import numpy as np
from numpy import linalg as LA
from numpy import matrix as matrix
from matplotlib import pyplot as plt
from scipy.optimize import fsolve
import math


A = matrix([[0.4, 0.4, 0.2],[0.2, 0.5, 0.4], [0.1, 0.1, 0.2]]);
E = matrix([[1, 0, 0],[0, 1, 0], [0, 0, 1]]);
print(A);
w, v = LA.eig(A);
print("Vector of eigen values of matrix A")
print(w);
print("Frobenius's number")
print(max(w));
print("Right eigen vectors")
print(v);
print("Right Frobenius's vector")
print(v[:,:1])
C = A
matrix.transpose(A);
A = C
w, v = LA.eig(A);

print("Left eigen vectors")
print(v)
print("Left Frobenius's vector")
print(v[:,:1])
B = LA.inv(E - A)
print("Matrix of full costs")
print(B)
ans = 0
res = E

for k in range(1000):
    flag = 1
    res = res + A ** (k + 1);
    for i in range(3):
        for j in range(3):
            if(abs(res[i, j] - B[i, j]) > 0.01):
                flag = 0;
    ans = flag


print(ans);
y = matrix([100, 70, 80])
y = matrix.transpose(y)
print(y)
B = LA.inv(B)
D = B * y;

print(D)