def logdet(self):
d, s = self._d, self._s_perp
fsh = full_shape([d.shape, s.shape])
logdet = np.zeros(fsh)
for idx in itertools.product(*map(range, fsh)):
d_idx, s_idx = broadcast(idx, d.shape), broadcast(idx, s.shape)
logdet[idx] = np.log(d[d_idx]).sum() + \
(self.dim - d[d_idx].size) * np.log(s[s_idx])
return logdet
def logdet(self):
d, s = self._d, self._s_perp
fsh = full_shape([d.shape, s.shape])
logdet = np.zeros(fsh)
for idx in itertools.product(*map(range, fsh)):
d_idx, s_idx = broadcast(idx, d.shape), broadcast(idx, s.shape)
logdet[idx] = np.log(d[d_idx]).sum() + \
(self.dim - d[d_idx].size) * np.log(s[s_idx])
return logdet
def full(self):
S = np.zeros(full_shape([self._d.shape, self._Q.shape]) + (self.dim, self.dim))
for idx in itertools.product(*map(range, S.shape[:-2])):
d_idx, Q_idx = broadcast(idx, self._d.shape), broadcast(idx, self._Q.shape)
d, Q = self._d[d_idx], self._Q[Q_idx]
S[idx + (Ellipsis,)] = np.dot(Q*d, Q.T)
sp_idx = broadcast(idx, self._s_perp.shape)
sp = self._s_perp[sp_idx]
S[idx + (Ellipsis,)] += (np.eye(self.dim) - np.dot(Q, Q.T)) * sp
return FullMatrix(S)
def _QDQ_x(Q, d, x):
fsh = full_shape([x.shape[:-1], Q.shape, d.shape])
prod = np.zeros(fsh + (x.shape[-1],))
for full_idx in itertools.product(*map(range, fsh)):
Q_idx = broadcast(full_idx, Q.shape)
d_idx = broadcast(full_idx, d.shape)
x_idx = broadcast(full_idx, x.shape[:-1])
curr_d, curr_Q = d[d_idx], Q[Q_idx]
curr_x = x[x_idx + (slice(None),)]
curr_QTx = np.dot(curr_Q.T, curr_x)
prod[full_idx + (slice(None),)] = np.dot(curr_Q, curr_d * curr_QTx)
return prod
def _QDQ_x(Q, d, x):
fsh = full_shape([x.shape[:-1], Q.shape, d.shape])
prod = np.zeros(fsh + (x.shape[-1], ))
for full_idx in itertools.product(*map(range, fsh)):
Q_idx = broadcast(full_idx, Q.shape)
d_idx = broadcast(full_idx, d.shape)
x_idx = broadcast(full_idx, x.shape[:-1])
curr_d, curr_Q = d[d_idx], Q[Q_idx]
curr_x = x[x_idx + (slice(None), )]
curr_QTx = np.dot(curr_Q.T, curr_x)
prod[full_idx + (slice(None), )] = np.dot(curr_Q, curr_d * curr_QTx)
return prod
def full(self):
S = np.zeros(
full_shape([self._d.shape, self._Q.shape]) + (self.dim, self.dim))
for idx in itertools.product(*map(range, S.shape[:-2])):
d_idx, Q_idx = broadcast(idx, self._d.shape), broadcast(
idx, self._Q.shape)
d, Q = self._d[d_idx], self._Q[Q_idx]
S[idx + (Ellipsis, )] = np.dot(Q * d, Q.T)
sp_idx = broadcast(idx, self._s_perp.shape)
sp = self._s_perp[sp_idx]
S[idx + (Ellipsis, )] += (np.eye(self.dim) - np.dot(Q, Q.T)) * sp
return FullMatrix(S)
def assign_one(self, idx, j, x_new):
if type(idx) == int:
idx = (idx,)
diff = x_new - self._X[idx + (j,)]
self._X[idx + (j,)] = x_new
Lambda_idx = broadcast(idx, self._Lambda.shape)
self._Z_diff[idx] += self._J_diff[idx + (j,)] * diff + -0.5 * self._Lambda[Lambda_idx].elt(j, j) * diff ** 2
self._J_diff[idx + (slice(None),)] -= diff * self._Lambda[Lambda_idx].col(j)
def assign_one(self, idx, j, x_new):
if type(idx) == int:
idx = (idx,)
diff = x_new - self._X[idx + (j,)]
self._X[idx + (j,)] = x_new
Lambda_idx = broadcast(idx, self._Lambda.shape)
self._Z_diff[idx] += self._J_diff[idx + (j,)] * diff + \
-0.5 * self._Lambda[Lambda_idx].elt(j, j) * diff ** 2
self._J_diff[idx + (slice(None),)] -= diff * self._Lambda[Lambda_idx].col(j)
def random(d_shape, Q_shape, sp_shape, dim, low_rank=False):
s_perp = np.random.gamma(1., 1., size=sp_shape)
smsh = tuple(np.array([d_shape, Q_shape]).min(0))
if low_rank:
rank = np.random.randint(1, dim+1, size=smsh)
else:
rank = dim * np.ones(smsh, dtype=int)
d = np.zeros(d_shape, dtype=object)
for idx in itertools.product(*map(range, d_shape)):
sm_idx = broadcast(idx, smsh)
d[idx] = np.random.gamma(1., 1., size=rank[sm_idx])
Q = np.zeros(Q_shape, dtype=object)
for idx in itertools.product(*map(range, Q_shape)):
sm_idx = broadcast(idx, smsh)
Q[idx], _ = np.linalg.qr(np.random.normal(size=(dim, rank[sm_idx])))
return EigMatrix(d, Q, s_perp, dim)
def random(d_shape, Q_shape, sp_shape, dim, low_rank=False):
s_perp = np.random.gamma(1., 1., size=sp_shape)
smsh = tuple(np.array([d_shape, Q_shape]).min(0))
if low_rank:
rank = np.random.randint(1, dim + 1, size=smsh)
else:
rank = dim * np.ones(smsh, dtype=int)
d = np.zeros(d_shape, dtype=object)
for idx in itertools.product(*map(range, d_shape)):
sm_idx = broadcast(idx, smsh)
d[idx] = np.random.gamma(1., 1., size=rank[sm_idx])
Q = np.zeros(Q_shape, dtype=object)
for idx in itertools.product(*map(range, Q_shape)):
sm_idx = broadcast(idx, smsh)
Q[idx], _ = np.linalg.qr(np.random.normal(size=(dim,
rank[sm_idx])))
return EigMatrix(d, Q, s_perp, dim)