xmeans does not agree to paper?

[kno10]

The last term, p * 0.5 * log(N), should be in the sum only once IMHO. It is in the top BIC equation (j is the model index, not the cluster index), not in the l(Dn) equation where n is the cluster index) in https://web.cs.dal.ca/~shepherd/courses/csci6403/clustering/xmeans.pdf No guarantees that everything else is fine.

I also rename sigma_sqrt to sigma_sq because it is supposed to be sigma square, not square root.

Note that if sigma_multiplier = float('-inf'), the result will always be infinity, won't it?