Finding unique slices of a multidimensional array

I'm trying to find unique slices of a multi-dimensional array. For example, if I have something like

A = repmat(magic(4),1,1,3);
A(:,:,2) = A(:,:,2) - 1
A(:,:,1) =
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1
A(:,:,2) =
    15     1     2    12
     4    10     9     7
     8     6     5    11
     3    13    14     0
A(:,:,3) =
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1
     
     

I would like to be able to call something (with the dimension along which I'm slicing specified) and get

     [C, ia, ic] = highdim_unique(A, 3)
     
C(:,:,1) =
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1
C(:,:,2) =
    15     1     2    12
     4    10     9     7
     8     6     5    11
     3    13    14     0
ia =
     1
     2
ic =
     1
     2
     1
     
     

Any chance that something like this exists or has a straightforward solution? Ideally I would want to do this for arbitrariliy many dimensions, but doing it in 3 would be fine.

Thanks,

Jake

Answer 1

[the cyclist]

% Define a 3-d array of pretend data, that has a couple duplicate slices
% (Use your data instead)
rng default
A = rand(2,2,4) > 0.5;

% Find the size of A, for generality
[s1,s2,s3] = size(A);

% Reshape the slices into rows (by working down column-wise, and then across columns)
A_r = reshape(A,s1*s2,s3,1)';

% Find the unique rows (which corresponds to unique slices of original array)
A_ru = unique(A_r,'rows','stable');

% Reshape the rows back to 3-d
A_u = reshape(A_ru',s1,s2,[]);

[Jake Martin]

Works great, thanks!

[the cyclist]

Excellent.

I didn't really think about how to do it for N-dimensional array for N>3, but I see no reason why you could not do the same "reshape into rows" method.