def check_nn_gradients(check_nn_lambda=0):
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 = 1 + np.mod(np.arange(m) + 1, num_labels)
# Unroll parameters
nn_params = np.append(np.ravel(theta1, order='F'),
np.ravel(theta2, order='F'))
cost, grad = nn_cost_function(nn_params, input_layer_size,
hidden_layer_size, num_labels, x, y,
check_nn_lambda)
numgrad = compute_numerical_gradient(nn_cost_function, nn_params,
input_layer_size, hidden_layer_size,
num_labels, x, y, check_nn_lambda)
# Visually examine the two gradient computations. The two columns
# you get should be very similar.
print(
np.append(numgrad.reshape(numgrad.size, 1),
grad.reshape(grad.size, 1),
axis=1))
print('The above two columns you get should be very similar.\n' +
'(Left-Your Numerical Gradient, Right-Analytical Gradient)\n\n')
diff = np.linalg.norm(numgrad - grad) / np.linalg.norm(numgrad + grad)
print('If your backpropagation implementation is correct, then \n' +
'the relative difference will be small (less than 1e-9). \n' +
'\nRelative Difference: %e\n' % diff)
def check_gradients(check_nn_lambda=0):
# Create small problem
x_t = np.random.rand(4, 3)
theta_t = np.random.rand(5, 3)
# Zap out most entries
y = np.dot(x_t, theta_t.T)
rand_x_axis, rand_y_axis = np.where(
np.random.rand(y.shape[0], y.shape[1]) > 0.5)
y[rand_x_axis, rand_y_axis] = 0
y_not_0_x_axis, y_not_0_y_axis = np.where(y == 0)
r = np.ones(y.shape)
r[y_not_0_x_axis, y_not_0_y_axis] = 0
y[rand_x_axis, rand_y_axis] = 0
# Run Gradient Checking
x = np.random.randn(x_t.shape[0], x_t.shape[1])
theta = np.random.randn(theta_t.shape[0], theta_t.shape[1])
num_users = y.shape[1]
num_movies = y.shape[0]
num_features = theta_t.shape[1]
numgrad = compute_numerical_gradient(
cofi_cost_func,
np.hstack((np.ravel(x, order='F'), np.ravel(theta, order='F'))), y, r,
num_users, num_movies, num_features, check_nn_lambda)
cost, grad = cofi_cost_func(
np.hstack((np.ravel(x, order='F'), np.ravel(theta, order='F'))), y, r,
num_users, num_movies, num_features, check_nn_lambda)
disp([numgrad, grad])
print('The above two columns you get should be very similar.\n'
'(Left-Your Numerical Gradient, Right-Analytical Gradient)\n\n')
diff = np.linalg.norm(numgrad - grad) / np.linalg.norm(numgrad + grad)
print('If your cost function implementation is correct, then \n'
'the relative difference will be small (less than 1e-9). \n\n'
'Relative Difference: %s\n' % diff)
def check_numerical_gradient(theta, X, levels=[64, 25, 64]):
grad = J(theta, X, X, levels)[1]
numeric_grad = compute_numerical_gradient(J, theta, X, X, levels)
for i, g in enumerate(grad):
print g, numeric_grad[i]
def check_numerical_gradient(theta, X, Y, num_classes, lbda=1e-4):
args = (X, Y, lbda, num_classes)
grad = J(theta, args)[1]
numeric_grad = compute_numerical_gradient(J, theta, args)
for i, g in enumerate(grad):
print g, numeric_grad[i]
