def m2(self):
"""matrix: Second moment."""
if self._m2 is None:
self._m2 = B.cholsolve(B.chol(self.prec),
self.prec + B.outer(self.lam))
self._m2 = B.cholsolve(B.chol(self.prec), B.transpose(self._m2))
return self._m2
def pinv(a: AbstractMatrix):
"""Compute the left pseudo-inverse.
Args:
a (matrix): Matrix to compute left pseudo-inverse of.
Returns:
matrix: Left pseudo-inverse of `a`.
"""
return B.cholsolve(B.chol(B.matmul(a, a, tr_a=True)), B.transpose(a))
def from_normal(cls, dist):
"""Construct from a normal distribution.
Args:
dist (distribution): Normal distribution to construct from.
Returns:
:class:`.NaturalNormal`: Normal distribution parametrised by the natural
parameters of `dist`.
"""
return cls(B.cholsolve(B.chol(dist.var), dist.mean),
B.pd_inv(dist.var))
def sample(self, state: B.RandomState, num: int = 1):
"""Sample.
Args:
state (random state): Random state.
num (int): Number of samples.
Returns:
tuple[random state, tensor]: Random state and sample.
"""
state, noise = Normal(self.prec).sample(state, num)
sample = B.cholsolve(B.chol(self.prec), B.add(noise, self.lam))
# Remove the matrix type if there is no structure. This eases working with
# JITs, which aren't happy with matrix types.
if not structured(sample):
sample = B.dense(sample)
return state, sample
def mean(self):
"""column vector: Mean."""
if self._mean is None:
self._mean = B.cholsolve(B.chol(self.prec), self.lam)
return self._mean