def test_default_construction_2d(self):
"""Tests the default parameters for 2 dimensional Brownian Motion."""
process = BrownianMotion(dim=2)
self.assertEqual(process.dim(), 2)
drift_fn = process.total_drift_fn()
# Drifts should be zero.
t0 = np.array([0.2, 0.7, 0.9])
delta_t = np.array([0.1, 0.8, 0.3])
t1 = t0 + delta_t
drifts = self.evaluate(drift_fn(t0, t1))
self.assertEqual(drifts.shape, (3, 2))
self.assertArrayNear(drifts.reshape([-1]), np.zeros([3 * 2]), 1e-10)
variances = self.evaluate(process.total_covariance_fn()(t0, t1))
self.assertEqual(variances.shape, (3, 2, 2))
expected_variances = np.eye(2) * delta_t.reshape([-1, 1, 1])
print(variances, expected_variances)
self.assertArrayNear(variances.reshape([-1]),
expected_variances.reshape([-1]), 1e-10)
def test_default_construction_1d(self):
"""Tests the default parameters."""
process = BrownianMotion()
self.assertEqual(process.dim(), 1)
drift_fn = process.drift_fn()
# Drift should be zero.
t0 = np.array([0.2, 0.7, 0.9])
t1 = t0 + [0.1, 0.8, 0.3]
drifts = self.evaluate(drift_fn(t0, None))
total_drift_fn = process.total_drift_fn()
self.assertAlmostEqual(self.evaluate(total_drift_fn(0.4, 0.5)),
0.0,
places=7)
self.assertArrayNear(drifts, np.zeros([3]), 1e-10)
variances = self.evaluate(process.total_covariance_fn()(t0, t1))
self.assertArrayNear(variances, t1 - t0, 1e-10)
self.assertAlmostEqual(self.evaluate(process.total_covariance_fn()(
0.41, 0.55)),
0.14,
places=7)
def test_time_dependent_construction(self):
"""Tests with time dependent drift and variance."""
def vol_fn(t):
return tf.expand_dims(0.2 - 0.1 * tf.exp(-t), axis=-1)
def variance_fn(t0, t1):
# The instantaneous volatility is 0.2 - 0.1 e^(-t).
tot_var = (t1 - t0) * 0.04 - (tf.exp(-2 * t1) -
tf.exp(-2 * t0)) * 0.005
tot_var += 0.04 * (tf.exp(-t1) - tf.exp(-t0))
return tf.reshape(tot_var, [-1, 1, 1])
process = BrownianMotion(dim=1,
drift=0.1,
volatility=vol_fn,
total_covariance_fn=variance_fn)
t0 = np.array([0.2, 0.7, 0.9])
delta_t = np.array([0.1, 0.8, 0.3])
t1 = t0 + delta_t
drifts = self.evaluate(process.total_drift_fn()(t0, t1))
self.assertArrayNear(drifts, 0.1 * delta_t, 1e-10)
variances = self.evaluate(process.total_covariance_fn()(t0, t1))
self.assertArrayNear(variances.reshape([-1]),
[0.00149104, 0.02204584, 0.00815789], 1e-8)