using tic toc function in matlab - matlab

Question

I have these two different ways to implement the same thing but I guess the second is the best. However, I get a better result when using tic toc for the first. How comes ?
j=6;
i=j;
Savings = zeros(i,j);
Costs = magic(400);
tic;
for x=2:i
for y=2:j
if(x ~= y)
Savings(x,y) = Costs(x,1) + Costs(1,y) - Costs(x,y);
end
end
end
first=toc;
disp(num2str(first))
Savings = zeros(i,j);
tic;
Ix=2:i;
Iy=2:j;
I = false(i,j);
I(Ix,Iy) = bsxfun(#ne, Ix', Iy);
S = bsxfun(#plus, Costs(Ix,1), Costs(1,Iy)) - Costs(Ix,Iy);
Savings(I) = S(I(Ix,Iy));
second=toc;
temp = Savings;
disp(num2str(second))

Answer 1

It depends on how MATLAB's JIT engine can improve the performance of for loops. For small matrices it works fine but for large ones not really. Seems for i less than 60, first method is faster, but not for larger matrices. Try this benchmark
for j=[6 30 60 100 200 400 600]
disp(['j=' num2str(j)]);
i=j;
Savings = zeros(i,j);
Costs = magic(600);
tic;
for mm=1:1e2
for x=2:i
for y=2:j
if(x ~= y)
Savings(x,y) = Costs(x,1) + Costs(1,y) - Costs(x,y);
end
end
end
end
first=toc;
disp(num2str(first));
Savings = zeros(i,j);
tic;
for mm=1:1e2
Ix=2:i;
Iy=2:j;
I = false(i,j);
I(Ix,Iy) = bsxfun(#ne, Ix', Iy);
S = bsxfun(#plus, Costs(Ix,1), Costs(1,Iy)) - Costs(Ix,Iy);
Savings(I) = S(I(Ix,Iy));
end
second=toc;
temp = Savings;
disp(num2str(second))
end
On my machine, it returns:
j=6
0.0001874
0.0052893
j=30
0.0034454
0.0057184
j=60
0.011097
0.01268
j=100
0.027957
0.023952
j=200
0.11529
0.058686
j=400
0.45791
0.37246
j=600
1.1496
0.74932