Question

Still very new to programming…

I have 9×1 Vectors at time t, t+1, t+2 etc.

[10 10 10 10 10 10 10 10 10]’

and matrices. Each matrix is 9×9 and also at time 1, t+1, t+2 etc. =

 1     0     0     0     0     0     0     0     0
 0     1     0     0     0     0     0     0     0
 0     0     1     0     0     0     0     0     0
 0     0     0     1     0     0     0     0     0
 0     0     0     0     1     0     0     0     0
 0     0     0     0     0     1     0     0     0
 0     0     0     0     0     0     1     0     0
 0     0     0     0     0     0     0     1     0
 0     0     0     0     0     0     0     0     1

They are 3d matrices and I want to make them 4d in the future.

I want to multiply vector(:,:,t) with the diagonal of matrix at time t and output vector(:,:,t+1).

So in short…

vector t multiplied by diag matrix t = vector t+1

vector t+1 multiplied by diag matrix t+1 = vector t+2

vector t+2 multiplied by diag matrix t+2 = vector t+3 … and so on.

the diagonal numbers change in each time step but for simplicity sake, let’s keep them all at 1 for the moment.

I’ve tried using diag but it states I have to use a 2D input so only works when I ignore t.

Cheers for your help guys – it’s helping me learn a lot. Any hints or solutions will be much appreciated. I know you guys know the simplest and most efficient solutions.

Answer 1

Here you go:

n = 10;

% Make sample data
t = zeros(9,1,n);
t(:,1,1) = 1;
T = repmat(diag(ones(9,1)), [1 1 n]);

% Loop though to fill in t based on previous t and T
for i = 2:n
  t(:,1,i) = t(:,1,i-1) .* diag(T(:,:,i-1));
end

Now all of t should be 1.