Circshift an ND array by values in an (N-1)D array w/out for loop

I have an ND array A that I would like to circshift (in its Nth dimension) by the corresponding values in an (N-1)D array b, ideally without a for loop (and/or fft/ifft). For example:

A(:,:,1) =
     1     3     5
     2     4     6
A(:,:,2) =
     7     9    11
     8    10    12
A(:,:,3) =
    13    15    17
    14    16    18
A(:,:,4) =
    19    21    23
    20    22    24

b =
     1    -1    -3
    -1    -1     0

with the result:

A_shift_b(:,:,1) =

      19     9    23
       8    10     6

A_shift_b(:,:,2) =

       1    15     5
      14    16    12

A_shift_b(:,:,3) =

       7    21    11
      20    22    18

A_shift_b(:,:,4) =

      13     3    17
       2     4    24

I've been trying to use arrayfun to get to a solution, but so far have been unsuccessful. Any help would be appreciated. Thanks!

Answer 1

[Andrei Bobrov]

A = reshape(1:24,[2 3 4]);
b = [1    -1    -3
    -1    -1     0];

[m,n,k]= size(A);
A1 = reshape(A,[],k);
mn = m*n;
try
    out = reshape(A1((1:mn)'+mn*rem((1:k) - b(:) + k-1,k)),[m,n,k]);% R2016b and later
catch
    out = reshape(A1(bsxfun(@plus,(1:mn)',...
               mn*rem(bsxfun(@minus,1:k,b(:)) + k-1,k))),[m,n,k]); %R2016a and earlier
end

[Ty Easley]

Could you explain the the role played by (1:k) in this code? It seems to me that it would require length(1:k) = length(b(:)), except that condition doesn't hold in the example given and the code still works. In addition, why doesn't (1:k) - b(:) throw an error, since one is a row vector and the other a column vector? I have started getting a "matrix dimensions must agree" error from this code and am not sure why I didn't earlier on.

[Ty Easley]

(and, fyi, the bsxfun catch does properly evaluate, but I'm also running on R2016b, so I'm curious about why the "try" code hits an error)