How can I form a Hankel matrix for the following example?

I have 6 separate matrix like R(:,:,1) R(:,:,2) R(:,:,3) R(:,:,4) R(:,:,5) R(:,:,6). Each R contains a 4x4 matrix. for example R(:,:,1)= [0.0479 0.0987 0.1126 -0.0126; 0.0547 0.1128 0.1287 -0.0144; 0.1093 0.2254 0.2573 -0.0288; -0.0118 -0.0243 -0.0278 0.0031]. Now, I want to make a Matrix like H: for p=3 & q=4 where,

H= [R1 R2 R3 Rq; 
  R2 R3 R4 R(q+1); 
  Rp R4 R5 R(q+2)]
Here R1=R(:,:,1),R2=R(:,:,2)...so on
*My question:* How can I make H matrix by matlab program if I want to change for p & q like p=6 & q =7 etc.?

Thanks in advance... D. Bhuiyan

Answer 1

[Roger Stafford]

Let R be an m x n x r array in which r >= p+q-1 using your definition for p and q. Then do this:

   T = reshape(permute(R(:,:,1:p+q-1),[1,3,2]),m*(p+q-1),n);
   H = zeros(p*m,q*n);
   for k = 1:q
     H(:,(k-1)*n+1:k*n) = T((1:p*m)+(k-1)*m,:);
   end

[Roger Stafford]

That 'permute' operation wasn't actually needed. You can do it this way instead:

   T = reshape(R(:,:,p+q-1),m,n*(p+q-1));
   H = zeros(m*p,n*q);
   for k = 1:p
     H((1:m)+m*(k-1),:) = T(:,(1:n*q)+n*(k-1));
   end

[D Bhuiyan]

Very good idea. Thank you so much for your nice comments. The first program works properly (permute operation) but the second program doesn't works. why? You can see the R array in the attached, where m =4, n=4, p=4, q=5 Thanks again :)

[Roger Stafford]

I see why the second version doesn't work. It should have been written this way:

   T = reshape(R(:,:,1:p+q-1),m,n*(p+q-1));  % <-- Corrected
   H = zeros(m*p,n*q);
   for k = 1:p
     H((1:m)+m*(k-1),:) = T(:,(1:n*q)+n*(k-1));
   end

Sorry about that.

[D Bhuiyan]

Thanks :)