def chol_up_insert(L, V12, V23, V22, Snn_noise_std_vec, insertionID):
R = L.T
N = R.shape[0]
n = V22.shape[0]
noise = np.diag(Snn_noise_std_vec ** 2)
R11 = R[:insertionID, :insertionID]
R33 = R[insertionID:, insertionID:]
S11 = R11
S12 = la.solve_triangular(R11.T, V12, lower=True)
S13 = R[:insertionID, insertionID:]
S22 = linalg.jitchol(V22 + noise - S12.T.dot(S12)).T
if V23.shape[1] != 0: # The data is being inserted between columns
S23 = la.solve_triangular(S22.T, (V23 - S12.T.dot(S13)), lower=True)
S33 = linalg.jitchol(R33.T.dot(R33) - S23.T.dot(S23)).T
else: # the data is being appended at the end of the matrix
S23 = np.zeros((n, 0))
S33 = np.zeros((0, 0))
On1 = np.zeros((n, insertionID))
On2 = np.zeros((N - insertionID, insertionID))
On3 = np.zeros((N - insertionID, n))
top = np.concatenate((S11, S12, S13), axis=1)
middle = np.concatenate((On1, S22, S23), axis=1)
bottom = np.concatenate((On2, On3, S33), axis=1)
return np.concatenate((top, middle, bottom), axis=0).T
def chol_up_insert(L, V12, V23, V22, Snn_noise_std_vec, insertionID):
R = L.T
N = R.shape[0]
n = V22.shape[0]
noise = np.diag(Snn_noise_std_vec**2)
R11 = R[:insertionID, :insertionID]
R33 = R[insertionID:, insertionID:]
S11 = R11
S12 = la.solve_triangular(R11.T, V12, lower=True)
S13 = R[:insertionID, insertionID:]
S22 = linalg.jitchol(V22 + noise - S12.T.dot(S12)).T
if V23.shape[1] != 0: # The data is being inserted between columns
S23 = la.solve_triangular(S22.T, (V23 - S12.T.dot(S13)), lower=True)
S33 = linalg.jitchol(R33.T.dot(R33) - S23.T.dot(S23)).T
else: #the data is being appended at the end of the matrix
S23 = np.zeros((n, 0))
S33 = np.zeros((0, 0))
On1 = np.zeros((n, insertionID))
On2 = np.zeros((N - insertionID, insertionID))
On3 = np.zeros((N - insertionID, n))
top = np.concatenate((S11, S12, S13), axis=1)
middle = np.concatenate((On1, S22, S23), axis=1)
bottom = np.concatenate((On2, On3, S33), axis=1)
return np.concatenate((top, middle, bottom), axis=0).T
def chol_up(L, Sn, Snn, Snn_noise_std_vec):
# Incremental cholesky update
Ln = la.solve_triangular(L, Sn, lower=True).T
On = np.zeros(Ln.shape).T
noise = np.diag(Snn_noise_std_vec ** 2)
Lnn = linalg.jitchol(Snn + noise - Ln.dot(Ln.T))
top = np.concatenate((L, On), axis=1)
bottom = np.concatenate((Ln, Lnn), axis=1)
return np.concatenate((top, bottom), axis=0)
def chol_up(L, Sn, Snn, Snn_noise_std_vec):
# Incremental cholesky update
Ln = la.solve_triangular(L, Sn, lower=True).T
On = np.zeros(Ln.shape).T
noise = np.diag(Snn_noise_std_vec**2)
Lnn = linalg.jitchol(Snn + noise - Ln.dot(Ln.T))
top = np.concatenate((L, On), axis=1)
bottom = np.concatenate((Ln, Lnn), axis=1)
return np.concatenate((top, bottom), axis=0)
def draws(ndraws, exp, cov):
# S: Standard Draw
# C: Transform to include covariance
# D: Transform to include expectance
L = linalg.jitchol(cov)
S = np.random.normal(loc=0.0, scale=1.0, size=(exp.shape[0], ndraws))
C = np.dot(L, S)
D = (C.T + exp)
return D
def chol_down(L, remIDList):
# This works but it might potentially be slower than the naive approach of
# recomputing the cholesky decomposition from scratch.
# The jitchol line can apparently be replaces with a chol that exploits the
# structure of the problem according to Osbourne's Thesis (as
# cholupdate does).
remIDList = np.sort(remIDList)
for i in range(len(remIDList)):
remID = remIDList[i]
S = L.T
n = S.shape[0]
On = np.zeros((n - (remID + 1), remID))
# Incremental cholesky downdate
top = np.concatenate((S[:remID, :remID], S[:(remID), (remID + 1) :]), axis=1)
S23 = S[remID, (remID + 1) :][np.newaxis, :]
S23TS23 = S23.T.dot(S23)
S33TS33 = S[(remID + 1) :, (remID + 1) :].T.dot(S[(remID + 1) :, (remID + 1) :])
R33 = linalg.jitchol(S23TS23 + S33TS33).T
bottom = np.concatenate((On, R33), axis=1)
L = np.concatenate((top, bottom), axis=0).T
remIDList -= 1
return L
def chol_down(L, remIDList):
# This works but it might potentially be slower than the naive approach of
# recomputing the cholesky decomposition from scratch.
# The jitchol line can apparently be replaces with a chol that exploits the
# structure of the problem according to Osbourne's Thesis (as
# cholupdate does).
remIDList = np.sort(remIDList)
for i in range(len(remIDList)):
remID = remIDList[i]
S = L.T
n = S.shape[0]
On = np.zeros((n - (remID + 1), remID))
# Incremental cholesky downdate
top = np.concatenate((S[:remID, :remID], S[:(remID), (remID + 1):]),
axis=1)
S23 = S[remID, (remID + 1):][np.newaxis, :]
S23TS23 = S23.T.dot(S23)
S33TS33 = S[(remID + 1):, (remID + 1):].T.dot(S[(remID + 1):,
(remID + 1):])
R33 = linalg.jitchol(S23TS23 + S33TS33).T
bottom = np.concatenate((On, R33), axis=1)
L = np.concatenate((top, bottom), axis=0).T
remIDList -= 1
return L