Why does batch generate a different sequence of random numbers even when seeding the rng?

My question can be understood by implementing the following MWE:

% Script

% PARAMETERS
replicates = 1000; % number of times the simulation is to be repeated

% Seed the random number generator
rng(0); % this ensures the seed values sampled below are always the same

%============================================================%

% Required arrays and matrices
seed = randi(2^32,1,replicates)-1; % this should ensure model 
                                   % (MWE_fn) outcomes are repeatable
solution_array = zeros(1,replicates);

% Loop through the number of replicates
parfor replicate = 1:replicates
    solution_array(1,replicate) = MWE_fn(seed,replicate);
end

% Store solution in .txt file
fid_dyn = fopen('MWE_solution_batch4.txt','wt');
fprintf(fid_dyn,'%f\n',solution_array);
fclose(fid_dyn);

function solution = MWE_fn(seed,replicate)
    % Seed the random number generator
    rng(seed(1,replicate));

    % Generate random number for solution
    solution = rand;
end

When the code is run using batch the command:

j = batch('MWE_script','Pool',2)

the results are different to when running the code from the command line as follows:

MWE_script

Why is that??? Shouldn't seeding the rng in each replicate with the same value (irrespective of the method used to implement the code) mean the results are the same?

Answer 1

[Edric Ellis]

The problem here is that desktop MATLAB has a different default random number generator type than a Parallel Computing Toolbox worker. In particular, desktop MATLAB uses 'twister' by default, and PCT workers use 'combRecursive' by default (this is because 'twister' is not suitable for use in parallel - there is no way to generate parallel streams).

When you call

rng(0)

you are setting the seed of the generator, without changing the generator type. This means that simply calling rng(0) is actually not sufficient to fully specify the random numbers that MATLAB (client or worker) will generate.

To fix this, you need to specify fully the generator state and type. You can do this like so:

rng(0, 'combRecursive');

I'm not an expert on these matters, but my understanding is that for this case, you'd probably be better of generating a single 'combRecursive' stream, and picking a different substream for each iteration of your parfor loop. This is described in some detail in the doc.

[Simpet]

Thanks, I assumed the MATLAB desktop client and PCT workers would use the same default rng - apparently not for the reason you described.

What I still don't understand though is that when I stipulate the rng to be 'twister' (in either or both locations within the code) the code still works...I would have expected it to run into problems based on your reasoning. Or is it just that the random numbers generated in each parfor iteration are not independent?

[Edric Ellis]

Using 'twister' on the workers will still function - the problems with using 'twister' are that (as I understand it) the random numbers you get will not have good statistical properties.

There's an interesting blog post over here on Cleve's blog that might be useful.

[Simpet]

Yes, the blog certainly was helpful and confirms that when stipulating 'twister' as the rng for a parfor loop the resulting streams are not independent as is required for a parallel loop. Thanks again for your assistance.