def test_sigmoid():
arr = sigmoid(array([[1, 2]]))
assert_allclose(
arr,
array([[0.73105858, 0.88079708]])
)
def test_model_backward_dropout():
random_state = RandomState(1)
X = random_state.randn(3, 5)
Y = np.array([[1, 1, 0, 1, 0]])
cache = (
np.array([[-1.52855314, 3.32524635, 2.13994541, 2.60700654, -0.75942115],
[-1.98043538, 4.1600994, 0.79051021, 1.46493512, -0.45506242]]),
np.array([[True, False, True, True, True],
[True, True, True, True, False]],
dtype=bool),
np.array([[0., 0., 4.27989081, 5.21401307, 0.],
[0., 8.32019881, 1.58102041, 2.92987024, 0.]]),
np.array([[-1.09989127, -0.17242821, -0.87785842],
[0.04221375, 0.58281521, -1.10061918]]),
np.array([[1.14472371],
[0.90159072]]),
np.array([[0.53035547, 8.02565606, 4.10524802, 5.78975856, 0.53035547],
[-0.69166075, -1.71413186, -3.81223329, -4.61667916, -0.69166075],
[-0.39675353, -2.62563561, -4.82528105, -6.0607449, -0.39675353]]),
np.array([[True, False, True, False, True],
[False, True, False, True, True],
[False, False, True, False, False]],
dtype=bool),
np.array([[1.06071093, 0., 8.21049603, 0., 1.06071093],
[0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.]]),
np.array([[0.50249434, 0.90085595],
[-0.68372786, -0.12289023],
[-0.93576943, -0.26788808]]),
np.array([[0.53035547],
[-0.69166075],
[-0.39675353]]),
np.array([[-0.7415562, -0.0126646, -5.65469333, -0.0126646, -0.7415562]]),
np.array([[0.32266394, 0.49683389, 0.00348883, 0.49683389, 0.32266394]]),
np.array([[-0.6871727, -0.84520564, -0.67124613]]),
np.array([[-0.0126646]])
)
Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3 = cache
parameters = dict(
W={1: W1, 2: W2, 3: W3},
b={1: b1, 2: b2, 3: b3}
)
caches = dict(
Z={1: Z1, 2: Z2, 3: Z3},
A={0: X, 1: A1, 2: A2, 3: sigmoid(Z3)},
D={0: 1, 1: D1, 2: D2}
)
grads = model_backward(A3, Y, parameters, caches, alpha=0, keep_prob=0.8)
dA1 = np.array([[0.36544439, 0., -0.00188233, 0., -0.17408748],
[0.65515713, 0., -0.00337459, 0., -0.]])
dA2 = np.array([[0.58180856, 0., -0.00299679, 0., -0.27715731],
[0., 0.53159854, -0., 0.53159854, -0.34089673],
[0., 0., -0.00292733, 0., -0., ]])
assert_allclose(grads['dA'][1], dA1, rtol=1e-05)
assert_allclose(grads['dA'][2], dA2, rtol=1e-05)
def test_model_backward_l2_regularization():
random_state = RandomState(1)
X = random_state.randn(3, 5)
Y = np.array([[1, 1, 0, 1, 0]])
cache = (
np.array([[-1.52855314, 3.32524635, 2.13994541, 2.60700654, -0.75942115],
[-1.98043538, 4.1600994, 0.79051021, 1.46493512, -0.45506242]]),
np.array([[0., 3.32524635, 2.13994541, 2.60700654, 0.],
[0., 4.1600994, 0.79051021, 1.46493512, 0.]]),
np.array([[-1.09989127, -0.17242821, -0.87785842],
[0.04221375, 0.58281521, -1.10061918]]),
np.array([[1.14472371],
[0.90159072]]),
np.array([[0.53035547, 5.94892323, 2.31780174, 3.16005701, 0.53035547],
[-0.69166075, -3.47645987, -2.25194702, -2.65416996, -0.69166075],
[-0.39675353, -4.62285846, -2.61101729, -3.22874921, -0.39675353]]),
np.array([[0.53035547, 5.94892323, 2.31780174, 3.16005701, 0.53035547],
[0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.]]),
np.array([[0.50249434, 0.90085595],
[-0.68372786, -0.12289023],
[-0.93576943, -0.26788808]]),
np.array([[0.53035547],
[-0.69166075],
[-0.39675353]]),
np.array(
[[-0.3771104, -4.10060224, -1.60539468, -2.18416951, -0.3771104]]),
np.array(
[[0.40682402, 0.01629284, 0.16722898, 0.10118111, 0.40682402]]),
np.array([[-0.6871727, -0.84520564, -0.67124613]]),
np.array([[-0.0126646]])
)
Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, _, W3, b3 = cache
parameters = dict(
W={1: W1, 2: W2, 3: W3},
b={1: b1, 2: b2, 3: b3}
)
caches = dict(
Z={1: Z1, 2: Z2, 3: Z3},
A={0: X, 1: A1, 2: A2, 3: sigmoid(Z3)},
D={0: 1, 1: 1, 2: 1}
)
AL = caches["A"][3]
grads = model_backward(AL, Y, parameters, caches, alpha=0.7, keep_prob=1)
dW1 = np.array([[-0.25604646, 0.12298827, - 0.28297129],
[-0.17706303, 0.34536094, - 0.4410571]])
dW2 = np.array([[0.79276486, 0.85133918],
[-0.0957219, - 0.01720463],
[-0.13100772, - 0.03750433]])
dW3 = np.array([[-1.77691347, - 0.11832879, - 0.09397446]])
assert_allclose(grads['dW'][1], dW1)
assert_allclose(grads['dW'][2], dW2, rtol=1e-05)
assert_allclose(grads['dW'][3], dW3)
def test_model_backward():
rand = RandomState(3)
AL = rand.randn(1, 2)
Y = np.array([[1, 0]])
X = rand.randn(4, 2)
W1 = rand.randn(3, 4)
b1 = rand.randn(3, 1)
Z1 = rand.randn(3, 2)
A1 = rand.randn(3, 2)
W2 = rand.randn(1, 3)
b2 = rand.randn(1, 1)
Z2 = rand.randn(1, 2)
parameters = dict(
W={1: W1, 2: W2},
b={1: b1, 2: b2}
)
caches = dict(
Z={1: Z1, 2: Z2},
A={0: X, 1: A1, 2: sigmoid(Z2)},
D={0: 1, 1: 1}
)
grads = model_backward(AL, Y, parameters, caches, alpha=0, keep_prob=1)
assert_allclose(
grads["dW"][1],
np.array([
[0.41010002, 0.07807203, 0.13798444, 0.10502167],
[0., 0., 0., 0.],
[0.05283652, 0.01005865, 0.01777766, 0.0135308]]),
rtol=1e-05
)
assert_allclose(
grads["db"][1],
np.array([
[-0.22007063],
[0.],
[-0.02835349]])
)
assert_allclose(
grads["dA"][1],
np.array([
[0.12913162, -0.44014127],
[-0.14175655, 0.48317296],
[0.01663708, -0.05670698]]),
rtol=1e-05
)
def test_linear_backward_activation_sigmoid():
rand = RandomState(2)
dA = rand.randn(1, 2)
A = rand.randn(3, 2)
W = rand.randn(1, 3)
_ = rand.randn(1, 1) # noqa: F841
Z = rand.randn(1, 2)
dA_prev, dW, db = linear_backward_activation(dA, ((A, 1, W), (Z, sigmoid(Z))), sigmoid_backward, alpha=0, keep_prob=1)
assert_allclose(dA_prev, np.array([
[0.11017994, 0.01105339],
[0.09466817, 0.00949723],
[-0.05743092, -0.00576154]]), rtol=1e-05)
assert_allclose(dW, np.array([[0.10266786, 0.09778551, -0.01968084]]), rtol=1e-05)
assert_allclose(db, np.array([[-0.05729622]]), rtol=1e-05)