How to set up a repeating series of terms

Hi all

For the below code, I'm trying to set up a series where instead of just the most recent value of k, it increases the size of the matrix every time it runs, so it would be Xt = [ones(t-h+1,1), Lt*yt, Lt^2*yt, ... Lt^k*yt]

for k = 1:p
    Xt = [ones(t-h+1,1), Lt^k*yt]; 
end

I know this code will only use the most recent value of k, so how would I be able to create it the way I described before? I'm pretty new to coding in general so apologies if this is a silly question.

[DGM]

You could do it with a loop, but it's unnecessary and generally slower.

Lt = 2;
t = 100;
h = 5;
p = 50;

yt = rand(t-h+1,1);

% using a loop without preallocation
tic
xt = ones(t-h+1,1);
for k = 1:p
    xt = [xt Lt^k*yt]; 
end
toc

Elapsed time is 0.005837 seconds.

% using a loop with preallocation
tic
xt2 = ones(t-h+1,p+1);
for k = 1:p
    xt2(:,k+1) = Lt^k*yt; 
end
toc

Elapsed time is 0.004077 seconds.

% vectorized instead (using implicit array expansion)
tic
xt3 = [ones(t-h+1,1) Lt.^(1:p).*yt];
toc

Elapsed time is 0.002683 seconds.

% show that results match
immse(xt,xt2)

ans = 0

immse(xt,xt3)

ans = 0

[Bethany Bloomfield]

Thank you very much.

I have a similar question with a different bit of code.

for k = 1:p
    yhat(t-T0+1,:) = [1, y(t), y(t-k)]*betahat + uhat(end)*psi'
end

I can't quite get the 3rd solution working there, this is my code but it gives an incorrect dimensions error when trying to multiply the matrices

yhat(t-T0+1,:) = [1, y(t), y(t-(1:p))]*betahat + uhat(end)*psi'

[DGM]

I don't know what size any of these are, nor what the goal is.

Answer 1

[Prateek Rai]

To my understanding, you want to set up a repeating series of terms so that,

Xt = [ones(t-h+1,1), Lt*yt, Lt^2*yt, ... Lt^k*yt].

Here is a possible workaround:

cat = [];
for k = 1 : p
    cat = [cat, Lt^k*yt];
    Xt = [ones(t-h+1,1), cat]; 
end