Is there an alternative way to perform the following matrix transformation?

Is there a better way to perform the following operation.

For example, for the following matrix:

A =
     1    13    25
     2    14    26
     3    15    27
     4    16    28
     5    17    29
     6    18    30
     7    19    31
     8    20    32
     9    21    33
    10    22    34
    11    23    35
    12    24    36
    

I am looking to transform to:

    A_new =
     1    13    25     2    14    26     3    15    27
     2    14    26     3    15    27     4    16    28
     3    15    27     4    16    28     5    17    29
     

Note, I am combining groups of three rows in a row for the entired matrix.

The following piece of code is already able to perform this. However, I have a huge matrix, and I believe there is an optimal way to do this. Also, I would like to play aroung with the number of rows to create the new matrix.

% Matrix A
A=1:36; A = reshape(A,12,3)

j=1;
for i=1:3
    A_new(i,:) = [A(j,:) A(j+1,:) A(j+2,:)];
    j = j +1;
end
A_new

Answer 1

[Andrei Bobrov]

i = 3;
[m,n] = size(A);
j = hankel(1:i,i:m);
out = A(sub2ind([m,n],kron(j,ones(1,n)),repmat(1:n,i,m-n+1)));

or in your case

j = hankel(1:i,i:2*i-1);
out = A(sub2ind([m,n],kron(j,ones(1,i)),repmat(1:n,i,i)));

or for out:

out = reshape(permute(reshape(A(j,:),i,n,[]),[1,3,2]),i,[]);

Answer 2

[Stephen23]

>> N = 3;
>> [R,C] = size(A); % specify R to change the number of rows of A used.
>> X = hankel(1:N,N:R);
>> B = reshape(A(X,:).',N*C,[]).'
B =
    1   13   25    2   14   26    3   15   27
    2   14   26    3   15   27    4   16   28
    3   15   27    4   16   28    5   17   29
    4   16   28    5   17   29    6   18   30
    5   17   29    6   18   30    7   19   31
    6   18   30    7   19   31    8   20   32
    7   19   31    8   20   32    9   21   33
    8   20   32    9   21   33   10   22   34
    9   21   33   10   22   34   11   23   35
   10   22   34   11   23   35   12   24   36