def step3(L, Sigma, mu, mun):
temp2 = np.dot(-J12.T, Sigma)
Sigma_21 = solve_posdef_from_cholesky(L, temp2)
ExnxT = Sigma_21 + np.outer(mun, mu)
ExxT = Sigma + np.outer(mu, mu)
return mu, ExxT, ExnxT
def natural_sample(J, h, num_samples=None, rng=rng):
sample_shape = (num_samples,) + h.shape if num_samples else h.shape
J = -2*J
if J.ndim == 1:
return h / J + rng.normal(size=sample_shape) / np.sqrt(J)
else:
L = np.linalg.cholesky(J)
noise = solve_triangular(L, rng.normal(size=sample_shape).T, trans='T')
return solve_posdef_from_cholesky(L, h.T).T + noise.T
def natural_sample(J, h, num_samples=None, rng=rng):
sample_shape = (num_samples,) + h.shape if num_samples else h.shape
J = -2*J
if J.ndim == 1:
return h / J + rng.normal(size=sample_shape) / np.sqrt(J)
else:
L = np.linalg.cholesky(J)
noise = solve_triangular(L, rng.normal(size=sample_shape).T, trans='T')
return solve_posdef_from_cholesky(L, h.T).T + noise.T
def natural_rts_backward_step(next_smooth, next_pred, filtered, pair_param):
# p = "predicted", f = "filtered", s = "smoothed", n = "next"
(Jns, hns, mun), (Jnp, hnp), (Jf, hf) = next_smooth, next_pred, filtered
J11, J12, J22, _ = pair_param
# convert from natural parameter to the usual J definitions
Jns, Jnp, Jf, J11, J12, J22 = -2*Jns, -2*Jnp, -2*Jf, -2*J11, -J12, -2*J22
J11, J12, J22 = Jf + J11, J12, Jns - Jnp + J22
L = np.linalg.cholesky(J22)
temp = solve_triangular(L, J12.T)
Js = J11 - np.dot(temp.T, temp)
hs = hf - np.dot(temp.T, solve_triangular(L, hns - hnp))
mu, sigma = info_to_mean((Js, hs))
ExnxT = -solve_posdef_from_cholesky(L, np.dot(J12.T, sigma)) + np.outer(mun, mu)
ExxT = sigma + np.outer(mu, mu)
return -1./2*Js, hs, (mu, ExxT, ExnxT)
def natural_rts_backward_step(next_smooth, next_pred, filtered, pair_param):
# p = "predicted", f = "filtered", s = "smoothed", n = "next"
(Jns, hns, mun), (Jnp, hnp), (Jf, hf) = next_smooth, next_pred, filtered
J11, J12, J22, _ = pair_param
# convert from natural parameter to the usual J definitions
Jns, Jnp, Jf, J11, J12, J22 = -2*Jns, -2*Jnp, -2*Jf, -2*J11, -J12, -2*J22
J11, J12, J22 = Jf + J11, J12, Jns - Jnp + J22
L = np.linalg.cholesky(J22)
temp = solve_triangular(L, J12.T)
Js = J11 - np.dot(temp.T, temp)
hs = hf - np.dot(temp.T, solve_triangular(L, hns - hnp))
mu, sigma = info_to_mean((Js, hs))
ExnxT = -solve_posdef_from_cholesky(L, np.dot(J12.T, sigma)) + np.outer(mun, mu)
ExxT = sigma + np.outer(mu, mu)
return -1./2*Js, hs, (mu, ExxT, ExnxT)
def natural_sample(J, h, eps):
L = np.linalg.cholesky(J)
mu = solve_posdef_from_cholesky(L, h)
noise = solve_triangular(L, eps, 'T')
return mu + noise