def log_likelihood(x, mu, Sigma):
x = np.atleast_2d(x)
mu = np.atleast_2d(mu)
Sigma = np.atleast_2d(Sigma)
sign, Slogdet = sl.slogdet(Sigma)
Sinv = sl.inv(Sigma)
return -.5 * x.shape[1] * np.log(2. * np.pi) - .5 * Slogdet - .5 * (
(x - mu).T) * Sinv * (x - mu)
def log_prior(mu, Sigma, nu0=None, kappa0=None, Sigma0=None, mu0=None, N=1000):
nu0 = N + 1
kappa0 = 1
Sigma0 = np.ones((mu.shape[0], mu.shape[0]))
mu0 = np.ones((mu.shape[0], 1))
sign, Slogdet = sl.slogdet(Sigma)
Sinv = sl.inv(Sigma)
return -.5 (nu0 + mu.shape[0] + 2.) * Slogdet - .5 * kappa0 * (
mu - mu0) ^ T * Sinv * (mu - mu0) - .5 * np.trace(Sinv * Sigma0)
def compute_d(M):
"""Compute the average rate of change of matrix M, where M is the matrix
for either a discrete or continuous Markov Chain."""
if isP(M):
return -0.25*(linalg.slogdet(M)[1])
elif isQ(M):
return -0.25*mean(diagonal(M))
else:
raise MatCalcExcep("compute_d given a matrix that was not a correct probability or rate matrix")
def loglikelihood(self,
z: np.ndarray,
ekfstate: GaussParams,
sensor_state: Dict[str, Any] = None) -> float:
"""Calculate the log likelihood of ekfstate at z in sensor_state"""
# we need this function in IMM, PDA and IMM-PDA exercises
# not necessary for tuning in EKF exercise
v, S = self.innovation(z, ekfstate, sensor_state=sensor_state)
ll = -0.5 * (self.NIS(z, ekfstate) + la.slogdet(S))
return ll
def test_works_with_underflow_case(self):
for np_dtype, atol in [(np.float32, 0.05), (np.float64, 1e-5),
(np.complex64, 0.05), (np.complex128, 1e-5)]:
with self.subTest(np_dtype=np_dtype, atol=atol):
matrix = (np.eye(20) * 1e-6).astype(np_dtype)
sign_np, log_abs_det_np = np.linalg.slogdet(matrix)
with self.session():
sign_tf, log_abs_det_tf = linalg.slogdet(matrix)
self.assertAllClose(log_abs_det_np,
self.evaluate(log_abs_det_tf),
atol=atol)
self.assertAllClose(sign_np,
self.evaluate(sign_tf),
atol=atol)
def test_works_with_five_different_random_pos_def_matrices(self):
for n in range(1, 6):
for np_dtype, atol in [(np.float32, 0.05), (np.float64, 1e-5),
(np.complex64, 0.05),
(np.complex128, 1e-5)]:
with self.subTest(n=n, np_dtype=np_dtype, atol=atol):
matrix = _RandomPDMatrix(n, self.rng, np_dtype)
sign_np, log_abs_det_np = np.linalg.slogdet(matrix)
with self.session():
sign_tf, log_abs_det_tf = linalg.slogdet(matrix)
self.assertAllClose(log_abs_det_np,
self.evaluate(log_abs_det_tf),
atol=atol)
self.assertAllClose(sign_np,
self.evaluate(sign_tf),
atol=atol)
def getDeterminant(K):
f, logDet = linalg.slogdet(K)
return f * exp(logDet)
