Combination of elements in 2 different vectors

Hello to everyone, I have the following two vectors:

yes = [y1 y2 y3 y4];

no = [n1 n2 n3 n4]

My question is if there is a simple way of doing combinations (just as nchoosek would do) but between these two vectors in the following way:

I need to fill a matrix C, whose elements are described by C_ij, where 'i' is the number of elements from the vectors that we take, and 'j' is the number of elements that are correct (from vector 'yes'). For instance: C_21 = y1·n2 + y1·n3 + y1·n4 + y2·n1 + y2·n3 + y2·n4 + y3·n1 + y3·n2 + y3·n4 + y4·n1 + y4·n2 + y4·n3. Note that a combination where i=j (for example C_22) is not possible, since one element can only be either 'yes' or 'no'.

Many thanks in advance.

Answer 1

[BhaTTa]

To solve this problem, you can use MATLAB to generate the required combinations and fill the matrix ( C ). The goal is to create a matrix ( C ) where each element ( C_{ij} ) represents the sum of all possible products of i elements, with j of them being from the yes vector.

% Define the vectors
yes = [y1, y2, y3, y4];
no = [n1, n2, n3, n4];

% Define the size of the vectors
n_yes = length(yes);
n_no = length(no);

% Initialize the matrix C
C = zeros(n_yes + n_no, n_yes);

% Loop through the number of elements taken (i)
for i = 1:(n_yes + n_no)
    % Loop through the number of correct elements (j)
    for j = 1:min(i, n_yes)
        % Ensure we do not exceed the number of 'no' elements
        if (i - j) <= n_no
            % Generate all combinations of 'yes' and 'no' elements
            yes_combinations = nchoosek(1:n_yes, j);
            no_combinations = nchoosek(1:n_no, i - j);
            
            % Initialize the sum for C_ij
            sum_C_ij = 0;
            
            % Loop through all combinations of 'yes' elements
            for y_comb = 1:size(yes_combinations, 1)
                % Loop through all combinations of 'no' elements
                for n_comb = 1:size(no_combinations, 1)
                    % Calculate the product for the current combination
                    product = prod(yes(yes_combinations(y_comb, :))) * prod(no(no_combinations(n_comb, :)));
                    % Add the product to the sum for C_ij
                    sum_C_ij = sum_C_ij + product;
                end
            end
            
            % Store the sum in the matrix C
            C(i, j) = sum_C_ij;
        end
    end
end

% Display the matrix C
disp('Matrix C:');
disp(C);