MATLAB: Random matrix – Code efficiency

optimizationrandom number generatorvectorization

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.

Best Answer

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);
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