def cov(X0, Y, theta):
A = theta.sig_alpha * np.dot(
np.array(X0)[:, :-3],
np.array(X0)[:, :-3].T)
B = theta.sig_beta * np.diag(np.ones(len(X0)))
C = theta.sig_zeta
D = mk52(np.array(X0)[:, -3:-1], [theta.l1, theta.l2], theta.sig_m)
Kx = A + B + C + D
L = np.array([
np.array([
theta.rho[str(sorted([i, j]))] if i >= j else 0.0
for j in range(theta.n_IS)
]) for i in range(theta.n_IS)
])
# Normalize L to stop over-scaling values small
if theta.normalize_L:
L = L / np.linalg.norm(L)
# Force it to be positive semi-definite
Ks = L.dot(L.T)
if theta.normalize_Ks:
Ks = Ks / np.linalg.norm(Ks)
e = np.diag(np.array([theta.e1, theta.e2]))
Ks = e.dot(Ks.dot(e))
return np.kron(Ks, Kx)
def cov(X, Y, theta):
A = theta.sig_alpha * np.dot(np.array(X)[:, 1:-3], np.array(X)[:, 1:-3].T)
B = theta.sig_beta * np.diag(np.ones(len(X)))
C = theta.sig_zeta
D = mk52(np.array(X)[:, -3:-1], [theta.l1, theta.l2], theta.sig_m)
return A + B + C + D
def cov_old2(X, Y, theta):
A = theta.sig_alpha * np.dot(
np.array(X)[:, 1:-3],
np.array(X)[:, 1:-3].T)
B = theta.sig_beta * np.diag(np.ones(len(X)))
C = theta.sig_zeta
D = mk52(np.array(X)[:, -3:-1], [theta.l1, theta.l2], theta.sig_m)
return theta.rho_matrix(X, use_psd=True) * (A + B + C + D)
def cov_new(X, Y, theta):
# Get a list of all unique X, removing initial IS identifier
X0 = []
for x in X:
if not any(
[all([a == b for a, b in zip(x[1:], xchk)]) for xchk in X0]):
X0.append(x[1:])
A = theta.sig_alpha * np.dot(
np.array(X0)[:, :-3],
np.array(X0)[:, :-3].T)
B = theta.sig_beta * np.diag(np.ones(len(X0)))
C = theta.sig_zeta
D = mk52(np.array(X0)[:, -3:-1], [theta.l1, theta.l2], theta.sig_m)
Kx = A + B + C + D
L = np.array([
np.array([
theta.rho[str(sorted([i, j]))] if i >= j else 0.0
for j in range(theta.n_IS)
]) for i in range(theta.n_IS)
])
# Normalize L to stop over-scaling values small
L = L / np.linalg.norm(L)
# Force it to be positive semi-definite
Ks = L.dot(L.T)
return np.kron(Ks, Kx)
#K = np.kron(Ks, Kx)
# Now, we get the sub-covariance matrix for the specified sampled X and Y
indices = []
for l in range(theta.n_IS):
for i, x in enumerate(X0):
test = [l] + list(x)
if any(
[all([a == b for a, b in zip(test, xchk)]) for xchk in X]):
indices.append(l * len(X0) + i)
K_local = K[np.ix_(indices, indices)]
return K_local
def cov(X0, Y, theta):
A = theta.sig_alpha * np.dot(
np.array(X0)[:, :-3],
np.array(X0)[:, :-3].T)
B = theta.sig_beta * np.diag(np.ones(len(X0)))
C = theta.sig_zeta
D = mk52(np.array(X0)[:, -3:-1], [theta.l1, theta.l2], theta.sig_m)
Kx = A + B + C + D
Ks = np.array([
np.array(
[theta.rho[str(sorted([i, j]))] for j in range(theta.n_IS)])
for i in range(theta.n_IS)
])
if theta.normalize_Ks:
Ks = Ks / np.linalg.norm(Ks)
e = np.diag(np.array([theta.e1, theta.e2]))
Ks = e.dot(Ks.dot(e))
return np.kron(Ks, Kx)
def cov(X0, Y, theta):
A = theta.sig_alpha * np.dot(
np.array(X0)[:, :-3],
np.array(X0)[:, :-3].T)
B = theta.sig_beta * np.diag(np.ones(len(X0)))
C = theta.sig_zeta
D = mk52(np.array(X0)[:, -3:-1], [theta.l1, theta.l2], theta.sig_m)
Kx = A + B + C + D
if unitary is not None:
Ks = np.array([[1.0, unitary], [unitary, 1.0]])
else:
L = np.array([
np.array([
theta.rho[str(sorted([i, j]))] if i >= j else 0.0
for j in range(theta.n_IS)
]) for i in range(theta.n_IS)
])
# Force it to be positive semi-definite
Ks = L.dot(L.T)
e = np.diag(np.array([theta.e1, theta.e2]))
Ks = e.dot(Ks.dot(e))
return np.kron(Ks, Kx)