e435

function e435
%
%  Example 4.3.5
%    
P=zeros(7,7);
P(1,:)=[0 0 0 .65 0 .35 0];
P(2,:)=[0 0 0 .9 0 .1 0];
P(3,:)=[.1 .1 0 0 0 0 .8];
P(4,:)=[0 0 .12 0 .88 0 0];
P(5,:)=[.15 .35 0 0 0 0 .5];
P(6,:)=[0 0 .75 0 .25 0 0];
P(7,:)=[0 0 0 .4 0 .6 0];
fprintf('  The original  P  matrix: \n'); P
[PC,f]=mc_canop(P);
fprintf('   list of state labels: \n',f); f
fprintf('  The trnasition matrix in canonical form \n');
PC
[p]=mc_limsr(PC);
fprintf('  the time average  pi  \n'); p
%
%  Look at the three closed communication classes
%
P3=PC^3; 
fprintf('  the  P3  matrix \n'); P3
Q1=P3(1:2,1:2); Q2=P3(3:5,3:5); Q3=P3(6:7,6:7);
[p1]=mc_limsr(Q1); [p2]=mc_limsr(Q2); [p3]=mc_limsr(Q3);
fprintf('  p1: '); p1
fprintf('  p2: '); p2
fprintf('  p3: '); p3
pp=[p1 p2 p3]; pp=pp/3