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  1. PO
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    <p>I think that you only need to store the initial seed (in your case the <code>std::uint_least32_t seed_data[std::mt19937::state_size]</code> array) and the number <code>n</code> of warmup steps you made (eg. using <code>discard(n)</code> as mentioned) for each run/simulation you wish to reproduce.</p> <p>With this information, you can always create a new MT instance, seed it with the previous <code>seed_data</code> and run it for the same <code>n</code> warmup steps. This will generate the same sequence of values onwards since the MT instance will have the same inner state when the warmup ends.</p> <p>When you mention the <code>std::random_device</code> affecting reproducibility, I believe that in your code it is simply being used to generate the seed data. If you were using it as the <em>source</em> of random numbers itself, then you would not be able to have reproducible results. Since you are using it only to generate the seed there shouldn't be any problem. You just <em>can't generate a new seed</em> every time if you want to reproduce values!</p> <p>From the definition of <code>std::random_device</code>: </p> <blockquote> <p>"std::random_device is a uniformly-distributed integer random number generator that produces non-deterministic random numbers."</p> </blockquote> <p>So if it's not deterministic you cannot reproduce the sequence of values produced by it. That being said, use it <em>simply</em> to generate good random seeds only to store them afterwards for the re-runs.</p> <p>Hope this helps</p> <p><strong>EDIT :</strong></p> <p>After discussing with @SteveJessop, we arrived at the conclusion that a simple hash of the dataset (or part of it) would be sufficient to be used as a decent seed for the purpose you need. This allows for a deterministic way of generating the same seeds every time you run your simulations. As mentioned by @Steve, you will have to guarantee that the size of the hash isn't too small compared with <code>std::mt19937::state_size</code>. If it is too small, then you can concatenate the hashes of m, m+M, m+2M, ... until you have enough data, as he suggested.</p> <p>I am posting the updated answer here as the idea of using a hash was mine, but I will upvote @SteveJessop's answer because he contributed to it.</p>
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    1. USAndré Neves
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    1. COI need to create `M` different data sets, which will be used in `M` different simulations. I need the data sets to be independent, i.e., each data set is generated using a PRNG whose seed is unique for the specific simulation. My current solution achieves uniqueness by using a sequence of seeds from `1` to `M`. It seems that you are suggesting to create at the beggining of the code a _master_ seed sequence `q` so that the resulting `std::mt19937` will be modified in each simulation by using `discard(n)`, where `n` is different for each simulation. Right?
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    2. COYou need to create a _master_ seed sequence (`seed_data` array) and a _master_ `n` for **each** simulation you want to reproduce. So, if I understood correctly you will have `M` different _master_ `seed_data`and `M` `n`'s, one for each simulation. For each simulation, you will then call `seed(seed_data)` and then `discard(n)`. You could create arrays of size `M` for your `M` sets of parameters and then update your `std::mt19937` instance using `seed(seed_data_array[i])` and then `discard(n_array[i])`, where i is the dataset identifier (0..M-1).
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    3. COSo the problem is where to take the `M` different master seed sequences and `n`s. I edited the original question to stress that by _different executions_ I mean re-launching the executable.
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