Test based on inequality of two vectors does not succeed.

Question

Oddur Bjarnason 2016-10-30

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/309846-test-based-on-inequality-of-two-vectors-does-not-succeed

评论： Oddur Bjarnason 2016-10-31

([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

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Massimo Zanetti 2016-10-31

Adding some explanation to summarize your problem?

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Answer 1

Image Analyst 2016-10-31

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https://ww2.mathworks.cn/matlabcentral/answers/309846-test-based-on-inequality-of-two-vectors-does-not-succeed#answer_241354

编辑：Image Analyst 2016-10-31

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.

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Steven Lord 2016-10-31

>> 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 2016-10-31

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

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Answer 2

Oddur Bjarnason 2016-10-31

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/309846-test-based-on-inequality-of-two-vectors-does-not-succeed#answer_241429

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

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Oddur Bjarnason 2016-10-31

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.

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