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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.
- rec, tr
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)
- genmarkov — generates random markov matrix with recurrent and transient classes
- eigenmarkov — normalized left and right Markov eigenvectors
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