classmarkov — recurrent and transient classes of Markov matrix
real N x N Markov matrix. Sum of entries in each row should add to one.
integer permutation vector.
integer vector, number (number of states in each recurrent classes, number of transient states).
integer vectors. (Indexes of recurrent and transient states).
Returns a permutation vector
perm such that
M(perm,perm) = [M11 0 0 0 0 0] [0 M22 0 0 0] [0 0 M33 0] [ ... ] [0 0 Mrr 0] [* * * Q]
Mii is a Markov matrix of dimension
Q is sub-Markov matrix of dimension
States 1 to sum(rec) are recurrent and states from r+1 to n
perm=[indsRec,indsT] where indsRec is a vector of size sum(rec)
and indsT is a vector of size tr.
//P has two recurrent classes (with 2 and 1 states) 2 transient states P=genmarkov([2,1],2,'perm') [perm,rec,tr,indsRec,indsT]=classmarkov(P); P(perm,perm)