def test_output_linear_backward(self):
print_test("Testing linear backward function:")
np.random.seed(395)
x = np.random.randn(10, 2, 3)
w = np.random.randn(6, 5)
b = np.random.randn(5)
dout = np.random.randn(10, 5)
dx_num = eval_numerical_gradient_array(
lambda x: layers.linear_forward(x, w, b), x, dout)
dw_num = eval_numerical_gradient_array(
lambda w: layers.linear_forward(x, w, b), w, dout)
db_num = eval_numerical_gradient_array(
lambda b: layers.linear_forward(x, w, b), b, dout)
dx, dw, db = layers.linear_backward(dout, x, w, b)
dX_e = rel_error(dx_num, dx)
dW_e = rel_error(dw_num, dw)
db_e = rel_error(db_num, db)
print('dX relative error: ', dX_e)
print('dW relative error: ', dW_e)
print('db realtive error: ', db_e)
self.assertTrue(dX_e <= 5e-10)
self.assertTrue(dW_e <= 5e-10)
self.assertTrue(db_e <= 5e-10)
def test_output_linear_forward(self):
print_test("Testing linear forward function:")
n_X = 10
X_shape = [4, 2, 5]
n_out = 3
n_input = n_X * np.prod(X_shape)
n_weights = np.prod(X_shape) * n_out
X = np.linspace(-0.2, 0.5, num=n_input).reshape([n_X] + X_shape)
W = np.linspace(-0.4, 0.2, num=n_weights).reshape(
np.prod(X_shape), n_out)
b = np.linspace(0.5, 1, num=n_out)
# test
print ("n_input: ", n_input)
print ("n_weights: ", n_weights)
print ("X: ", X.shape, "\n", X)
print ("W: ", W.shape, "\n", W)
print ("b: ", b.shape, "\n", b)
out = layers.linear_forward(X, W, b)
correct_out = np.asarray([[1.33803627, 1.55459973, 1.7711632],
[1.04318148, 1.27389798, 1.50461448],
[0.7483267 , 0.99319623, 1.23806575],
[0.45347192, 0.71249447, 0.97151703],
[0.15861713, 0.43179272, 0.7049683],
[-0.13623765, 0.15109096, 0.43841958],
[-0.43109244, -0.12961079, 0.17187085],
[-0.72594722, -0.41031255, -0.09467787],
[-1.02080201, -0.6910143 , -0.3612266 ],
[-1.31565679, -0.97171605, -0.62777532]])
e = np.max(np.abs(correct_out - out))
e = rel_error(out, correct_out)
print("Relative difference", e)
self.assertTrue(e <= 5e-08)
def test_derivative_softmax(self):
print_test("Test gradients softmax")
np.random.seed(395)
X = np.random.randn(5, 10)
y = np.random.uniform(0, 10, 5).astype(np.int16)
expected_grads = np.asarray(
[[
0.00322816, 0.01188412, 0.00185757, 0.04150573, -0.19303544,
0.00260126, 0.08516417, 0.02764608, 0.00912691, 0.01002143
],
[
-0.19497483, 0.00531375, 0.04302849, 0.03511828, 0.00303517,
0.04190564, 0.0038523, 0.01478627, 0.02427056, 0.02366437
],
[
-0.18935209, 0.00978672, 0.00897249, 0.02791175, 0.04489496,
0.00676774, 0.0171222, 0.00539931, 0.0294198, 0.03907712
],
[
0.02925289, -0.19129923, 0.00521769, 0.00132343, 0.01317178,
0.03008875, 0.00245856, 0.00113738, 0.01814663, 0.09050212
],
[
0.01018762, 0.0232368, 0.0049424, 0.01980616, 0.01467162,
0.00463897, 0.03473582, 0.007073, 0.03897701, -0.15826939
]])
_, grads = classifiers.softmax(X, y)
e = rel_error(expected_grads, grads)
print("Relative error", e)
self.assertTrue(e <= 1e-05)
def test_output_softmax(self):
print_test("Test output softmax")
np.random.seed(395)
X = np.random.randn(3073, 10)
y = np.random.uniform(0, 10, 3073).astype(np.int16)
expected_loss = 2.7536201727859835
loss, _ = classifiers.softmax(X, y)
e = rel_error(loss, expected_loss)
print("Relative error", e)
self.assertTrue(e <= 5e-12)
def test_output_relu_backward(self):
print_test("Testing relu backward function:")
np.random.seed(395)
x = np.random.randn(10, 10)
dout = np.random.randn(*x.shape)
dx_num = eval_numerical_gradient_array(
lambda x: layers.relu_forward(x), x, dout)
dx = layers.relu_backward(dout, x)
dx_e = rel_error(dx, dx_num)
print('dX relative difference:', dx_e)
self.assertTrue(dx_e <= 1e-11)
def test_output_relu_forward(self):
print_test("Testing relu forward function:")
x = np.linspace(-0.7, 0.5, num=20).reshape(5, 4)
out = layers.relu_forward(x)
correct_out = np.array([[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0.05789474, 0.12105263, 0.18421053, 0.24736842],
[0.31052632, 0.37368421, 0.43684211, 0.5]])
e = rel_error(out, correct_out)
print('Relative difference:', e)
self.assertTrue(e <= 5e-08)
def test_output_dropout_forward(self):
print_test("Testing dropout forward function:")
seed = 395
np.random.seed(seed)
p = 0.7
x = np.linspace(-0.7, 0.5, num=10).reshape(2, 5)
out_train, _ = layers.dropout_forward(x, p=p, seed=seed, train=True)
out_test, _ = layers.dropout_forward(x, p=p, seed=seed, train=False)
correct_out = np.asarray([[-0., -0., -0., -1., -0.],
[-0., 0., 0., 0., 0.]])
e_train = rel_error(out_train, correct_out)
e_test = rel_error(out_test, x)
print("Relative difference train:", e_train)
print("Relative difference test:", e_test)
self.assertTrue(e_train < 1e-12)
self.assertTrue(e_test < 1e-12)
def test_output_relu_backward(self):
print_test("Testing dropout backward function:")
seed = 395
np.random.seed(seed)
x = np.random.randn(16, 16) + 8
dout = np.random.randn(*x.shape)
p = 0.7
# Test for train
dout, mask = layers.dropout_forward(x, train=True, p=p, seed=seed)
dx = layers.dropout_backward(dout, mask, p=p, train=True)
dx_num = eval_numerical_gradient_array(
lambda xx: layers.dropout_forward(
xx, p=0.7, train=True, seed=seed)[0], x, dout)
e_train = rel_error(dx, dx_num)
print('dx train relative error: ', e_train)
self.assertTrue(e_train <= 5e-11)
# Test for test
dx_test = layers.dropout_backward(dout, mask, train=False, p=p)
e_test = rel_error(dout, dx_test)
print('dx test relative error: ', e_test)
self.assertTrue(e_test <= 1e-12)