how to traverse a multidimensional array

Given a multidimensional array A = MxMxMx...xM, where ndims(A)=n. My problem can be described by the following pseudo-code:

sum(A(i, :, :, :, ..., :)) i = 1, ... M
sum(A(:, i, :, :, ..., :)) i = 1, ... M
...
sum(A(:, :, :, :, ..., i)) i = 1, ... M

I really don't know how to do this. Can anyone help me?

Thanks

Answer 1

[Sean de Wolski]

A trick here is to use the string ':' as an element in a cell array that you can pass in as a comma-separated list.

Simple example:

c = {':',3}  % all elements, third column
x = magic(5)
x(c{:})

(This is an advanced manuever)

% Build a random rand-d matrix
k = randi(5)+3;
sz = randperm(8,k);
Z = rand(sz);
nd = numel(sz);

% Some function
do_something_with = @size; % size is just an example

for ii = 1:numel(sz)
    % loop over dimensions

    % build cell array with only iith dimension having values, everything else ':'
    traverse = repmat({':'},1,nd);
    for kk = 1:sz(ii)
        % loop over the iith dimension
        traverse{ii} = kk;
        do_something_with(Z(traverse{:}))
    end    
end

Answer 2

[David Young]

Maybe I'm oversimplifying the problem, but if I've understood the pseudocode this should work:

n = ndims(A);
s = cell(1, n);
for d = 1:n
  s{d} = squeeze(sum(A, d));
end

Afterwards, s{d} has an n-1 dimensional array which is A summed over the d'th dimension.

Sean de Wolski's solution is more general if you want something other than the sum, of course.