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classmarkov Scilab Group Scilab Function classmarkov
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.
EXAMPLE
//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
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