Question

I have written a small loop in matlab to generate a random NxN matrix. The loop is

tic
for i=1:10000
    u=rand(1,10000);
    tau(i,:)=d.*(u(1,:)-0.5);
end
toc

I first tried the loop routine only once,

    u=rand(1,10000);
    tau=d.*(u(1,:)-0.5);

which gave me tau in 0.000169 seconds. I assumed that the loop then would take about 1.69s. It didn’t, it took 555.018280s with the fans going wild.

Is there
a) a reason why the speed is not linearly related to the number of iterations?
b) a reason to why it takes so much longer to do the routine many times
c) a way to speed this one up (I actually would like to generate larger matrices), for instance a better loop or way to give me, say, a 1’000’000×1’000’000 matrix of the same kind?

Answer 1

You have firstly to pre-allocate your matrix tau, i.e.

  tau = zeros(10000,10000);

otherwise matlab will continuously re-allocate it in regions where there is sufficiently free memory (=> find a region with sufficiently free space + hard copy).

In general, you would achieve better performance vectorizing the whole process:

 u=rand(10000,10000);
 tau=d.*(u-0.5);

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EDIT: Above all, listen to the wise advice of Rody in the comment below. (In any case, I suppose that rand(a,b) would run a little faster than a serial executions of rand(1,b)).