Random matrix - Code efficiency

Hi, I've got a code to fill a matrix with random numbers. However, I haven't found a way to use efficient code and I must use for loop. Here is the code I would like to optimize :

PoissonZ=poissrnd(Lambda,NbTraj,NbDay);
for i=1:NbDay
     for j=1:NbTraj
         PoissonSauts(j,i)=sum(randn(PoissonZ(j,i),1));
     end
 end

As NbTraj and/or NbDay can achieve quickly high value, the code become very slow... I did not found a way to vectorize it. Thanks for suggestions !

G.

Answer 1

[the cyclist]

Looks to me that each element of PoissonSauts is the sum of K normally distributed variables, where K is itself drawn from a Poisson. I believe you can take advantage of the fact that the sum of K i.i.d. variables that are N(0,1) distributions is equal to sqrt(K) times an N(0,1):

 PoissonZ=poissrnd(Lambda,NbTraj,NbDay);
 PoissonSauts = randn(NbTraj,NbDay).*sqrt(PoissonZ);

[Guillaume A.]

hmmm very interesting approach ! I'll try it asap, thanks !

Answer 2

[Matt Fig]

I would bet that your code is slow primarily because you did not pre-allocate the PoissonSauts array before the loops. Thus every time through the loop you are causing MATLAB to re-allocate memory for the array, which, as you discovered, is slow.

PoissonZ=poissrnd(Lambda,NbTraj,NbDay);
PoisonSauts = zeros(NBTraj,NbDay);  % Pre-allocate the array!
for i=1:NbDay
     for j=1:NbTraj
         PoissonSauts(j,i)=sum(randn(PoissonZ(j,i),1));
     end
end

Try that and see if your code speeds up dramatically.

[Guillaume A.]

In fact it is preallocated... just wanted to not surcharge the code presented