g5.py

import numpy as np

# Initial Guess
w_old = np.array([0, 0]).reshape((2,1))
w_new = np.array([-1.8,-.8]).reshape((2,1))
gamma = .0002 # set the learning rate
nu = .00001 # set the precision

def f1_primew1(w1, w2):
    return -2 * (1 - w1) - 400 * (w2 - w1**2) * w1

def f1_primew2(w1, w2):
    return 200 * (w2 - w1**2)

# Gradient Vector
def g_vec(w1, w2):
    return np.array([f1_primew1(w1, w2), f1_primew2(w1, w2)]).reshape((2,1))

# Perform Gradient Descent
r = 0
while np.linalg.norm(w_old - w_new) > nu:
    w_old = w_new
    w_new = w_old - gamma * g_vec(w_old[0,:], w_old[1,:])
    r = r + 1

print r
print w_new

# OUTPUT
23374
[[ 0.94648413]
 [ 0.89561108]]