Question

I can’t remove this loops by myself, if anybody can help me with optimization this piece of code – welcome.

M = length(w);
expt = exp(-t .* (phis * w'));
G = zeros(M, M);
for i = 1 : M
    for j = 1 : M
        last = 2 * reg_coef * eye(M);
        G(i,j) = last(i, j) + mean(expt .* t .^2 .* phis(:,i) .* phis(:,j) ./ (1 + expt) .^ 2);
    end
end

• w – size is (1xM)
• phis – size is (NxM)
• t – size is (Nx1)

Answer 1

You can do alot better by just writing cleaner code – ensure that you allocate properly, ensure that you remove duplicate calculations from loops etc:

EDIT: You can also see that the resulting matrix G is symmetric, so you get an immediate 2x speed-up by only calculating the upper triangle and filling in the lower triangle afterwards as a transpose.

At least with my MATLAB another big speed-up is achieved by vectorising the call to mean() through the use of a temporary array.

N = 100;
M = 100;

w = rand(1,M);
t = rand(N,1);
phis = rand(N,M);
reg_coeff = rand(1,1);

expt = exp(-t .* (phis * w'));

%% Initial version
tic
for i = 1 : M
   for j = 1 : M
      last = 2 * reg_coeff * eye(M,M);
      G1(i,j) = last(i,j) + mean(expt .* t .^ 2 .* phis(:,i) .* phis(:,j) ./ (1 + expt) .^ 2);
   end
end
t1 = toc;

%% Faster version
tic
coeff = expt .* t .^ 2 ./ (1 + expt) .^ 2;
G2 = zeros(M,M);
TT = zeros(M,M);
for i = 1 : M
   for j = i : M % only form upper triangle
      TT(:,j) = coeff .* phis(:,i) .* phis(:,j);
   end
   G2(i,i:M) = mean(TT(:,i:M),1); % vectorise call to mean()
end
G2 = 2 * reg_coeff * eye(M,M) + G2 + triu(G2,+1)';
t2 = toc;

%% Compare versions
speed = t1/t2
error = max(max(abs(G2 - G1)))

For this 100x100 case the speed-up was around 41.0 on my machine.

Hope this helps.