def observe(self, obs_mesh, obs_V):
__doc__ = Covariance.observe.__doc__
ndim = obs_mesh.shape[1]
nobs = obs_mesh.shape[0]
if self.ndim is not None:
if not ndim==self.ndim:
raise ValueError, "Dimension of observation mesh is not equal to dimension of base mesh."
else:
self.ndim = ndim
# bases_o is the basis evaluated on the observation mesh.
basis_o = asmatrix(self.eval_basis(obs_mesh, regularize=False))
# chol(basis_o.T * coef_cov * basis_o)
chol_inner = self.coef_U * basis_o
# chol(basis_o.T * coef_cov * basis_o + diag(obs_V)). Really should do this as low-rank update of covariance
# of V.
U, piv, m = ichol_basis(basis=chol_inner, nug=obs_V, reltol=self.relative_precision)
U = asmatrix(U)
piv_new = piv[:m]
self.obs_piv = piv_new
obs_mesh_new = obs_mesh[piv_new,:]
self.Uo = U[:m,:m]
# chol(basis_o.T * coef_cov * basis_o + diag(obs_V)) ^ -T * basis_o.T
self.Uo_cov = trisolve(self.Uo, basis_o[:,piv[:m]].T, uplo='U', transa='T')
# chol(basis_o.T * coef_cov * basis_o + diag(obs_V)).T.I * basis_o.T * coef_cov
self.Uo_cov = self.Uo_cov * self.coef_cov
# coef_cov -= coef_cov * basis_o * (basis_o.T * coef_cov * basis_o + diag(obs_V)).I * basis_o.T * coef_cov
self.coef_cov -= self.Uo_cov.T * self.Uo_cov
# coef_U = chol(coef_cov)
U, m, piv = ichol_full(c=self.coef_cov, reltol=self.relative_precision)
U = asmatrix(U)
self.coef_U = U[:m,argsort(piv)]
self.m = m
return piv_new, obs_mesh_new, None
def observe(self, obs_mesh, obs_V, output_type='o'):
__doc__ = Covariance.observe.__doc__
ndim = obs_mesh.shape[1]
nobs = obs_mesh.shape[0]
if self.ndim is not None:
if not ndim == self.ndim:
raise ValueError, "Dimension of observation mesh is not equal to dimension of base mesh."
else:
self.ndim = ndim
# bases_o is the basis evaluated on the observation mesh.
basis_o = asmatrix(self.eval_basis(obs_mesh, regularize=False))
# chol(basis_o.T * coef_cov * basis_o)
chol_inner = self.coef_U * basis_o
if output_type == 's':
C_eval = dot(chol_inner.T, chol_inner).copy('F')
U_eval = linalg.cholesky(C_eval).T.copy('F')
U = U_eval
m = U_eval.shape[0]
piv = arange(m)
else:
# chol(basis_o.T * coef_cov * basis_o + diag(obs_V)). Really should do this as low-rank update of covariance
# of V.
U, piv, m = ichol_basis(basis=chol_inner,
nug=obs_V,
reltol=self.relative_precision)
U = asmatrix(U)
piv_new = piv[:m]
self.obs_piv = piv_new
obs_mesh_new = obs_mesh[piv_new, :]
self.Uo = U[:m, :m]
# chol(basis_o.T * coef_cov * basis_o + diag(obs_V)) ^ -T * basis_o.T
self.Uo_cov = trisolve(self.Uo,
basis_o[:, piv[:m]].T,
uplo='U',
transa='T')
# chol(basis_o.T * coef_cov * basis_o + diag(obs_V)).T.I * basis_o.T * coef_cov
self.Uo_cov = self.Uo_cov * self.coef_cov
# coef_cov = coef_cov - coef_cov * basis_o * (basis_o.T * coef_cov * basis_o + diag(obs_V)).I * basis_o.T * coef_cov
self.coef_cov = self.coef_cov - self.Uo_cov.T * self.Uo_cov
# coef_U = chol(coef_cov)
U, m, piv = ichol_full(c=self.coef_cov, reltol=self.relative_precision)
U = asmatrix(U)
self.coef_U = U[:m, argsort(piv)]
self.m = m
if output_type == 'o':
return piv_new, obs_mesh_new
if output_type == 's':
return U_eval, C_eval, basis_o
raise ValueError, 'Output type not recognized.'
