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)