How to programme to calculate transition probability matrix?

Suppose I have a sequence of states like 1,3,3,1,2,1,4,2,3,1,4,2,4,4,4,3,1,2,5,1. Transition probability matrix calculated by following equation probability=(number of pairs x(t) followed by x(t+1))/(number of pairs x(t) followed by any state). transition probability matrix calculated by manually by me as follows

1 3 2 4 5

1 0 1/5 2/5 2/5 0

3 3/4 1/4 0 0 0

2 1/4 1/4 0 1/4 1/4

4 0 1/5 2/5 2/5 0

5 1 0 0 0 0

The following code (by James Tursa) gives the answer

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m = max(x);

n = numel(x);

y = zeros(m,1);

p = zeros(m,m);

for k=1:n-1

y(x(k)) = y(x(k)) + 1;

p(x(k),x(k+1)) = p(x(k),x(k+1)) + 1;

end

p = bsxfun(@rdivide,p,y); p(isnan(p)) = 0;

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How to programme for transition probability matrix if x have 2D vectors or 3D vectors or N dimensional vectors. For example take 2D vectors matrix

x=[0 0;

1 0;

2 1;

2 1;

2 1;

1 1;

1 1;

1 1;

1 1;

1 0;

2 1;

2 1;

2 1;

3 2;

2 2;

2 2;

2 2;

3 2;

3 2;

4 2;

4 2;

4 2;

3 2;

3 2;

3 2]

Answer 1

[emami.m]

I guess you should define unique combinations as states so you can map each pair of x to a state, then adopt your code to the new set of states.

[Categories,freq,new_seq] = unique(string(num2str(x)));

Now you can use new_seq as x in your code.