input_layer_size = 3

hidden_layer_size = 5

num_labels = 3

m = 5

# We generate some 'random' test data

theta1 = debug_initialize_weights(hidden_layer_size, input_layer_size)

theta2 = debug_initialize_weights(num_labels, hidden_layer_size)

# Reusing debugInitializeWeights to generate X

x = debug_initialize_weights(m, input_layer_size - 1)

y = np.mod(np.arange(1, m+1), num_labels).T

yk = recode_labels(y, num_labels)

x_bias = np.r_[np.ones((1, x.shape[0] )), x.T]

nn_params = np.concatenate((theta1.T.ravel(), theta2.T.ravel()))

def cost_function(p):

return compute_cost(p, input_layer_size, hidden_layer_size, num_labels, x, y, _lambda, yk, x_bias)

def gradients_function(p):

return compute_gradients(p, input_layer_size, hidden_layer_size, num_labels, x, y, _lambda, yk, x_bias)

gradients = gradients_function(nn_params)

num_gradients = compute_numerical_gradient(cost_function, nn_params)

print('Gradients:')

for i in range(len(gradients)):

print(num_gradients[i], gradients[i])

diff = np.linalg.norm(num_gradients-gradients) / np.linalg.norm(num_gradients+gradients)

numgrad = np.zeros(theta.shape)

perturb = np.zeros(theta.shape)

e = 1e-4

for p in range(len(theta)):

# Set perturbation vector

perturb[p] = e

loss1 = cost_fn(theta - perturb)

loss2 = cost_fn(theta + perturb)

# Compute Numerical Gradient

numgrad[p] = (loss2 - loss1) / (2*e)

perturb[p] = 0