Replacing for loop with matrix math to increase computational efficiency.

I am using the following code to compute the Sx, Su, Sw and Sd matrices. But I have found out them to be very computationally expensive and also I understand there is a better way to do this. Can anyone please suggest how these computations can be done more efficiently? I am also considering converting these matrices to sparce matrices after assignment for the further calculations.

N = pred_horizon/Ts;    % N = 500
Sx = zeros(8*(N+1),8);
Su = zeros(8*(N+1),8*(N));
Sw = zeros(8*(N+1),8*(N));
Sd = zeros(8*(N+1),1);
for i=1:(length(Sx)-7)
    Sx(i:i+7,:) = power(Ad,(i-1));
end
for i=2:size(Su,1)-7
    for j=1:min((i-1),size(Su,2)-7)
        Su(i:i+7,j:j+7) = power(Ad,(i-j-1))*Bd;
    end
end
for i=2:size(Sw,1)-7
    for j=1:min((i-1),size(Sw,2)-7)
        Su(i:i+7,j:j+7) = power(Ad,(i-j-1))*Ed;
    end
end
for i=2:length(Sd)-7
    Sd(i:i+7,:) = power(Ad,i-2)*Dd;
end

Answer 1

[darova]

You can increase for loop step

You are overwriting same values all the time. THere is no need of it