Name

classmarkov — recurrent and transient classes of Markov matrix

Calling Sequence

[perm,rec,tr,indsRec,indsT]=classmarkov(M)

Parameters

M

real N x N Markov matrix. Sum of entries in each row should add to one.

perm

integer permutation vector.

rec, tr

integer vector, number (number of states in each recurrent classes, number of transient states).

indsRec,indsT

integer vectors. (Indexes of recurrent and transient states).

Description

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]

Each Mii is a Markov matrix of dimension rec(i) i=1,..,r. Q is sub-Markov matrix of dimension tr. States 1 to sum(rec) are recurrent and states from r+1 to n are transient. One has perm=[indsRec,indsT] where indsRec is a vector of size sum(rec) and indsT is a vector of size tr.

Examples

 
//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)

See Also

genmarkov , eigenmarkov