MATLAB: Sum of a product with i differnt to j

Question

Hi All,

I want to calculate a sum of a product as following:

I think my problem is quite relative to this topic: Double sum of a product, but in my case I have j ~= i.

I think something like that should work:

t = 1:100;
n = 10;
a = randn(n,1);
P = [];
for i = 1:n
    F = [];
    for j = 1:n
        if j~=i
            f = (a(j)-a(i))^n*t;
            F = [F,f'];
        end
    end
    p = prod(F,2);
    P = [P,p];
end
res = sum(P,2);

But I feel that this solution is not good and something easier should exist?

Thanks a lot,

M.

Answer 1

Something like this, perhaps,

A=a(:)-a(:).';  
  A(1:n+1:n^2)=1;  %nullify i==j
f=sum(prod(A,2).^n)*t;