Change language to:
English - Français - 日本語 - Português -

Please note that the recommended version of Scilab is 2024.0.0. This page might be outdated.
See the recommended documentation of this function

Scilab help >> Linear Algebra > Markov Matrices > classmarkov

# classmarkov

recurrent and transient classes of Markov matrix

### Calling Sequence

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

### Arguments

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 — generates random markov matrix with recurrent and transient classes
• eigenmarkov — normalized left and right Markov eigenvectors
 Report an issue << Markov Matrices Markov Matrices eigenmarkov >>

 Copyright (c) 2022-2023 (Dassault Systèmes)Copyright (c) 2017-2022 (ESI Group)Copyright (c) 2011-2017 (Scilab Enterprises)Copyright (c) 1989-2012 (INRIA)Copyright (c) 1989-2007 (ENPC)with contributors Last updated:Tue Apr 02 17:37:55 CEST 2013