Accelerate nested bsxfun double loop?

I have a simple double loop that requires multiple 'repmat' tasks in each iteration. I'm currently using bsxfun to avoid repmats, but have found it to be only a little faster than repmat/elementwise multiplication.

Any suggestions on speeding this up?

n = 200;
U = rand(n);

M = zeros(n); % preallocate matrix 

a = rand(1,n); 
b = rand(1,n);

SZI = bsxfun(@times,a,b');

for j = 1 : n
    j
    for i = 1 : n
        if i ~= j
            plusvec = U(j,:).^2 - U(i,:).*U(j,:);
            timesvec = U(i,:) - U(j,:);
            M(i,j) = sum(sum(SZI.*(bsxfun(@plus,bsxfun(@times,U,timesvec),plusvec))));  
        end
    end
end

Answer 1

[Sean de Wolski]

Usually two dimensional:

bsxfun(@times

Can be replaced with matrix multiplication:

SZC = b'*a;
isequal(SZC,SZI)
ans =
   1

More Being a fan of "ez" speedups, I turned the outer for-loop into a parfor-loop:

With two for-loops:

timeit(@()A89455(200),0)
ans =
  6.3238

With the outer loop being a parfor-loop with four local workers:

timeit(@()A89455(200),0)
ans =
  3.7519

A89455 is your code in a function taking n as an input.

Answer 2

[Matt J]

Without loops:

    tic;

      a=a(:);
      Ut=U.';

      S=U*spdiags(a,0,n,n)*Ut;
       S=bsxfun(@minus,diag(S).',S)*sum(b);

      c=(b*U)*bsxfun(@times,Ut,a);
      T=bsxfun(@minus,c(:),c);

      M=S+T;

    toc;
   %Elapsed time is 0.002864 seconds.