def _build_conditional(self, Xnew):
Xs, f = self.Xs, self.f
X = cartesian(*Xs)
delta = f - self.mean_func(X)
covs = [stabilize(cov(Xi)) for cov, Xi in zip(self.cov_funcs, Xs)]
chols = [cholesky(cov) for cov in covs]
cholTs = [at.transpose(chol) for chol in chols]
Kss = self.cov_func(Xnew)
Kxs = self.cov_func(X, Xnew)
Ksx = at.transpose(Kxs)
alpha = kron_solve_lower(chols, delta)
alpha = kron_solve_upper(cholTs, alpha)
mu = at.dot(Ksx, alpha).ravel() + self.mean_func(Xnew)
A = kron_solve_lower(chols, Kxs)
cov = stabilize(Kss - at.dot(at.transpose(A), A))
return mu, cov
def test_kron_solve_lower():
np.random.seed(1)
# Create random matrices
Ls = [np.tril(np.random.rand(3, 3)) for i in range(3)]
# Create random vector with correct shape
tot_size = np.prod([L.shape[1] for L in Ls])
x = np.random.rand(tot_size).reshape((tot_size, 1))
# Construct entire kronecker product then solve
big = kronecker(*Ls)
slow_ans = at.slinalg.solve_lower_triangular(big, x)
# Use tricks to avoid construction of entire kronecker product
fast_ans = kron_solve_lower(Ls, x)
np.testing.assert_array_almost_equal(slow_ans.eval(), fast_ans.eval())
def test_kron_solve_lower():
np.random.seed(1)
# Create random matrices
Ls = [np.tril(np.random.rand(3, 3)) for i in range(3)]
# Create random vector with correct shape
tot_size = np.prod([L.shape[1] for L in Ls])
x = np.random.rand(tot_size).reshape((tot_size, 1))
# Construct entire kronecker product then solve
big = kronecker(*Ls)
slow_ans = tt.slinalg.solve_lower_triangular(big, x)
# Use tricks to avoid construction of entire kronecker product
fast_ans = kron_solve_lower(Ls, x)
np.testing.assert_array_almost_equal(slow_ans.eval(), fast_ans.eval())