def test_relu_backward():
# Test the relu_backward function.
x = np.random.randn(10, 10)
dout = np.random.randn(*x.shape)
dx_num = eval_numerical_gradient_array(lambda x: relu_forward(x)[0], x, dout)
_, cache = relu_forward(x)
dx = relu_backward(dout, cache)
assert rel_error(dx, dx_num) < 1e-10
def test_affine_backward():
# Test the affine_backward function
x = np.random.randn(10, 6)
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: affine_forward(x, w, b)[0], x, dout)
dw_num = eval_numerical_gradient_array(lambda w: affine_forward(x, w, b)[0], w, dout)
db_num = eval_numerical_gradient_array(lambda b: affine_forward(x, w, b)[0], b, dout)
_, cache = affine_forward(x, w, b)
dx, dw, db = affine_backward(dout, cache)
dx_error = rel_error(dx_num, dx)
dw_error = rel_error(dw_num, dw)
db_error = rel_error(db_num, db)
max_error = max(dx_error, dw_error, db_error)
assert max_error < 1e-7