Refactor normal distribution into protected subclasses

[JonathanWenger]

Write an (abstract) superclass Normal which has subclasses:

• _UnivariateNormal
• _MultivariateNormal
• _MatrixvariateNormal
• _OperatorvariateNormal

The _MatrixvariateNormal class should implement specific methods for (symmetric) Kronecker structured covariance. Maybe it could have two subclasses:

• _MatrixvariateKroneckerCovNormal
• _MatrixvariateSymmKroneckerCovNormal

This relates to #15 .

[JonathanWenger]

Subclasses

* `_UnivariateNormal`

* `_MultivariateNormal`

* `_MatrixvariateNormal`

* `_OperatorvariateNormal`

implemented by f3601622ff8f2cec3b7c23eb3b8464910649c550 and 6035e98cf4f719eec19b0531ec0e6c3b1d4e6f08.

[JonathanWenger]

The structural assumptions allow implementation of faster sampling and density evaluation methods than the naive implementation, in particular for Kronecker structured covariances.

[pnkraemer]

I found it a lot easier to just have a MultivariateGaussian class, for compatibility reasons. It was way easier to write the code such that everything is a (d,), respectively (d, d) numpy array. UnivariateNormal could be automatically turned into a MultivariateGaussian. MatrixvariateNormal classes would have the same structure anyway, no? Is the speedup noticeable for Kronecker-structured covariances?

[JonathanWenger]

It looks the way to the user as you described, there being only on class Normal that is public. However we need the subclass structure to reduce complexity. There is a substantial speedup for kronecker structured covariances, i.e. Sigma^{-1} in O(n^3) vs O(n^6) for matrix-variate normal distributions.

Regarding shapes of random variable realizations, we can discuss that in #39 .