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graph_sampling.sage
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from matplotlib import pyplot as plt
@interact
def graph_samples(start_word = input_box(default=['a'],label = 'Initial letter: '),
letter_walk = selector(['Scrabble','Uniform','Keyboard','Cycle','Path' ], label = 'Walk on Individual Letters: '), num_steps = input_box(default=10,label='Number of Steps: '),num_trials = input_box(default=100,label='Number of Trials: '),
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)
dd=h.distance_all_pairs()
print(h.diameter())
if letter_walk == 'Scrabble':
bag = scrabble_bag
bvg = 1
elif letter_walk == 'Uniform':
bag = alphabet
bvg = 1
elif 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
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]
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
for z in range(num_trials):
state=[start_word[0]]
#print('start',start_word)
#print('start',state)
ll=[state[0]]
for y 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
ll.append(new_state)
#print(ll)
for l in range(letters):
emp_vec[alpha_pos[state[l]]]+=1
emp_s = sum(emp_vec)
emp_n = [float(emp_vec[alpha_pos[x]])/emp_s for x in alphabet]
#print(proposal_vec)
#print(target_vec)
#print(emp_n)
plt.figure()
plt.bar(range(len(alphabet)),proposal_vec)
plt.title('Long Term Distribution')
ax = plt.gca()
ax.set_xticks(range(len(alphabet)))
ax.set_xticklabels(alphabet)
plt.xlabel('Letter')
plt.ylabel('Frequency')
plt.show()
plt.figure()
plt.bar(range(len(alphabet)),emp_n)
ax = plt.gca()
ax.set_xticks(range(len(alphabet)))
ax.set_xticklabels(alphabet)
plt.title('Empirical Distribution')
plt.xlabel('Letter')
plt.ylabel('Frequency')
plt.show()