#Practical 3

import numpy as np
import scipy as sc
import pandas as pd
from fractions import Fraction

def display_format(my_vector,my_decimal):
    return np.round((my_vector).astype(float),decimals=my_decimal)

my_dp = Fraction(1,3)
print(my_dp)

Mat = np.matrix([[Fraction(1,2),Fraction(1,2),0],
                [Fraction(1,2),0,1],
                [0,Fraction(1,2),0]])

print(Mat)
Ex = np.zeros((3,3))
print(Ex)
Ex[:] = my_dp
print(Ex)

beta = 0.7
A = beta * Mat + ((1-beta) * Ex)
r = np.matrix([my_dp, my_dp, my_dp])
print(r)

r = np.transpose(r)
print(r)

previous_r = r
counter_variable=0
while True:
    r=A*r
    m=display_format(r,4)
    n=display_format(previous_r,4)
    if(abs(r-previous_r)<=0.0001).all():
        break
    previous_r=r
    counter_variable+=1
    
print ("Final:\n", display_format(r,4))