Combine arrays to form another arrays

Hello, can we combine many arrays into another arrays?

for example:

    k = 5;
    for u=1:k
       H(:,:,u)=randn(M,N)+j*randn(M,N); 
    end

    for u=1:k 
       Hi(:,:,1)=[H(:,:,2);H(:,:,3);H(:,:,4);H(:,:,5)];
       Hi(:,:,2)=[H(:,:,1);H(:,:,3);H(:,:,4);H(:,:,5)];
       Hi(:,:,3)=[H(:,:,1);H(:,:,2);H(:,:,4);H(:,:,5)];
       Hi(:,:,4)=[H(:,:,1);H(:,:,2);H(:,:,3);H(:,:,5)];
       Hi(:,:,5)=[H(:,:,1);H(:,:,2);H(:,:,3);H(:,:,4)];
    end

what if k=19, should I repeat all the steps. Are there other simpler programs to combine it. Thank you

[Pierre Benoit]

What is the relation between the number of arrays you wish to concatenate each time and k ? Is it always 4, or k-1 or something else ?

Answer 1

[Guillaume]

 H = randn(M, N, k) + j*randn(M, N, k);   %no need for loop
 c = num2cell(H, [1 2]);                  %split H into cell array along 3rd dimension
 for u=1:k
     indices = [1:u-1 u+1:k];             %get numbers 1:k without u
     Hi(:, :, u) = vertcat(c{indices});   %use cell array to comma separated list expansion to feed vertcat
 end

[Ellina]

It's work. Thank you so much. :-)

Answer 2

[Pierre Benoit]

M = 5;
N = 5;
k = 5;
H = randn(M, N, k) + j*randn(M, N, k); 
permut = nchoosek(1:k,k-1); % Find all permutations
permut = permut(end:-1:1,:); % Flip array
Hi = reshape(permute(reshape(H(:,:,permut'),[M N k-1 k]),[1 3 2 4]),
[M*(k-1) N k]);

Or with a for-loop to be more explicit

Hi = zeros(M*(k-1),N,k); % Pre-allocation
for ii = 1:k-1
    Hi(:,:,ii) = reshape(permute(H(:,:,permut(ii,:)),[1 3 2]),[M*(k-1) N]);
end

[Andrei Bobrov]

variant

M = 4;
N = 3;
k = 5;
H = randn(M, N, k) + 1i*randn(M, N, k); 
p = flipud(nchoosek(1:k,k-1));
Tout = permute(reshape(permute(H(:,:,p),[1 3 2]),[],k-1,N),[1 3 2]);