import numpy as np
import random
from scipy import linalg

n = 4
A = np.array([[3,2,9,5],
              [3,1,3,11],
              [3,7,4,8],
              [5,2,4,9]])
x1 = np.zeros(n)
x2 = np.zeros(n)
l1 = np.zeros(n)
l2 = np.zeros(n)
y = np.zeros(n)

def otn(y, x):
    result = np.zeros(x.size)
    for i in range(x.size):
        if x[i] != 0:
            result[i] = y[i]/x[i]
    return result

def usl(y, x):
    eps = 0.00001
    result = False
    for i in range(x.size):
        if abs(y[i]-x[i])<=eps:
            result = True
    return result

for i in range(n):
    y[i] = 1
    l2[i] = 1
k = 1
x2 = y/np.linalg.norm(y)

while True:
    x1 = x2
    l1 = l2
    y = A.dot(x1)
    x2 = y/np.linalg.norm(y)
    l2 = otn(y, x1)
    k += 1
    if usl(l1,l2):
        break
print("k =",k)
s= 0
for i in range(n):
    s += l2[i]
L = s / n
print(L)
print(linalg.eigvals(A))