need help optimizing this code...

how can I do this without a loop:

(consider vectors w and s of length n)...

dTot = 0;
for i=1:n
    for j=i+1:n
        v = w(i) * w(j) * (s(i)) * (s(j));
        dTot = dTot + v;
    end
end
dTot = dTot * 2;

Answer 1

[Andrei Bobrov]

Variant

ws = w.*s;
dTot = bsxfun(@times,ws,triu(ones(numel(w),1)*ws.',1));
dTot = sum(dTot(:))*2;

Answer 2

[Teja Muppirala]

You can simplify the loop like this:

for i=1:n
    v = w(i)*s(i)*sum( w(i+1:n) .* s(i+1:n) );
    dTot = dTot + v;
end
dTot = dTot * 2

[EDITED:]

Aha! I knew there had to be an easier way to do this!

ws = w.*s;
Cws = cumsum(ws(n:-1:2));
dTot = 2 * (sum(ws(n-1:-1:1) .* Cws))

[Jan]

In former days dTot+dTot has been faster than dTot*2. Is this still true on modern processors?

[Teja Muppirala]

Is X + X is faster than 2*X? I'm not really sure... but just trying it out, it seems they are both about the same to me.

[Andrei Bobrov]

+1

Answer 3

[Jakob Sørensen]

Wouldn't it work with:

% Turn vectors to matrix form
W1 = repmat(w, [n 1]);
W2 = repmat(w',[1 n]);

% Multiply these
Wm = W1 .* W2;

% Turn vectors to matrix form
S1 = repmat(s, [n 1]);
S2 = repmat(s',[1 n]);

% Multiply these
Sm = S1 .* S2;

% Multiply Wm and Sm matrices
Vm = Wm .* Sm

% Sum up and multiply by 2
V  = 2*sum(Vm(:))

Note that I haven't tested this, but i think it should work...

[Jakob Sørensen]

Kinda missed the j = i+1 part, this changes quite a few things. But you might be able to modify the concept. Sorry about that...

Answer 4

[Kevin Holst]

I don't think that will work actually. Try this, it's a little convoluted, but I think it's correct:

% this assumes w and s are row vectors
wm = triu(repmat(w,[n 1]),1);
sm = triu(repmat(s,[n 1]),1);
wsm = wm .* sm;
wsv = w .* s;
dTot = 2*(sum(wsv*wsm));

If you're wanting a one liner that no one will be able to read or understand then:

dTot = 2*(sum((w.*s)*(triu(repmat(w,[n 1]),1).*triu(repmat(s,[n 1]),1))));

Answer 5

[Oleg Komarov]

I would however use a loop:

ws   = w.*s;
wssw = bsxfun(@times,ws,ws.');

sum(wssw(~eye(n)))