def test_gbm_euler_step_nd_output_changes_with_key(self):
drift = np.asarray([0.1, 0.3, -0.05], dtype=np.float32)
vol_matrix = 0.2 * np.asarray(
[[1.5, 0.2, 0.3], [0.2, 1.1, -0.1], [0.3, -0.1, 0.8]],
dtype=np.float32)
t = 0.3
dt = 0.01
num_samples = 8
num_dims = drift.shape[0]
key_0 = 42
key_1 = 77
states = tf.ones([num_samples, num_dims])
next_states_0 = dynamics.gbm_euler_step_nd(states,
drift,
vol_matrix,
t,
dt,
key=key_0)
next_states_1 = dynamics.gbm_euler_step_nd(states,
drift,
vol_matrix,
t,
dt,
key=key_1)
with self.session() as session:
next_states_0_eval, next_states_1_eval = session.run(
(next_states_0, next_states_1))
self.assertEqual(next_states_0_eval.shape, (num_samples, num_dims))
self.assertEqual(next_states_1_eval.shape, (num_samples, num_dims))
# The step is a bijection w.r.t. dw_t, all terms should be different.
self.assertAllDistinct(next_states_0_eval, next_states_1_eval)
def test_gbm_euler_step_nd_is_deterministic(self):
drift = np.asarray([0.1, 0.3, -0.05], dtype=np.float32)
vol_matrix = 0.2 * np.asarray(
[[1.5, 0.2, 0.3], [0.2, 1.1, -0.1], [0.3, -0.1, 0.8]],
dtype=np.float32)
t = 0.3
dt = 0.01
num_samples = 8
num_dims = drift.shape[0]
key = 42
states = tf.ones([num_samples, num_dims])
eps_t = contrib_stateless.stateless_random_normal(
shape=[num_samples, num_dims], seed=[key, int(t / dt)])
next_states = dynamics.gbm_euler_step_nd(
states, drift, vol_matrix, t, dt, random_normal_op=lambda: eps_t)
next_states_bis = dynamics.gbm_euler_step_nd(states,
drift,
vol_matrix,
t,
dt,
key=key)
with self.session() as session:
next_states_eval, next_states_bis_eval = session.run(
(next_states, next_states_bis))
self.assertEqual(next_states_eval.shape, (num_samples, num_dims))
self.assertEqual(next_states_bis_eval.shape, (num_samples, num_dims))
self.assertAllClose(next_states_eval, next_states_bis_eval)
def test_gbm_euler_step_nd_expects_static_shape(self):
drift = np.asarray([0.1, 0.3, -0.05], dtype=np.float32)
vol_matrix = 0.2 * np.asarray(
[[1.5, 0.2, 0.3], [0.2, 1.1, -0.1], [0.3, -0.1, 0.8]], dtype=np.float32)
t = 0.0
dt = 0.01
num_dims = drift.shape[0]
states = tf.placeholder(dtype=tf.float32, shape=[None, num_dims])
with self.assertRaises(ValueError):
dynamics.gbm_euler_step_nd(states, drift, vol_matrix, t, dt)
def test_gbm_euler_step_nd_output_is_correct(self):
np.random.seed(0)
drift = np.asarray([0.1, 0.3, -0.05], dtype=np.float32)
vol_matrix = 0.2 * np.asarray(
[[1.5, 0.2, 0.3], [0.2, 1.1, -0.1], [0.3, -0.1, 0.8]],
dtype=np.float32)
t = 0.0
dt = 0.01
num_samples = 8
num_dims = drift.shape[0]
states = tf.ones([num_samples, num_dims])
eps_t = np.ndarray.astype(
np.random.normal(size=[num_samples, num_dims]), dtype=np.float32)
next_states = dynamics.gbm_euler_step_nd(
states, drift, vol_matrix, t, dt, random_normal_op=lambda: eps_t)
with self.session() as session:
next_states_eval = session.run(next_states)
self.assertEqual(next_states_eval.shape, (num_samples, num_dims))
for i in range(num_samples):
self.assertAllClose(
next_states_eval[i],
np.ones([num_dims], dtype=np.float32) *
(1.0 + drift * dt +
np.matmul(vol_matrix, eps_t[i] * np.sqrt(dt))))
def _dynamics_op(s, t, dt):
return dynamics.gbm_euler_step_nd(s, drift, vol_matrix, t, dt)
