Add low-rank-modified metric

[aseyboldt]

Add a low-rank-modified metric

This adds a new type of metric for hmc-style samlers:
Instead of just allowing a diagonal or a full mass matrix, we combine the diagonal mass matrix with a couple of additional eigenvectors and eigenvalues of the remaining correlation.

This leads to the following form for the mass matrix:

$$ \begin{align} P &= V(\Sigma^{-1} - I)V^T + I \\ M &= D^{-\frac{1}{2}}PD^{-\frac{1}{2}} \end{align} $$

$P$ has exactly the eigenvalues specified in $\Sigma$ with the corresponding eigenvectors in $V \in R^{n, k}$. All remaining eigenvalues are one.

All operations needed in hmc/nuts can be done in $O(nk)$, so if the number of eigenvalues is small this has a cost much closer to diagonal mass matrix estimation.

This PR for now only contributes the metric, but corresponding adaptation should come a bit later...

Related issue: #683

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[junpenglao]

I guess you want to store these as properties so it is easier for tuning later on? In any case I suggest removing it here, and add it in the subsequent PR when tuning is introduced (so we can discuss whether it is necessary)

[aseyboldt]

Yes, that was mostly for debugging and I forgot to take it out. Sorry :-)

[twiecki]

Suggested change

	The gaussian euclidean metric is a euclidean metric further characterized
	The Gaussian Euclidean metric is a Euclidean metric further characterized

[twiecki]

Suggested change

	to follow a standard gaussian distribution. A Newtonian hamiltonian
	to follow a standard Gaussian distribution. A Newtonian Hamiltonian