## Test based on inequality of two vectors does not succeed.

### Oddur Bjarnason (view profile)

on 30 Oct 2016
Latest activity Commented on by Oddur Bjarnason

on 31 Oct 2016

### Image Analyst (view profile)

([1,0],[0.8,0.2;0.6,0.4])
function stationarystates( S0,T )
%This function is a simple model of a Markov chain
% S0 is the initial state
% T is the transition matrix
% I want the cumulation of states to stop after state i if state i =
% state i+1. This does not happen with this code
M=S0
for i=1:1:10
if S0*T^i~=S0*T^(i-1) %Test for inequality of successive states
M((i+1),:)=S0*T^i; %M cumulates the states
else break
end
end
disp(M)
plot(M)
end

Massimo Zanetti

on 31 Oct 2016

### Tags ### Image Analyst (view profile)

on 31 Oct 2016
Edited by Image Analyst

### Image Analyst (view profile)

on 31 Oct 2016

And of course S0*T^i will never equal S0*T^(i-1) - the exponent is different! What you need to do is use i and (i-1) as indexes into the S0 array. It looks like S0 better be an array or you won't get it to work.

Oddur Bjarnason

### Oddur Bjarnason (view profile)

on 31 Oct 2016
>> [1,0]*[0.8,0.2;0.6,0.4]^5
ans =
0.7501 0.2499
>> [1,0]*[0.8,0.2;0.6,0.4]^6
ans =
0.7500 0.2500
>> [1,0]*[0.8,0.2;0.6,0.4]^7
ans =
0.7500 0.2500
Steven Lord

### Steven Lord (view profile)

on 31 Oct 2016
>> m1 = [1,0]*[0.8,0.2;0.6,0.4]^6
m1 =
0.7500 0.2500
>> m2 = [1,0]*[0.8,0.2;0.6,0.4]^7
m2 =
0.7500 0.2500
>> m1-m2
ans =
1.0e-04 *
0.1280 -0.1280
Just because m1 and m2 look the same using the default display format doesn't mean they contain the same values. You can see this more clearly using a different display format.
>> format longg
>> [m1; m2; m1-m2]
ans =
0.750016 0.249984
0.7500032 0.2499968
1.2800000000035e-05 -1.27999999999795e-05
Oddur Bjarnason

### Oddur Bjarnason (view profile)

on 31 Oct 2016
Thank you Steven, I have come to realize this. See my answer below which follows Image Analyst's answer and comments.

### Oddur Bjarnason (view profile)

on 31 Oct 2016

function stationarystates(S0,T) %This function is a simple model of a Markov chain % S0 is the initial state % T is the transition matrix % I want the cumulation of states to stop after state i if the difference % between states is small enough.
M=S0
for i=1:1:10
m1 = S0*T^i;
m2 = S0*T^(i-1);
mDiff = abs(m2-m1);
if max(mDiff(:)) > 0.00001; % The states are essentially equal.
M((i+1),:)=S0*T^i; % M cumulates the states
else break
end
end
disp(M)
plot(M)
end

Oddur Bjarnason

### Oddur Bjarnason (view profile)

on 31 Oct 2016
Thank you Image Analyst. This code is accordance with your answer and comments and yields the results I needed. I realize that the rows of the matrix approach the stationary matrix asymptotically but never becomes equal to the stationary state. So I have to be satisfied with a difference between states that is small enough. Thank you again. Oddur.