def test_x_squared_optimization_bfgs(self):
def objective_func(x):
return x**2
var_init = np.array([2])
optimizer = Optimizer(objective_func, var_init)
min_value, var_value = optimizer.bfgs_optimize(num_iterations=2000)
self.assertAlmostEqual(min_value, 0, places=5)
self.assertAlmostEqual(var_value[0], 0, places=5)
def test_univariate_scalar_adagrad_optimization(self):
def objective_func(x):
return x * np.log(x)
var_init = np.array([2])
optimizer = Optimizer(objective_func, var_init)
min_value, var_value = optimizer.adagrad_optimize(
tolerance=None, num_iterations=100000)
self.assertAlmostEqual(min_value, -1 / np.e, places=3)
self.assertAlmostEqual(var_value[0], 1 / np.e, places=3)
def test_univariate_scalar_momentum_optimization(self):
def objective_func(x):
return x**6 - 2 * x
var_init = np.array([2])
optimizer = Optimizer(objective_func, var_init)
min_value, var_value = optimizer.momentum_optimize(tolerance=None,
num_iterations=1000)
self.assertAlmostEqual(min_value, -5 / (3 * 3**(1 / 5)), places=5)
self.assertAlmostEqual(var_value[0], 1 / (3**(1 / 5)), places=5)
def test_multivariate_vector_momentum_optimization(self):
def objective_func(x):
return x[0]**2 + x[0] * x[1] + x[1]**2
var_init = np.array([0.2, 0.5])
optimizer = Optimizer(objective_func, var_init, scalar=False)
min_value, var_value = optimizer.momentum_optimize(tolerance=None,
num_iterations=1000)
self.assertAlmostEqual(min_value, 0, places=5)
self.assertAlmostEqual(var_value[0], 0, places=5)
self.assertAlmostEqual(var_value[1], 0, places=5)
def test_multivariate_scalar_rmsprop_optimization(self):
def objective_func(x, y):
return x**2 + x * y + y**2
var_init = np.array([0.2, 0.5])
optimizer = Optimizer(objective_func, var_init)
min_value, var_value = optimizer.rmsprop_optimize(tolerance=None,
num_iterations=10000)
self.assertAlmostEqual(min_value, 0, places=5)
self.assertAlmostEqual(var_value[0], 0, places=3)
self.assertAlmostEqual(var_value[1], 0, places=3)
def test_beta_momentum_exception(self):
def objective_func(x):
return x
with self.assertRaises(ValueError) as e:
var_init = np.array([0.2])
optimizer = Optimizer(objective_func, var_init)
optimizer.momentum_optimize(beta=54, num_iterations=1000)
self.assertEqual(
"The value of beta (sample weight) should be between 0 and 1.",
str(e.exception),
)
def test_univariate_scalar_adam_optimize(self):
def objective_func(x):
return np.exp(-2.0 * np.sin(4.0 * x) * np.sin(4.0 * x))
var_init = np.array([2])
optimizer = Optimizer(objective_func, var_init)
min_value, var_value = optimizer.adam_optimize(learning_rate=0.001,
beta1=0.9,
beta2=0.999,
epsilon=1e-8,
num_iterations=1000)
self.assertEqual(min_value, 0.1353352832366127)
self.assertEqual(var_value[0], 1.963495408493621)
def test_beta_adam_exception(self):
def objective_func(x):
return x
with self.assertRaises(ValueError) as e:
var_init = np.array([0.2])
optimizer = Optimizer(objective_func, var_init)
optimizer.adam_optimize(learning_rate=0.01,
beta1=1.9,
beta2=0.999,
epsilon=1e-8,
num_iterations=1000,
tolerance=1.0e-08)
self.assertEqual(
"The value of beta (sample weight) should be between 0 and 1 (excluding 1).",
str(e.exception),
)
with self.assertRaises(ValueError) as e:
var_init = np.array([0.2])
optimizer = Optimizer(objective_func, var_init)
optimizer.adam_optimize(learning_rate=0.01,
beta1=0.9,
beta2=1.999,
epsilon=1e-8,
num_iterations=1000,
tolerance=1.0e-08)
self.assertEqual(
"The value of beta (sample weight) should be between 0 and 1 (excluding 1).",
str(e.exception),
)
def test_x_y_exp_func_adam_optimize(self):
def objective_func(x, y):
return x * y + np.exp(x * y)
var_init = np.array([2, 2])
optimizer = Optimizer(objective_func, var_init)
min_value, var_value = optimizer.adam_optimize(learning_rate=0.01,
beta1=0.9,
beta2=0.999,
epsilon=1e-8,
num_iterations=1000,
tolerance=1.0e-08)
self.assertEqual(min_value, 1.1762618133993703)
self.assertEqual(var_value[0], 0.2936289210258825)
self.assertEqual(var_value[1], 0.2936289210258825)
def test_x_y_z_squared_adam_optimize(self):
def objective_func(x):
return x[0]**2 + x[1]**2 + x[2]**2
var_init = np.array([-15, 100, -20])
optimizer = Optimizer(objective_func, var_init, scalar=False)
min_value, var_value = optimizer.adam_optimize(learning_rate=0.1,
beta1=0.9,
beta2=0.999,
epsilon=1e-8,
num_iterations=10000)
self.assertAlmostEqual(min_value, 0, places=5)
self.assertAlmostEqual(var_value[0], 0, places=5)
self.assertAlmostEqual(var_value[1], 0, places=5)
self.assertAlmostEqual(var_value[2], 0, places=5)
def objective_func(x, y, z):
return x**2 + y**2 + z**2
var_init = np.array([-15, 100, -20])
optimizer = Optimizer(objective_func, var_init)
min_value, var_value = optimizer.adam_optimize(learning_rate=0.1,
beta1=0.9,
beta2=0.999,
epsilon=1e-8,
num_iterations=10000)
self.assertAlmostEqual(min_value, 0, places=5)
self.assertAlmostEqual(var_value[0], 0, places=5)
self.assertAlmostEqual(var_value[1], 0, places=5)
self.assertAlmostEqual(var_value[2], 0, places=5)
def test_x_y_z_squared_optimization_bfgs(self):
def objective_func(x, y, z):
return x**2 + y**2 + z**2
var_init = np.array([-15, 100, -20])
optimizer = Optimizer(objective_func, var_init)
min_value, var_value = optimizer.bfgs_optimize(num_iterations=2000)
self.assertAlmostEqual(min_value, 0, places=5)
self.assertAlmostEqual(var_value[0], 0, places=5)
self.assertAlmostEqual(var_value[1], 0, places=5)
self.assertAlmostEqual(var_value[2], 0, places=5)
def objective_func(x):
return x[0]**2 + x[1]**2 + x[2]**2
var_init = np.array([-15, 100, -20])
optimizer = Optimizer(objective_func, var_init, scalar=False)
min_value, var_value = optimizer.bfgs_optimize(tolerance=0.0000001,
num_iterations=2000)
self.assertAlmostEqual(min_value, 0, places=4)
self.assertAlmostEqual(var_value[0], 0, places=4)
self.assertAlmostEqual(var_value[1], 0, places=4)
self.assertAlmostEqual(var_value[2], 0, places=4)