MATLAB: Evaluating a matrix at different time steps

matrix powertime steps

Dear all, I have a matrix which is a transition matrix. I need to calculate the time evolution of the associated probability distribution. The matrix is raised to 't', the time variable and I want to evaluate the matrix at different time steps. Is it possible in Matlab? The code to generate the square matrix is given below which is working well for a given value if t.
if true
  N=3;
w=0.2;
t=1;
G=zeros(N);
for j=1:N         %rows
 for n=1:N      %columns
    for k=1:N %summation
     G(j,n)=G(j,n)+1/N*(((1-w)+w*cos((2*pi*k)/N)).^t*cos((2*pi*(j-n)*k)/N));
    end 
 end
end
disp(G)
end

Best Answer

Add a separate loop for ‘t’, and a third dimension to your ‘G’ matrix:
N=3;
w=0.2;
tv = linspace(0, 10, 10);                       % Define Time Vector
G=zeros(N,N,length(tv));                        % Preallocate Here
for t = 1:length(tv)                            % ‘Time’ Loop
    for j=1:N         %rows
        for n=1:N      %columns
            for k=1:N %summation
                G(j,n,t)=G(j,n,t)+1/N*(((1-w)+w*cos((2*pi*k)/N)).^tv(t)*cos((2*pi*(j-n)*k)/N));
            end
        end
    end
    % disp(G)
end
Define the vector of times you want to evaluate your matrix in ‘tv’. The rest of the code will then work. Each ‘page’ (third dimension elements) of ‘G’ will be ‘G’ at the corresponding times.
Also, move the preallocation step to be before the loop! Otherwise, it resets all previous values of ‘G’ to zero.
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