import numpy as np
damping=0.85
epsilon=1e-8
graph = [(i,0) for i in range(1,9)]+[(i, i+1) for i in range(1,8)]+ [(i+1,i) for i in range(1,8)]+[(8,1),(1,8)]
A = np.zeros((9,9))
for nodes in graph:
    A[nodes[0],nodes[1]]=1
outlinks = np.ones(9)*3
outlinks[0]=9
K = np.identity(9)*outlinks
M = np.matmul(np.linalg.inv(K), A)
M[0,:]+=1/9
M=M.transpose()
matr =np.linalg.inv( np.identity(9) - damping*M)
v = np.ones(9)*((1-damping)/9)
ans = np.matmul(matr, v)
print('Exact answer')
print(ans)
M0 = matr
ans_iter = np.ones(9)*1/9
for i in range(10):
    matr = np.matmul(matr,M0)
    ans_iter1 = ((1-damping)/9)*np.ones(9) + damping*np.matmul(M, ans_iter)
    if sum([abs(ans_iter1[i]-ans_iter[i]) for i in range(len(ans_iter))])>epsilon:
         ans_iter = ans_iter1
    else:
        break
print('Answer obtained by iterations')
print(ans_iter)
import numpy as np
damping=0.85
epsilon=1e-8
graph = [(i,0) for i in range(1,9)]+[(i, i+1) for i in range(1,8)]+ [(i+1,i) for i in range(1,8)]+[(8,1),(1,8)]
A = np.zeros((9,9))
for nodes in graph:
    A[nodes[0],nodes[1]]=1
outlinks = np.ones(9)*3
outlinks[0]=9
K = np.identity(9)*outlinks
M = np.matmul(np.linalg.inv(K), A)
M[0,:]+=1/9
M=M.transpose()
matr =np.linalg.inv( np.identity(9) - damping*M)
v = np.ones(9)*((1-damping)/9)
ans = np.matmul(matr, v)
print('Exact answer')
print(ans)
M0 = matr
ans_iter = np.ones(9)*1/9
for i in range(10):
    matr = np.matmul(matr,M0)
    ans_iter1 = ((1-damping)/9)*np.ones(9) + damping*np.matmul(M, ans_iter)
    if sum([abs(ans_iter1[i]-ans_iter[i]) for i in range(len(ans_iter))])>epsilon:
         ans_iter = ans_iter1
    else:
        break
print('Answer obtained by iterations')
print(ans_iter)