dtmc_simulate.m

%{ @file dtmc_simulate.m
 %  @brief Simulates a trajectory of a discrete-time Markov chain
 %
 %  @author LINE Development Team
%}
 
%{
 % @brief Simulates a trajectory of a discrete-time Markov chain
 %
 % @details
 % Generates a sample path of the Markov chain for n time steps.
 %
 % @par Syntax:
 % @code
 % sts = dtmc_simulate(P, pi0, n)
 % @endcode
 %
 % @par Parameters:
 % <table>
 % <tr><th>Name<th>Description
 % <tr><td>P<td>Stochastic transition matrix
 % <tr><td>pi0<td>Initial probability distribution vector
 % <tr><td>n<td>Number of steps to simulate
 % </table>
 %
 % @par Returns:
 % <table>
 % <tr><th>Name<th>Description
 % <tr><td>sts<td>Vector of state indices visited in the simulation
 % </table>
%}
function [sts]=dtmc_simulate(P, pi0, n)
 
rnd  = rand;
cpi0  = cumsum(pi0);
if isempty(intersect(find( rnd - cpi0 > 0), find(pi0>0)))
    st = min(find(pi0));
else
    st = min(intersect(1 + find( rnd - cpi0 > 0),find(pi0>0)));
end
 
F = cumsum(P,2);
for i=1:n
    sts(i) = st; soujt(i)=1;
    if F(st,end)==0 || P(st,st)==1
        return;
    end
    rnd = rand;
    if isempty(intersect(find( rnd - F(st,:) > 0),find(P(st,:)>0)))
        st = min(find(P(st,:)>0));
    else
        st = min(intersect(1 + find( rnd - F(st,:) > 0),find(P(st,:)>0)));
    end
end
end