Speed improvement of the random generator

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Guillaume A.
Guillaume A. 2011-4-12
Hi,
I've built a Monte Carlo program, very simple, and I want to improve the CPU time because as soon as I increase the number of simulations, the time exponentially exploses. I've run a profiler on it, and suprisingly, most of the time (>60%) is spent in the generation of the random numbers. If there is a way to reduce this computing time, it would improve a lot the speed of my program.
Any suggestion ?

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回答（5 个）

the cyclist
the cyclist 2011-4-12
It would be best if you could post a snippet of code that illustrates the problem.
My guess is that it is not really the random number generation that is slow. Could it be that, instead, you are growing an array by appending a random number to it every iteration of a loop? Preallocating that array would speed it up.
Also, could you pregenerate all your random numbers first, in a vectorized way, then access them later as you need them?
  2 个评论
Jan
Jan 2011-4-12
I agree: exponential slowdown is often a hint to a missing pre-allocation. Try this:
tic; x=[]; for i=1:1e5; x(i)=rand; end; toc
tic; x=zeros(1,1e5); for i=1:1e5; x(i)=rand; end; toc
Andrew Newell
Andrew Newell 2011-4-12
If the number of iterations isn't too large, you might save even more time using
tic; x = rand(1,1e5); toc

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Oleg Komarov
Oleg Komarov 2011-4-12
Even generating all the random numbers at once (moving it outside of the loops the gain is small), but the difference lies in the legacy mode:
k = 20;
NbTraj = 10000;
NbPas = 100;
tic
s = RandStream('mcg16807','Seed',100);
dW = randn(s,NbTraj,5,NbPas,20);
toc % Elapsed time is 8.288121 seconds.
% No legacy mode
tic
dW = randn(NbTraj,5,NbPas,20);
toc % Elapsed time is 2.695166 seconds.
  2 个评论
Guillaume A.
Guillaume A. 2011-4-12
well, it makes no difference on my computer :
Elapsed time is 10.211157 seconds. (part I)
Elapsed time is 10.012667 seconds. (part II)
Oleg Komarov
Oleg Komarov 2011-4-12
Even if you clear the seed before executing the second part?

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Guillaume A.
Guillaume A. 2011-4-12
Ok, here is a sample code and the profiler result :
s = RandStream('mcg16807','Seed',100);
NbTraj=10000;
NbPas=100;
dW1 = zeros(NbTraj,NbPas);
dW2 = zeros(NbTraj,NbPas);
dW3 = zeros(NbTraj,NbPas);
dW4 = zeros(NbTraj,NbPas);
dW5 = zeros(NbTraj,NbPas);
for k=1:20
for i=1:NbPas
dW = randn(s,NbTraj,5);
dW = dW-repmat(mean(dW,1),NbTraj,1);
MatCov_rand = cov(dW);
dW = dW*inv(chol(MatCov_rand))*A_theo;
dW1(:,i) = dW(:,1);
dW2(:,i) = dW(:,2);
dW3(:,i) = dW(:,3);
dW4(:,i) = dW(:,4);
dW5(:,i) = dW(:,5);
end
%...
%Do some calculus on dW1, dW2,...
%...
end
And the result of the profiler :
RandStream.randn (MEX-function) 2000 10,559s
cov 2000 0,988s
repmat 2000 0,579s
mean 2021 0,245s
  1 个评论
Matt Fig
Matt Fig 2011-4-12
Also needed is the sizes of the arrays involved. Perhaps put a call to the WHOS function after these loops then show the output.

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the cyclist
the cyclist 2011-4-12
Crap. I accidentally just deleted a whole answer instead of a comment I made. Sorry!
One more suggestion. You should be able to pull the random number generation outside of at least one of those loops, assuming it does not use too much memory to do so. That should give you some more speedup.
  3 个评论
显示 1更早的评论
the cyclist
the cyclist 2011-4-12
Be aware that your code, with the parameters you have put in, is generating 100,000,000 random normals (in about 10 seconds on my machine). That is by no means "slow". Fully vectorized [r=randn(1.e8,1)] takes 7 seconds. So, I would say you need to find another way!
Guillaume A.
Guillaume A. 2011-4-12
It is not slow, but increase NbTraj to 2e6 and k to 50e3, and it could become an issue ;-)

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Guillaume A.
Guillaume A. 2011-4-12
Oleg, thanks for your answer, but unfortunately it does not change anything....

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