# -*- coding: utf-8 -*-
import numpy as np

A = np.array([[4.,-1.,1.],
              [-1.,4.,-2.],
              [1.,-2.,4.]])

b = np.array([12.,-1.,5.])

emax=10**-13
N=30

x=np.zeros_like(b)

for k in range(N):
    x_new=x.copy()
    for i in range (len(b)):
        x[i] = (b[i] - np.sum(A[i, :i]* x[:i]) \
         - np.sum(A[i, i + 1:]* x[i + 1:]))/ A[i, i]
    
    e=np.linalg.norm(x_new-x)
    if e<emax:
        break
    print(k,x,e)