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import operator
import numpy as np
import numpy.random as rm
lsave=0
#theta=[pi,L11-L14,L21-L24,R11-R14,R21-R24]
A={}
for xx in range(500):
u=np.array([[4,2,2,2],[2,4,2,2],[2,2,4,2],[2,2,2,4]])
L1=rm.random_sample(4)
L2=rm.random_sample(4)
R1=rm.random_sample(4)
R2=rm.random_sample(4)
L1=L1/sum(L1)
L2=L1/sum(L2)
R1=R1/sum(R1)
R2=R2/sum(R2)
pi=rm.random_sample(1)[0]
N=sum(u.reshape(16,1))[0]
while True:
FL=np.array([[pi*L1[i]*L2[j] for i in range(4)] for j in range(4)])
FR=np.array([[(1-pi)*R1[i]*R2[j] for i in range(4)] for j in range(4)])
F=FL+FR
lobs=sum((u*np.log(F)).reshape(16,1))[0]
uL=u*FL/F
NL=sum(uL.reshape(16,1))[0]
uR=u*FR/F
NR=sum(uR.reshape(16,1))[0]
pistar=sum(uL.reshape(16,1))[0]/N
L1star=sum(uL.T)/NL
L2star=sum(uL)/NL
R1star=sum(uR.T)/NR
R2star=sum(uR)/NR
if np.abs(lobs-lsave)<.000001:
A[lobs]=F
break
R1=R1star
R2=R2star
L2=L2star
L1=L1star
pi=pistar
lsave=lobs
print 40*A[sorted(A.iterkeys(),reverse=True)[0]]
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