def test_variable_exp():
a_array = np.array([1, 2])
a = Variable(np.array([1, 2], dtype=float))
expected_result_variable = Variable(
np.array([2.718281828459045, 7.3890560989306495]))
expected_result_array = np.array([2.718281828459045, 7.3890560989306495])
assert np.all(a_array == a.data)
assert np.all(expected_result_variable == expected_result_array)
assert id(a_array) != id(a.data)
assert id(expected_result_variable) != id(expected_result_array)
def validate_variable_result(result) -> None:
assert expected_result_variable.isclose(result).all()
assert isinstance(result, Variable)
return
def validate_array_result(result) -> None:
assert np.isclose(result, expected_result_array).all()
assert isinstance(result, np.ndarray)
return
# Variable
validate_variable_result(np.exp(a))
validate_variable_result(a.exp())
# numpy
validate_array_result(np.exp(a_array))
# Verify Derivative
sgd = autograd.optimizer.SGD(learning_rate=1e-3)
exp_result = a.exp()
variable_to_gradient = sgd.take_training_step(exp_result)
assert all(
isinstance(var, Variable) and isinstance(grad, np.ndarray)
for var, grad in variable_to_gradient.items())
assert np.all(
np.isclose(variable_to_gradient[a], exp_result, rtol=1e-3, atol=1e-4))
# Verify Trainability
x = Variable(np.random.rand(2))
y = 1
sgd = autograd.optimizer.SGD(learning_rate=1)
for training_step_index in range(1_000):
y_hat = x.exp()
diff = np.subtract(y, y_hat)
loss = np.sum(diff**2)
if training_step_index > 10 and loss.sum() < 1e-15:
break
sgd.take_training_step(loss)
def softmax(x: Variable) -> Variable:
e = x.exp()
return e / e.sum()
