Bit Generators#
The random values produced by Generator
originate in a BitGenerator. The BitGenerators do not directly provide
random numbers and only contains methods used for seeding, getting or
setting the state, jumping or advancing the state, and for accessing
low-level wrappers for consumption by code that can efficiently
access the functions provided, e.g., numba.
Supported BitGenerators#
The included BitGenerators are:
PCG-64 - The default. A fast generator that can be advanced by an arbitrary amount. See the documentation for
advance. PCG-64 has a period of \(2^{128}\). See the PCG author’s page for more details about this class of PRNG.PCG-64 DXSM - An upgraded version of PCG-64 with better statistical properties in parallel contexts. See Upgrading PCG64 with PCG64DXSM for more information on these improvements.
MT19937 - The standard Python BitGenerator. Adds a
MT19937.jumpedfunction that returns a new generator with state as-if \(2^{128}\) draws have been made.Philox - A counter-based generator capable of being advanced an arbitrary number of steps or generating independent streams. See the Random123 page for more details about this class of bit generators.
SFC64 - A fast generator based on random invertible mappings. Usually the fastest generator of the four. See the SFC author’s page for (a little) more detail.
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Base Class for generic BitGenerators, which provide a stream of random bits based on different algorithms. |
Seeding and Entropy#
A BitGenerator provides a stream of random values. In order to generate
reproducible streams, BitGenerators support setting their initial state via a
seed. All of the provided BitGenerators will take an arbitrary-sized
non-negative integer, or a list of such integers, as a seed. BitGenerators
need to take those inputs and process them into a high-quality internal state
for the BitGenerator. All of the BitGenerators in numpy delegate that task to
SeedSequence, which uses hashing techniques to ensure that even low-quality
seeds generate high-quality initial states.
from numpy.random import PCG64
bg = PCG64(12345678903141592653589793)
SeedSequence is designed to be convenient for implementing best practices.
We recommend that a stochastic program defaults to using entropy from the OS so
that each run is different. The program should print out or log that entropy.
In order to reproduce a past value, the program should allow the user to
provide that value through some mechanism, a command-line argument is common,
so that the user can then re-enter that entropy to reproduce the result.
SeedSequence can take care of everything except for communicating with the
user, which is up to you.
from numpy.random import PCG64, SeedSequence
# Get the user's seed somehow, maybe through `argparse`.
# If the user did not provide a seed, it should return `None`.
seed = get_user_seed()
ss = SeedSequence(seed)
print('seed = {}'.format(ss.entropy))
bg = PCG64(ss)
We default to using a 128-bit integer using entropy gathered from the OS. This is a good amount of entropy to initialize all of the generators that we have in numpy. We do not recommend using small seeds below 32 bits for general use. Using just a small set of seeds to instantiate larger state spaces means that there are some initial states that are impossible to reach. This creates some biases if everyone uses such values.
There will not be anything wrong with the results, per se; even a seed of
0 is perfectly fine thanks to the processing that SeedSequence does. If you
just need some fixed value for unit tests or debugging, feel free to use
whatever seed you like. But if you want to make inferences from the results or
publish them, drawing from a larger set of seeds is good practice.
If you need to generate a good seed “offline”, then SeedSequence().entropy
or using secrets.randbits(128) from the standard library are both
convenient ways.
If you need to run several stochastic simulations in parallel, best practice
is to construct a random generator instance for each simulation.
To make sure that the random streams have distinct initial states, you can use
the spawn method of SeedSequence. For instance, here we construct a list
of 12 instances:
from numpy.random import PCG64, SeedSequence
# High quality initial entropy
entropy = 0x87351080e25cb0fad77a44a3be03b491
base_seq = SeedSequence(entropy)
child_seqs = base_seq.spawn(12) # a list of 12 SeedSequences
generators = [PCG64(seq) for seq in child_seqs]
An alternative way is to use the fact that a SeedSequence can be initialized
by a tuple of elements. Here we use a base entropy value and an integer
worker_id
from numpy.random import PCG64, SeedSequence
# High quality initial entropy
entropy = 0x87351080e25cb0fad77a44a3be03b491
sequences = [SeedSequence((entropy, worker_id)) for worker_id in range(12)]
generators = [PCG64(seq) for seq in sequences]
Note that the sequences produced by the latter method will be distinct from
those constructed via spawn.
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SeedSequence mixes sources of entropy in a reproducible way to set the initial state for independent and very probably non-overlapping BitGenerators. |