Matlab: optimization

OP here.

Q:
Is there a way to optimize this for loop?

f = 0;
for i = 1:n
for j = i+1:n
z = y(i) - y(j) ;
f = f + z*z ;
end
end
f = 2*f;

A1:

yy = meshgrid(y);
f = sum(sum((yy - yy.').^2));

A2:
Assuming y is column vector:

f = 2*((n+1)*sum(y.^2)-2*cumsum(y')*y);

A little bit explanation:

Suppose

y = [y1 y2 y3 y4]

f =
(y1-y2).^2 + (y1-y3).^2 + (y1-y4).^2 +
(y2-y3).^2 + (y2-y4).^2 +
(y3-y4).^2
=
y1y1+y2y2-2*y1y2 + y1y1+y3y3-2*y1y3 + y1y1+y4y4-2*y1y4 +
y2y2+y3y3-2*y2y3 + y2y2+y4y4-2*y2y4 +
y3y3+y4y4-2*y3y4
=
y1y1 + y1y1 + y1y1 +
y2y2 + y2y2 + y2y2 +
y3y3 + y3y3 + y3y3 +
y4y4 + y4y4 + y4y4 - 2*(
y1y2 + y1y3 + y1y4 + y2y3 + y2y4 + y3y4
)
=
3*sum(y.^2) - 2*(
(y1).*y2
(y1+y2).*y3
(y1+y2+y3).*y4
)