How to automatically introduce a nested layer of for-loop?

Given a set of x-values , I want to create a script that generates a product of n numbers.

For example, if I want to generate products of 2 numbers, i.e. and so on, the script would be:

for i_1=1:3
    for i_2=1:3
        Product=X(i_1)*X(i_2)
    end
end

There will be 2 for-loops, one nested in another.

If I want to generate products of 3 numbers, i.e. and so on, the script would be:

for i_1=1:3
    for i_2=1:3
        for i_3=1:3
        Product=X(i_1)*X(i_2)*X(i_3)
        end
    end
end

There will be 3 for-loops, i.e. 2 nested loops in an external loop.

Is there a way to automate this, like a recursion, so when n increases, it will automatically introduce a nested for-loop in the original script? The concept is like this:

n=n
for i_1=1:3
    for i_2=1:3
        for i_3=1:3
            .
            .
            .
            for i_n=1:3
                Product=X(i_1)*X(i_2)*X(i_3)*...*X(i_n)
            end
            .
            .
            .
        end
    end
end

[Yasasvi Harish Kumar]

The Product variable gets over written in each iteration. I dont see why you would have a loop for it.

If you still need to write multiple loops, try recursive function as a solution.

[Wh Khu]

I know my Product will get overwritten for every loop, so I'm gonna store it into a cell for each iteration, it's just that I don't want to include that unrelated intricacy in my example above because that's not the point. I want to simplify the bigger picture, which is to add nested for-loops automatically based on the number n I assign.

Answer 1

[Shunichi Kusano]

Hi, This is a possibility:

N = 4; % the loop number
X = rand(1,3); % simulated X

products = ones(ones(1,N)*3);
reshape_arr = [3 ones(1,N-1)];
repmat_arr = [1 ones(1,N-1)*3];
for i = 1:N
    temp = repmat(reshape(X, circshift(reshape_arr, i-1)), circshift(repmat_arr,i-1));
    products = products .* temp;
end

hope this helps.