-
Notifications
You must be signed in to change notification settings - Fork 1
/
mc_ev.sage
164 lines (118 loc) · 4.8 KB
/
mc_ev.sage
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
from matplotlib import pyplot as plt
from operator import lt
@interact
def scrabble_expected(start_word = input_box(default=['a'],label = 'Initial letter: '),
letter_walk = selector(['Keyboard','Cycle', 'Path' ], label = 'Walk on Individual Letters: '), score_fn = selector(['Scrabble Score','Alphabetical (a=1, etc.)', 'Scrabble Count', 'Uniform', '# Vowels'], label = "Score function on letters:"), num_steps = input_box(default=10,label='Number of Steps: '),
disp = input_box(default = 10, label ='Number of states to display: '), auto_update=False):
scrabble_bag = ['a','a','a','a','a','a','a','a','a','b','b','c','c','d','d','d','d','e','e','e','e','e','e','e','e','e','e','e','e','f','f','g','g','g','h','h','i','i','i','i','i','i','i','i','i','j','k','l','l','l','l','m','m','n','n','n','n','n','n','o','o','o','o','o','o','o','o','p','p','q','r','r','r','r','r','r','s','s','s','s','t','t','t','t','t','t','u','u','u','u','v','v','w','w','x','y','y','z',' ',' ']
scrabble_points = {' ':0,'a':1,'b':3,'c':3,'d':2,'e':1,'f':4,'g':2,'h':4,'i':1,'j':8,'k':5,'l':1,'m':3,'n':1,'o':1,'p':3,'q':10,'r':1,'s':1,'t':1,'u':1,'v':4,'w':4,'x':8,'y':4,'z':10 }
scrabble_count = {' ':2,'a':9,'b':2,'c':2,'d':4,'e':12,'f':2,'g':3,'h':2,'i':9,'j':1,'k':1,'l':4,'m':2,'n':6,'o':8,'p':2,'q':1,
'r':6,'s':4,'t':6,'u':4,'v':2,'w':2,'x':1,'y':2,'z':1 }
alphabet=['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z',' ']
key1 ={'q':['w','a'],'w':['e','a','s'],'e':['r','s','d'],'r':['t','d','f'],'t':['y','f','g'],'y':['u','g','h'],'u':['i','h','j'],'i':['o','j','k'],'o':['p','k','l'],
'p':['l'],'a':['s','z'],'s':['d','z','x'],'d':['f','x','c'],'f':['g','c','v'],'g':['h','v','b'],'h':['j','b','n'],'j':['k','n','m'],'k':['l','m'],'z':['x'],'x':['c'],'c':['v',' '],'v':['b',' '],'b':['n',' '],'n':['m',' '],'m':[' ']}
cyclic = {alphabet[x]:[alphabet[(x+1)%27]] for x in range(27)}
pathic = {alphabet[x]:[alphabet[x+1]] for x in range(26)}
g2=Graph(pathic)
g=Graph(cyclic)
h=Graph(key1)
if letter_walk == 'Cycle':
graph = g
bag = alphabet
bvg = 0
elif letter_walk == 'Path':
graph = g2
bag = alphabet
bag = bag + bag
bag.pop(0)
bag.pop(-1)
bvg = 0
elif letter_walk == 'Keyboard':
graph = h
bag = []
for e in graph.edges():
bag.append(e[0])
bag.append(e[1])
bvg = 0
alpha_pos = {alphabet[x]:x for x in range(len(alphabet))}
if score_fn == 'Scrabble Score':
scores = scrabble_points
if score_fn == 'Scrabble Count':
scores = scrabble_count
if score_fn == 'Uniform':
scores = {x:1 for x in alphabet}
if score_fn == '# Vowels':
scores = {x:1 for x in alphabet}
scores['a'] = 100
scores['e'] = 100
scores['i'] = 100
scores['o'] = 100
scores['u'] = 100
scores['y'] = 50
if score_fn == 'Alphabetical (a=1, etc.)':
scores = {alphabet[i]: i+1 for i in range(27)}
vals = [ ]
sums = [0]
means = []
error = []
tvt=[]
tvp=[]
evt=[]
evp=[]
accepts=[]
state = start_word[0]
letters = 1
#expected = letters * mean([scores[x] for x in bag])
#print(expected)
alpha_pos = {alphabet[x]:x for x in range(len(alphabet))}
proposal_vec = [bag.count(x) for x in alphabet]
#print(alpha_pos)
proposal_sum = sum(proposal_vec)
proposal_vec = [float(proposal_vec[alpha_pos[x]])/proposal_sum for x in alphabet]
vals =[scores[start_word[0]]]
sums=[scores[start_word[0]]]
ses=[start_word[0]]
means=[scores[start_word[0]]]
target = sum([proposal_vec[x]*scores[alphabet[x]] for x in range(27)])
error=[scores[start_word[0]]-target]
proposal_vec = [float(proposal_vec[alpha_pos[x]])/proposal_sum for x in alphabet]
emp_vec = [0 for x in alphabet]
q_vec = [0 for x in alphabet]
for l in range(letters):
emp_vec[alpha_pos[state[l]]]+=1
state=[start_word[0]]
for z in range(num_steps):
k = choice(range(letters))
old_state = state[k]
if bvg == 1:
new_state = choice(bag)
elif bvg == 0:
new_state = choice(graph.neighbors(old_state))
state[k] = new_state
vals.append(scores[new_state])
sums.append(sums[-1]+vals[-1])
means.append(sums[-1]/(z+2))
error.append(means[-1]-target)
#ses.append(state[k])
#print(ses)
#print(len(vals))
plt.figure()
plt.plot(vals, 'o',markersize=1)
plt.title('Sample Values')
plt.xlabel('Step #')
plt.show()
plt.figure()
plt.plot(means,'o',markersize=2)
plt.axhline(y=target,color='r')
plt.title('Average of Samples')
plt.show()
plt.figure()
plt.plot(error,'o',markersize=2)
plt.axhline(y=0,color='r')
plt.title('Error: Expected - Empirical')
plt.show()
plt.figure()
pretty_print('Final estimate: ', means[-1].n())
pretty_print('Actual expected value: ', target)
pretty_print('Error: ', error[-1])
pretty_print('Percent Error: ', error[-1]/target)