from  matplotlib import pyplot as plt
import numpy as np

# Define dimension of matrix and vectors
Dim = 4
#Setting up a transition probability matrix
TransitionMatrix = np.matrix('0.25 0.1111 0.375 0.3333; 0.5 0.2222 0.0 0.3333; 0.0 0.1111 0.375 0.0; 0.25 0.5556 0.25 0.3334')
# Making a copy of the transition matrix
W = TransitionMatrix
print(W)
# our first state
wold = np.zeros(Dim)
wold[0] = 1.0
wnew = np.zeros(Dim)

# diagonalize and obtain eigenvalues, not necessarily sorted
EigValues, EigVectors = np.linalg.eig(TransitionMatrix)
# sort eigenvectors and eigenvalues
permute = EigValues.argsort()
EigValues = EigValues[permute]
EigVectors = EigVectors[:,permute]
for i in range(Dim):
    print(EigValues[i])


count = 0
while count < 20:
      for i in range(Dim):
          wnew[i] = W[i,:] @ wold
      count = count + 1
      print(count, wnew)
      wold = wnew