from pprint import pprint
from numpy import array, zeros, diag, diagflat, dot


def simpleiter(A, b, N=25, x=None):

    if x is None:
        x = zeros(len(A[0]))


    D = diag(A)
    R = A - diagflat(D)

    #
    for i in range(N):
        x = (b - dot(R,x)) / D
    return x

A = array([[0.405, 0.05, 0.04, 0, 0.09],
                [-0.061, 0.53, 0.073, 0.11, -0.06],
                [0.07, -0.036, 0.38, 0.03, 0.02],
                [-0.05, 0, 0.066, 0.58, 0.23],
                [0, 0.081, -0.05, 0, 0.41]])
b = array([1.065, 0.975, -1.312, 1.096, -0.048])
guess = array([1.0, 1.0, 1.0, 1.0, 1.0])

sol = simpleiter(A, b, N = 25, x = guess)

print ("A:")
pprint(A)

print ("b:")
pprint(b)

print ("x:")
pprint(sol)