www.pudn.com > HMM1.zip > mc_stat_distrib.m

function pi = mc_stat_distrib(P) 
% MC_STAT_DISTRIB Compute stationary distribution of a Markov chain 
% function pi = mc_stat_distrib(P) 
%  
% Each row of P should sum to one; pi is a column vector 
 
% Kevin Murphy, 16 Feb 2003 
 
% The stationary distribution pi satisfies pi P = pi 
% subject to sum_i pi(i) = 1,  0 <= pi(i) <= 1 
% Hence 
% (P'  0n   (pi  = (pi  
%  1n  0)    1)     1) 
% or P2 pi2 = pi2. 
% Naively we can solve this using (P2 - I(n+1)) pi2 = 0(n+1) 
% or P3 pi2 = 0(n+1), i.e., pi2 = P3 \ zeros(n+1,1) 
% but this is singular (because of the sum-to-one constraint). 
% Hence we replace the last row of P' with 1s instead of appending ones to create P2,  
% and similarly for pi. 
 
n = length(P); 
P4 = P'-eye(n); 
P4(end,:) = 1; 
pi = P4 \ [zeros(n-1,1);1];