Distribution: Randomly Pivoted Cholesky

[nathanielpritchard]

Please describe your motivation for this feature request
The sampling compressor needs new distributions. One effective distribution is Randomly Pivoted Cholesky, which samples entries based on the trace of the gram matrix. To update this distribution, it is important to maintain a matrix of the selected vectors; thus, having a max selections parameter may be useful.

Describe the solution you'd like
I would like for a new distribution type implemented that utilizes the Randomly Pivoted Cholesky distribution. This distribution will need to be computed at every iteration. This implementation should include a:

1. complete_distribution function which forms the recipe and computes the distribution.
2. update_distribution! function which updates the distribution to correspond with a new matrix.
3. sample_distribution! function which samples from the distribution.

Describe alternatives you've considered
N/A

Additional context
See uniform.jl for an example of a distribution. See this paper for a definition of the distribution. A simple Matlab implementation of this distribution can be found here.