Shift rows by different amounts

I have a N^2 x N^2 matrix where N = 4, and I wish to shift rows 1, 5, 9, and 13 by 0. Rows 2, 6, 10, 14 by 4. Rows 3, 7, 11, 15 by 8. Finally rows 4, 8, 12, 16 by 12. Ideally it would be a general code, as I plan to apply it to more than just this example. I have tried many things but to no avail. Any help would be appreciated. Thanks

Answer 1

[Cedric]

 N = 4 ;
 A = repmat( 1:N^2, N^2, 1 ) ; % Dummy example.
 for k  = 2 : N
    A(k:N:N^2,:) = circshift( A(k:N:N^2,:), (k-1) * N, 2 ) ;
 end

With that, the the original A is:

 A =
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16

and the final:

 A =
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
    13    14    15    16     1     2     3     4     5     6     7     8     9    10    11    12
     9    10    11    12    13    14    15    16     1     2     3     4     5     6     7     8
     5     6     7     8     9    10    11    12    13    14    15    16     1     2     3     4
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
    13    14    15    16     1     2     3     4     5     6     7     8     9    10    11    12
     9    10    11    12    13    14    15    16     1     2     3     4     5     6     7     8
     5     6     7     8     9    10    11    12    13    14    15    16     1     2     3     4
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
    13    14    15    16     1     2     3     4     5     6     7     8     9    10    11    12
     9    10    11    12    13    14    15    16     1     2     3     4     5     6     7     8
     5     6     7     8     9    10    11    12    13    14    15    16     1     2     3     4
     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16
    13    14    15    16     1     2     3     4     5     6     7     8     9    10    11    12
     9    10    11    12    13    14    15    16     1     2     3     4     5     6     7     8
     5     6     7     8     9    10    11    12    13    14    15    16     1     2     3     4

I am not sure that the solutions that don't involve a FOR loop are more efficient ultimately, because the FOR loop has only N-1 iterations and no realloc or conversion to/from cell arrays. You'd have to profile every approach to be sure.

[Cedric]

PS: Andrei's BSXFUN-based solution can beat the loop though.

[Ellie]

Thanks!

Answer 2

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/79169-circshift-the-columns-of-an-array-with-different-shiftsize-withou-using-for-loop

http://www.mathworks.com/matlabcentral/answers/197158-circshift-columns-of-array-by-different-shift-size

http://www.mathworks.com/matlabcentral/answers/111673-how-to-shift-rows-in-a-matrix-by-different-values-e-g-line-1-n-spots-line-2-m-spots-and-so-on-wi

[Ellie]

I have seen all of those and have attempted to modify them for my code but have been having issues.