def dlogp(inputs, gradients):
(g_logp, ) = gradients
cov, delta = inputs
g_logp.tag.test_value = floatX(1.0)
n, k = delta.shape
chol_cov = cholesky(cov)
diag = at.diag(chol_cov)
ok = at.all(diag > 0)
chol_cov = at.switch(ok, chol_cov, at.fill(chol_cov, 1))
delta_trans = solve_lower(chol_cov, delta.T).T
inner = n * at.eye(k) - at.dot(delta_trans.T, delta_trans)
g_cov = solve_upper(chol_cov.T, inner)
g_cov = solve_upper(chol_cov.T, g_cov.T)
tau_delta = solve_upper(chol_cov.T, delta_trans.T)
g_delta = tau_delta.T
g_cov = at.switch(ok, g_cov, -np.nan)
g_delta = at.switch(ok, g_delta, -np.nan)
return [-0.5 * g_cov * g_logp, -g_delta * g_logp]
def MvNormalLogp():
"""Compute the log pdf of a multivariate normal distribution.
This should be used in MvNormal.logp once Theano#5908 is released.
Parameters
----------
cov: at.matrix
The covariance matrix.
delta: at.matrix
Array of deviations from the mean.
"""
cov = at.matrix("cov")
cov.tag.test_value = floatX(np.eye(3))
delta = at.matrix("delta")
delta.tag.test_value = floatX(np.zeros((2, 3)))
cholesky = Cholesky(lower=True, on_error="nan")
n, k = delta.shape
n, k = f(n), f(k)
chol_cov = cholesky(cov)
diag = at.diag(chol_cov)
ok = at.all(diag > 0)
chol_cov = at.switch(ok, chol_cov, at.fill(chol_cov, 1))
delta_trans = solve_lower(chol_cov, delta.T).T
result = n * k * at.log(f(2) * np.pi)
result += f(2) * n * at.sum(at.log(diag))
result += (delta_trans**f(2)).sum()
result = f(-0.5) * result
logp = at.switch(ok, result, -np.inf)
def dlogp(inputs, gradients):
(g_logp, ) = gradients
cov, delta = inputs
g_logp.tag.test_value = floatX(1.0)
n, k = delta.shape
chol_cov = cholesky(cov)
diag = at.diag(chol_cov)
ok = at.all(diag > 0)
chol_cov = at.switch(ok, chol_cov, at.fill(chol_cov, 1))
delta_trans = solve_lower(chol_cov, delta.T).T
inner = n * at.eye(k) - at.dot(delta_trans.T, delta_trans)
g_cov = solve_upper(chol_cov.T, inner)
g_cov = solve_upper(chol_cov.T, g_cov.T)
tau_delta = solve_upper(chol_cov.T, delta_trans.T)
g_delta = tau_delta.T
g_cov = at.switch(ok, g_cov, -np.nan)
g_delta = at.switch(ok, g_delta, -np.nan)
return [-0.5 * g_cov * g_logp, -g_delta * g_logp]
return OpFromGraph([cov, delta], [logp], grad_overrides=dlogp, inline=True)