%File: decompose

function y=state_vs_time(P,s0,n,step)

%STATE_VS_TIME finds state vector time development

%The program accepts a Markov matrix

%and finds the time progression

%of a given initial state vector.

%The output of the program is a matrix whose columns

%are the state vector values at different

%time steps that are specified by the user.

%P=state matrix

%s0=initial state vector (column vector)

%n=number of iterations desired

%step = increment of time step

state_size = size(s0);

if state_size(1)==1

s0 = s0'; %turn s into a column vector

end

m = size(P,1); %determine the number of rows.

S = zeros(m,n);

S(:,1) = s0;

time = 0;

for i=2:n

time = time+step;

S(:,i)=P*S(:,i-1);

end

y=S;