matlab random number generation in parfor loop-CodePudding

I want to generate same normal random numbers for loop and parfor loop. Following MATLAB documentation I tried three different method:

Method 1: Using rng(seed, 'twister')

N = 1;

for ind = 1:10
    rng(ind, 'twister')
    samps(ind) = normrnd(0,1,N,1);
end

plot(samps); hold on

parfor ind = 1:10
    rng(ind, 'twister')
    samps(ind) = normrnd(0,1,N,1);
end

scatter(1:length(samps), samps)
legend({'using for loop', 'using parfor loop'})

Method 2: Using RandStream Method

N = 1;
 
sc = parallel.pool.Constant(RandStream('Threefry'));
for ind = 1:10
    stream = sc.Value;
    stream.Substream = ind;
    samps(ind) = normrnd(0,1,N,1);
end

plot(samps); hold on

sc = parallel.pool.Constant(RandStream('Threefry'));
parfor ind = 1:10
       stream = sc.Value;
       stream.Substream = ind;
       samps(ind) = normrnd(0,1,N,1);
end

scatter(1:length(samps), samps)
legend({'using for loop', 'using parfor loop'})

Method 3: Using another RandStream method

N = 1;
 
stream = RandStream('mrg32k3a');
for ind = 1:10
    stream.Substream = ind;
    samps(ind) = normrnd(0,1,N,1);
end

plot(samps); hold on

stream = RandStream('mrg32k3a');
parfor ind = 1:10
       set(stream,'Substream',ind);
       samps(ind) = normrnd(0,1,N,1);
end

scatter(1:length(samps), samps)
legend({'using for loop', 'using parfor loop'})

My question is why the last two methods are not working. If I understood MATLAB documentation correctly, they should have worked. Also, is there anything wrong with using rng(seed, 'twister') method with different seeds to produce statistically independent samples?

Edit: Here is the link to the MATLAB documentation that I used.

CodePudding user response：

I'm inferring that your concern is that the pseudorandomly generated numbers for your for and parfor loops did not match. This is however expected behavior. You used a MRG32K3A pseudorandom algorithm, which "does not make a guarantee that a fixed seed and a fixed series of calls to mrg32k3a.RandomState methods using the same parameters will always produce the same results." Source.

So it appears that everything is working correctly.

CodePudding user response：

When you do normrnd(0,1,N,1), you are not using stream to generate a random number, but rather the default RNG. Instead, use randn(stream,N,1), see the documentation.

As far as I can tell, normrnd and other generators from the Statistics and a Machine Learning toolbox always use the default RNG, and cannot use a custom RandStream object.