function S_permuted = xpxp_to_xxpp(S)
    % Permutes the entries of the input from xpxp ordering to xxpp ordering.
    %
    % Args:
    %   S (array): input even dimensional square matrix or a row vector
    %
    % Returns:
    %   S_permuted (array): permuted matrix or vector

    shape = size(S);
    if length(shape) > 2
        error('The input matrix is not 2 dimensional');
    end

    n = shape(2);

    if mod(n, 2) ~= 0
        error('The input array is not even-dimensional');
    end

    n = n / 2;
    ind = reshape(1:2*n, 2, [])';
    ind = ind(:)';

    
    if shape(1) == shape(2)
        S_permuted = S(ind, ind);
    else
        S_permuted = S(ind);
    end
end

%!test
%! [X, Y]=meshgrid (1:4, 1:4);
%! Mxpxp=xxpp_to_xpxp(X);
%! assert(any(any(X != Mxpxp)));
%! Mxxpp=xpxp_to_xxpp(Mxpxp);
%! assert(X, Mxxpp)
%! Mxpxp=xxpp_to_xpxp(Y);
%! assert(any(any(Y != Mxpxp)));
%! Mxxpp=xpxp_to_xxpp(Mxpxp);
%! assert(Y, Mxxpp)