Vectorization in cell array assignment without nested for loop

I have c being a large sparse matrix computed before and want to assign value to cell array D by using the outer product of c columns. However, I have to implemented special rules and cannot get outer product of same c columns.

From column 1 using the first for loop, I have to implemented another for loop and an if-else statement to skip the same index assignment by flagging.

Eventually, after the nested for loop, I want to add up all the G in one loop to get a matrix K. I add this 100 times.

    c = rand(100,100);G = cell(1,100);
    G{1} = eye(100);
    for i = 1:100
            flag = false;
            for z = 2 :100
                j = z-1;
                if j == i
                   flag = true;
                end 
                if flag == true
                   G{z} = (c(:,j+1)*c(:,i)');
                else 
                   G{z} = (c(:,j)*c(:,i)');
                end
            end
             for z = 2 : 100
                 K = K + G{z}';
             end
    end

By using array I can reduce to a first layer of loop only. But i need multiple loops, is there a smarter way to do this?

Answer 1

[Andrei Bobrov]

n = size(c,2);
[jj,ii] = ndgrid(1:n-1,1:n);
ij = [ii(:),jj(:)];
t = diff(ij,1,2) == 0;
ij(t,2) = ij(t,2) + 1;
G = bsxfun(@times,c(:,ij(:,1)), permute( c(:,ij(:,2)),[3,2,1]));
K = squeeze(sum(G,2));