Test based on inequality of two vectors does not succeed.

([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]

Adding some explanation to summarize your problem?

Answer 1

[Image Analyst]

Are S0 and T integers? Otherwise see the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

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]

S0 is an initial state row vector of a Markov chain. In the example it is [1,0]. T is a corresponding transitional matrix. In the example it is [0.8,0.2;0.6,0.4]. When S0 is multiplied by increasing powers of T the states eventually become equal. I accumulate the states into the matrix M. My problem is that M does not stop accumulating the states when they become equal.

[Image Analyst]

Add these lines before the if and see what gets reported to the command line:

S0*T^i
S0*T^(i-1)

Don't use semicolons so you can see what they give. If you think they're equal, then you really need to read the FAQ like I already gave you the link for. You'd need to do something like

m1 = S0*T^i
m2 = S0*T^(i-1)
mDiff = abs(m2-m1);
if max(mDiff(:)) < someSmallNumber
    % They're essentially equal.

[Oddur Bjarnason]

 >> [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]

>> 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]

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

Answer 2

[Oddur Bjarnason]

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]

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.