Question

I want to compute an outer product of the same vector in Matlab. A representative example would be:

x=rand(1e5,1);
sigma=x*x'-spdiags(x,0,length(x),length(x));

Is there any obvious way to speed this up? x*x’ is a symmetric matrix, but have not figured out a way to help Matlab use that information to speed things up.

EDIT: There is a way to do this with loops but I cannot see the benefit yet:

for k=1:length(x)
   sigma(k:length(x),k)=x(k).*x(k:length(x));
end

The above might work with a sparse array.

Answer 1

Have you considered using pdist with custom distance function

sigmaCompact = pdist( x(:), @(x, Y) x.*Y );
sigma = squareform(sigmaCompact);

up to the special treatment of sigma( k, k );