unique vector with restrictions

Say I have these vector:

head_1=[1 6];
body_1=[1 4 5 6 8 9 15];

head_2=[7 9 13];
body_2=[5 7 8 9 13 20 30];

head_3=[20 30];
body_3=[4 5 8 11 19 20 30 40 50 100];

A vector head is a subset of vector body. Now I would like to have a collection of all the head vectors, but if a vector head_x is fully in vector body_y, then take head_y instead. If vector head_x is partially in vector body_y, then take head_y instead plus the other elements of head_x. So in my example, the collection would be:

head_final=[7 13 1 6];

In reality I can have several head and body vectors. Any hint will be apprecaitted!

Answer 1

[the cyclist]

I suggest you read this post about why dynamically named variables are a bad idea. Instead, you'd be better off storing your vectors in cell arrays, as in my code below.

% Define the inputs
head = {[1 6], [7 9 13], [20 30]};
body = {[1 4 5 6 8 9 15], [5 7 8 9 13 20 30], [4 5 8 11 19 20 30 40 50 100]};

% Count of number of inputs
N = numel(head);

% Initialize the vector that holds the head elements that do not appear in other bodies
head_final_cell = cell(1,N);

% Loop over each head
for ii = 1:N
    
    % Define an index that is 1:N, except for the current loop value
    other_bodies_index = setxor(1:N,ii);
    
    % Find index to head elements that are *not* in any other body, besides its own
    head_not_in_other_body = not(ismember(head{ii},[body{other_bodies_index}]));
    
    % For each head, fill the new cell array with the elements that do notappear in other bodies
    head_final_cell{ii} = head{ii}(head_not_in_other_body);
end

% Concatenate all the individual head elements into one vector
head_final = [head_final_cell{:}];

Note that a lot of this code could be compressed into fewer lines, but I separated each step so that I could comment it, and hopefully help you understand what is going on.

[Rub Ron]

Thank you. Does it makes sense that for this case the output should be: [1 6]?

head = {[1 6], [1 6]};
body = {[1 4 5 6 ], [1 6 7 8 9 13 20 30]};

[the cyclist]

Not by my understanding of your rules. I would expect head_final to be empty.

head{1} is [1 6], both elements of which appear in the body{2}.

head{2} is also [1 6], both elements of which appear in body{1}.

So I would not include any head elements. Is that wrong? If so, then please explain the reasoning.

[the cyclist]

Regarding your question about vector orientation ...

There are probably a few different ways to handle that, but I think yours should work, yes.