split_merge: Split-merge type update of clusterings
In oslerinhealth/rewind: Reconstructing Etiology with Binary Decomposition

This function uses restricted_gibbs to arrive at a launch state and then propose a split-merge move. Based on the computed acceptance probability, this function accepts or rejects the proposal arriving at an old or new state for the cluster indicators.

split_merge(
  Y,
  z,
  zs,
  S,
  mylist,
  N,
  t,
  b,
  log_v,
  n_split,
  Q,
  p,
  theta,
  psi,
  MORE_SPLIT = NULL,
  partition_partial = NULL
)

`Y`	multivariate binary data (row for subjects, column for dimensions)
`z`	original cluster indicators
`zs`	temporary variable used for split-merge assignments
`S`	temporary set of indicies for restricted Gibbs
`mylist`	the cluster ID list
`N`	a vector of the numbers of subjects in the list of clusters
`t`	total number of non-empty clusters
`b`	gamma parameter in the mixture of finite mixture formulation
`log_v`	coefficients in MFM (check Miller and Harrison 2016 JASA)
`n_split`	the number of intermediate Gibbs scan to arrive at the launch split state (usually 5)
`Q`	a Q matrix of dimension M by L
`p`	a vector of machine (factor) prevalences of length M
`theta`	a vector of true positive rates of length L
`psi`	a vector of false positive rates of length L
`MORE_SPLIT`	Default is `NULL`. When getting to launch state of the partition, `TRUE` for biasing towards split; FALSE for uniformly choose a pair (i,j) and then deciding to merge (if they belong to distinct clusters) or split (if they belong to the identical cluster)
`partition_partial`	a list of subject ids that each belong to a few known clusters.

Returns the values at the end of the current iteration

t the number of clusters;
z the cluster assignment indicators for all subjects (taking values from mylist);
N the number of subjects for each cluster; please refer to mylist to get the matching cluster IDs;
mylist the non-empty and empty cluster IDs.