 13, 5, 7, 21, 15, 18, 1, 8, 10, 17]
1.0

---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-12-9c831e362cb6> in <module>()
13    y = -float("inf")
14    for i in xrange( 1000 ): #<=========
---> 15        cand = metropolisgenerator.next()
16        if (cand[1] > y):
17            y = cand[1]

<ipython-input-5-c1d614a58db1> in metropolis(desiredPDF, initValue, computableRVS, skipIterations)
81     for i in xrange( skipIterations ):
82         candidate = computableRVS( random_variable )
---> 83         candidateDensityValue = desiredPDF( candidate )
84         acceptanceProb = min(0, candidateDensityValue - random_variableDensityValue )
85         if math.log(random.random()) < acceptanceProb:

<ipython-input-5-c1d614a58db1> in get_desiredPDF_bigram(permutation)
67     logp = 0
68     for i in xrange(len(encrypted)-1):
---> 69         pr = stats[chr(permutation[ord(encrypted[i])-97]+97),
70                    chr(permutation[ord(encrypted[i+1])-97]+97)]
71         if pr>0:

KeyboardInterrupt:

``````
``````

In [13]:

counts = get_unicount(train_text)
stats = get_bigram_stats_dic(train_text)

for k in xrange(3):
init_p = uniform(26)
#Metropolis here
st = time.time()
computableGen = lambda t: applyTransposition(t)
metropolisgenerator = \
metropolis(get_desiredPDF_bigram, init_p, computableGen, 2000)

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)
q = quality(decrypted, original)
print q

``````
``````

metropolis time:  153.292999983
best density among 1000 last iterations:  -65548.7996672
corresponding permutation:  [9, 16, 11, 8, 25, 4, 0, 24, 23, 15, 6, 14, 22, 20, 7, 12, 19, 5, 13, 10, 2, 18, 1, 3, 21, 17]
0.538870851371
metropolis time:  157.934999943
best density among 1000 last iterations:  -58104.3291223
corresponding permutation:  [9, 16, 11, 19, 25, 4, 0, 3, 23, 12, 24, 14, 22, 20, 6, 2, 13, 5, 7, 10, 15, 18, 1, 8, 21, 17]
0.980068542569
metropolis time:  155.993000031
best density among 1000 last iterations:  -58104.3291223
corresponding permutation:  [9, 16, 11, 19, 25, 4, 0, 3, 23, 12, 24, 14, 22, 20, 6, 2, 13, 5, 7, 10, 15, 18, 1, 8, 21, 17]
0.980068542569

``````

war and peace as training text gives better results than super.txt confirming our intuition that english used in the super.txt file is not modern english