A few basic questions about a markov chain function

Question

John 2012-10-13

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https://ww2.mathworks.cn/matlabcentral/answers/50719-a-few-basic-questions-about-a-markov-chain-function

Hi there,

I'm using the code below to simulate a markov chain.

I have a basic question though about how to use it and I would be grateful if somebody could answer it. I have 2 questions:

1. How should the transition matrix be entered into the workspace

Like this (with the state names i.e State A)

          A  B  C
        A .2 .4. .4 
  P =   B .1 .3 .6
        C .2 .5 .3

or like this

      .2 .4. .4 
  P = .1 .3 .6
      .2 .5 .3

How would you call it in the command line?

Would this be it?

M=markvok(P,A,10);

Thank you

This function creates a Markov Chain based on a given transition matrix, P.
%   It uses the current state to index a row of P.  This row is passed into 
%   the Rand_Vect function, which returns a random value based on a probability 
%   vector.  This value becomes the current state, and the process is repeated
%   until the desired chain length is reached.
%
% Input:
%   P - Stochastic probability matrix (must be square with rows that add to 1)
%   initial_state - Initial state of the Markov Chain.  This state corresponds
%                   to one of the rows of P.
%   chain_length - Length of the output.
%
% Output:
%   Chain - Vector containing randomly generated Markov Chain.  The first value
%           will be initial_state and it will have chain_length values.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Chain] = Markvok_Chain( P, initial_state, chain_length )
sz = size(P);
cur_state = round(initial_state);
%
% Verify that the input parameters are valid
%
if (sz(1) ~= sz(2))
   error('Markov_Chain:  Probability matrix is not square');
end
num_states = sz(1);
if (cur_state < 1) | (cur_state > num_states)
   error('Markov_Chain:  Initial state not defined in P')
end
for i=1:num_states
   if (sum(P(i,:)) ~=1 )
      error('Markov_Chain:  Transition matrix is not valid')
   end
end
%
% Create the Markov Chain 
%
Chain(1) = cur_state;
for i = 1:chain_length
     cur_state = Rand_Vect(P(cur_state,:), 1);
     Chain(i) = cur_state;
end