def sqrt_unscented_predict(
period,
sigma_points,
flat_sigma_points,
s_weights_m,
s_weights_c,
q,
transform_sigma_points_args,
out_flat_states,
out_flat_covs,
):
"""Make a unscented Kalman filter predict step in square-root form.
The square-root form of the Kalman predict is much more robust than the
usual form and also much faster.
Args:
period (int): the development period in which the predict step is done.
sigma_points (np.ndarray): numpy array of (nemf * nind, nsigma, nfac)
flat_sigma_points (np.ndarray): array of (nemf * nind * nsigma, nfac).
It is a view on sigma_points.
s_weights_m (np.ndarray): numpy array of length nsigma with sigma
weights for the means.
s_weights_c (np.ndarray): numpy array of length nsigma with sigma
weights for the covariances.
q (np.ndarray): numpy array of (nperiods - 1, nfac, nfac) with vaiances of
the transition equation shocks.
transform_sigma_points_args (dict): (see transform_sigma_points).
out_flat_states (np.ndarray): output array of (nind * nemf, nfac).
out_flat_covs (np.ndarray): output array of (nind * nemf, nfac, nfac).
References:
Van Der Merwe, R. and Wan, E.A. The Square-Root Unscented Kalman
Filter for State and Parameter-Estimation. 2001.
"""
nemf_times_nind, nsigma, nfac = sigma_points.shape
q = q[period]
transform_sigma_points(period, flat_sigma_points,
**transform_sigma_points_args)
# get them back into states
predicted_states = np.dot(s_weights_m, sigma_points, out=out_flat_states)
devs = sigma_points - predicted_states.reshape(nemf_times_nind, 1, nfac)
qr_weights = np.sqrt(s_weights_c).reshape(nsigma, 1)
qr_points = np.zeros((nemf_times_nind, 3 * nfac + 1, nfac))
qr_points[:, 0:nsigma, :] = devs * qr_weights
qr_points[:, nsigma:, :] = np.sqrt(q)
out_flat_covs[:, 1:, 1:] = array_qr(qr_points)[:, :nfac, :]
def test_tsp_no_anchoring_no_endog(self, mock_trans):
mock_trans.fake1.side_effect = fake1
mock_trans.fake2.side_effect = fake2
exp = np.zeros((10, 2))
exp[:, 0] = np.arange(10) + 1
exp[:, 1] = np.arange(start=10, stop=20) + np.arange(10) - 0.2
transform_sigma_points(
stage=self.stage, flat_sigma_points=self.flat_sigma_points,
transition_argument_dicts=self.transition_argument_dicts,
transition_function_names=self.transition_function_names)
calc = self.flat_sigma_points.copy()
aaae(calc, exp)
def test_tsp_no_anchoring_no_endog(self, mock_trans):
mock_trans.fake1.side_effect = fake1
mock_trans.fake2.side_effect = fake2
exp = np.zeros((10, 2))
exp[:, 0] = np.arange(10) + 1
exp[:, 1] = np.arange(start=10, stop=20) + np.arange(10) - 0.2
transform_sigma_points(
stage=self.stage,
flat_sigma_points=self.flat_sigma_points,
transition_argument_dicts=self.transition_argument_dicts,
transition_function_names=self.transition_function_names)
calc = self.flat_sigma_points.copy()
aaae(calc, exp)
def normal_unscented_predict(
period,
sigma_points,
flat_sigma_points,
s_weights_m,
s_weights_c,
q,
transform_sigma_points_args,
out_flat_states,
out_flat_covs,
):
"""Make a unscented Kalman filter predict step in square-root form.
Args:
period (int): period in which the predict step is done.
sigma_points (np.ndarray): numpy array of (nemf * nind, nsigma, nfac)
flat_sigma_points (np.ndarray): array of (nemf * nind * nsigma, nfac).
It is a view on sigma_points.
s_weights_m (np.ndarray): numpy array of length nsigma with sigma
weights for the means.
s_weights_c (np.ndarray): numpy array of length nsigma with sigma
weights for the covariances.
q (np.ndarray): numpy array of (nperiods - 1, nfac, nfac) with vaiances of
the transition equation shocks.
transform_sigma_points_args (dict): (see transform_sigma_points).
out_flat_states (np.ndarray): output array of (nind * nemf, nfac).
out_flat_covs (np.ndarray): output array of (nind * nemf, nfac, nfac).
References:
Van Der Merwe, R. and Wan, E.A. The Square-Root Unscented Kalman
Filter for State and Parameter-Estimation. 2001.
"""
nemf_times_nind, nsigma, nfac = sigma_points.shape
q = q[period]
transform_sigma_points(period, flat_sigma_points,
**transform_sigma_points_args)
# get them back into states
predicted_states = np.dot(s_weights_m, sigma_points, out=out_flat_states)
devs = sigma_points - predicted_states.reshape(nemf_times_nind, 1, nfac)
# dev_outerprod has dimensions (nemf_times_nind, nsigma, nfac, nfac)
dev_outerprod = devs.reshape(nemf_times_nind, nsigma,
1, nfac) * devs.reshape(
nemf_times_nind, nsigma, nfac, 1)
out_flat_covs[:] = (np.sum(
(s_weights_c.reshape(nsigma, 1, 1) * dev_outerprod), axis=1) + q)
def test_tsp_with_anchoring_no_endog_integration(self, mock_trans):
mock_trans.fake1.side_effect = fake1
mock_trans.fake2.side_effect = fake2
exp = np.zeros((10, 2))
exp[:, 0] = np.arange(10) + 1
exp[:, 1] = np.arange(start=10, stop=20) + 0.5 * np.arange(10) - 0.1
transform_sigma_points(
stage=self.stage, flat_sigma_points=self.flat_sigma_points,
transition_argument_dicts=self.transition_argument_dicts,
transition_function_names=self.transition_function_names,
anchoring_type='linear', anchoring_positions=[1],
anch_params=np.array([0, 2.0]))
calc = self.flat_sigma_points.copy()
aaae(calc, exp)
def test_tsp_with_anchoring_no_endog_integration(self, mock_trans):
mock_trans.fake1.side_effect = fake1
mock_trans.fake2.side_effect = fake2
exp = np.zeros((10, 2))
exp[:, 0] = np.arange(10) + 1
exp[:, 1] = np.arange(start=10, stop=20) + 0.5 * np.arange(10) - 0.1
transform_sigma_points(
stage=self.stage,
flat_sigma_points=self.flat_sigma_points,
transition_argument_dicts=self.transition_argument_dicts,
transition_function_names=self.transition_function_names,
anchoring_type='linear',
anchoring_positions=[1],
anch_params=np.array([0, 2.0]))
calc = self.flat_sigma_points.copy()
aaae(calc, exp)
def sqrt_unscented_predict(stage, sigma_points, flat_sigma_points, s_weights_m,
s_weights_c, Q, transform_sigma_points_args,
out_flat_states, out_flat_covs):
"""Make a unscented Kalman filter predict step in square-root form.
The square-root form of the Kalman predict is much more robust than the
usual form and also much faster.
Args:
stage (int): the development stage in which the predict step is done.
sigma_points (np.ndarray): numpy array of (nemf * nind, nsigma, nfac)
flat_sigma_points (np.ndarray): array of (nemf * nind * nsigma, nfac).
It is a view on sigma_points.
s_weights_m (np.ndarray): numpy array of length nsigma with sigma
weights for the means.
s_weights_c (np.ndarray): numpy array of length nsigma with sigma
weights for the covariances.
Q (np.ndarray): numpy array of (nstages, nfac, nfac) with vaiances of
the transition equation shocks.
transform_sigma_points_args (dict): (see transform_sigma_points).
out_flat_states (np.ndarray): output array of (nind * nemf, nfac).
out_flat_covs (np.ndarray): output array of (nind * nemf, nfac, nfac).
References:
Van Der Merwe, R. and Wan, E.A. The Square-Root Unscented Kalman
Filter for State and Parameter-Estimation. 2001.
"""
nemf_times_nind, nsigma, nfac = sigma_points.shape
q = Q[stage]
transform_sigma_points(stage, flat_sigma_points,
**transform_sigma_points_args)
# get them back into states
predicted_states = np.dot(s_weights_m, sigma_points, out=out_flat_states)
devs = sigma_points - predicted_states.reshape(nemf_times_nind, 1, nfac)
qr_weights = np.sqrt(s_weights_c).reshape(nsigma, 1)
qr_points = np.zeros((nemf_times_nind, 3 * nfac + 1, nfac))
qr_points[:, 0: nsigma, :] = devs * qr_weights
qr_points[:, nsigma:, :] = np.sqrt(q)
out_flat_covs[:, 1:, 1:] = array_qr(qr_points)[:, :nfac, :]
def normal_unscented_predict(stage, sigma_points, flat_sigma_points,
s_weights_m, s_weights_c, Q,
transform_sigma_points_args,
out_flat_states, out_flat_covs):
"""Make a unscented Kalman filter predict step in square-root form.
Args:
stage (int): the development stage in which the predict step is done.
sigma_points (np.ndarray): numpy array of (nemf * nind, nsigma, nfac)
flat_sigma_points (np.ndarray): array of (nemf * nind * nsigma, nfac).
It is a view on sigma_points.
s_weights_m (np.ndarray): numpy array of length nsigma with sigma
weights for the means.
s_weights_c (np.ndarray): numpy array of length nsigma with sigma
weights for the covariances.
Q (np.ndarray): numpy array of (nstages, nfac, nfac) with vaiances of
the transition equation shocks.
transform_sigma_points_args (dict): (see transform_sigma_points).
out_flat_states (np.ndarray): output array of (nind * nemf, nfac).
out_flat_covs (np.ndarray): output array of (nind * nemf, nfac, nfac).
References:
Van Der Merwe, R. and Wan, E.A. The Square-Root Unscented Kalman
Filter for State and Parameter-Estimation. 2001.
"""
nemf_times_nind, nsigma, nfac = sigma_points.shape
q = Q[stage]
transform_sigma_points(stage, flat_sigma_points,
**transform_sigma_points_args)
# get them back into states
predicted_states = np.dot(s_weights_m, sigma_points, out=out_flat_states)
devs = sigma_points - predicted_states.reshape(nemf_times_nind, 1, nfac)
# dev_outerprod has dimensions (nemf_times_nind, nsigma, nfac, nfac)
dev_outerprod = devs.reshape(nemf_times_nind, nsigma, 1, nfac) \
* devs.reshape(nemf_times_nind, nsigma, nfac, 1)
out_flat_covs[:] = \
np.sum((s_weights_c.reshape(nsigma, 1, 1) * dev_outerprod), axis=1) + q