import numpy as np
import numpy.linalg as la

def F1(x):
    x_, y_ = x.item(0), x.item(1)
    return np.matrix([[np.sin(x_+.937)-.389*y_-1.822],
                      [x_+np.cos(y_-.149)-.59]])

def F2(x):
    x_, y_ = x.item(0), x.item(1)
    return np.matrix([[np.tan(x_*y_+.937) - np.power(x_, 2)],
                      [.803*np.power(x_, 2)-.389*np.power(y_, 2)-1]])

def W1(x):
    x_, y_ = x.item(0), x.item(1)
    return np.matrix([[np.cos(x_+.937), -.389],
                      [1, -np.sin(y_-.149)]])

def W2(x):
    x_, y_ = x.item(0), x.item(1)
    a00 = y_/(np.cos(x_*y_+.937)**2) - 2*x_
    a01 = x_/(np.cos(x_*y_+.937)**2)
    a10 = 1.606*x_
    a11 = -0.778*y_
    a = np.matrix([[a00, a01],
                   [a10, a11]])
    return a

x = np.matrix([[1], [-3]])
_x = np.matrix([[1], [1]])
lambd = -la.inv(W1(x))
k = 0
while (la.norm(F1(x)) > 10e-5) or   (la.norm(_x - x) > 10e-5):
    k += 1
    _x = x
    x = x + np.dot(lambd, F1(x))
    print('step#{}\nx={}\nF={}\n|F|={}'.format(
        k, x, F1(x), la.norm(F1(x))))
print(x)

x = np.matrix([[-1], [0]])
_x = np.matrix([[1], [1]])
k=0
while (la.norm(F2(x)) > 10e-5) or   (la.norm(_x - x) > 10e-5):
    k+=1
    _x = x
    delta = la.solve(W2(x), -F2(x))
    x = x + delta
    print('step#{}\nx={}\nF={}\n|F|={}'.format(
        k, x, F2(x), la.norm(F2(x))))
print(x)