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Markov transition matrix in Python
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#the following code takes a list such as | |
#[1,1,2,6,8,5,5,7,8,8,1,1,4,5,5,0,0,0,1,1,4,4,5,1,3,3,4,5,4,1,1] | |
#with states labeled as successive integers starting with 0 | |
#and returns a transition matrix, M, | |
#where M[i][j] is the probability of transitioning from i to j | |
def transition_matrix(transitions): | |
n = 1+ max(transitions) #number of states | |
M = [[0]*n for _ in range(n)] | |
for (i,j) in zip(transitions,transitions[1:]): | |
M[i][j] += 1 | |
#now convert to probabilities: | |
for row in M: | |
s = sum(row) | |
if s > 0: | |
row[:] = [f/s for f in row] | |
return M | |
#test: | |
t = [1,1,2,6,8,5,5,7,8,8,1,1,4,5,5,0,0,0,1,1,4,4,5,1,3,3,4,5,4,1,1] | |
m = transition_matrix(t) | |
for row in m: print(' '.join('{0:.2f}'.format(x) for x in row)) | |
#0.67 0.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | |
#0.00 0.50 0.12 0.12 0.25 0.00 0.00 0.00 0.00 | |
#0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 | |
#0.00 0.00 0.00 0.50 0.50 0.00 0.00 0.00 0.00 | |
#0.00 0.20 0.00 0.00 0.20 0.60 0.00 0.00 0.00 | |
#0.17 0.17 0.00 0.00 0.17 0.33 0.00 0.17 0.00 | |
#0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 | |
#0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 | |
#0.00 0.33 0.00 0.00 0.00 0.33 0.00 0.00 0.33 |
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