def test_sigma(self):
self.assertAlmostEqual(Sigmoid.activation(0), 0.5, places=2)
self.assertAlmostEqual(Sigmoid.activation(50), 1, places=2)
self.assertAlmostEqual(Sigmoid.activation(-50), 0, places=2)
self.assertAlmostEqual(Sigmoid.activation(1), 0.731, places=2)
self.assertAlmostEqual(Sigmoid.activation(-1), 0.2689, places=2)
def test_sigma_prime(self):
self.assertAlmostEqual(Sigmoid.gradient(0), 0.25, places=3)
self.assertAlmostEqual(Sigmoid.gradient(-50), 0, places=3)
self.assertAlmostEqual(Sigmoid.gradient(50), 0, places=3)
self.assertAlmostEqual(Sigmoid.gradient(50),
Sigmoid.activation(50) *
(1 - Sigmoid.activation(50)),
places=3)
def test_get_final_layer_error_for_1_element_vectors(self):
cross_entropy = cost_functions.CrossEntropyCost(self.net)
z_last = np.array([3], float)
z_last_prime = Sigmoid.gradient(z_last)
y = np.array([0], float)
a_last = Sigmoid.activation(z_last)
nabla = cross_entropy.get_final_layer_error(a_last, y, z_last_prime)
self.assertAlmostEqual(nabla[0], (a_last - y), places=2)
z_last = np.array([-1], float)
z_last_prime = Rectifier.gradient(z_last)
y = np.array([0.5], float)
a_last = Sigmoid.activation(z_last)
nabla = cross_entropy.get_final_layer_error(a_last, y, z_last_prime)
self.assertAlmostEqual(nabla[0], (a_last - y), places=2)
def test_get_final_layer_error_for_arrays(self):
quadratic = cost_functions.QuadraticCost(neural_net=self.net)
z_last = np.array([3, -1], float)
z_last_prime = Sigmoid.gradient(z_last)
y = np.array([0, 0.5], float)
a_last = Sigmoid.activation(z_last)
nabla = quadratic.get_final_layer_error(a_last, y, z_last_prime)
self.assertAlmostEqual(nabla[0], (a_last[0] - y[0]) * z_last_prime[0], places=2)
self.assertAlmostEqual(nabla[1], (a_last[1] - y[1]) * Sigmoid.gradient(z_last[1]),
places=2)