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A Python implementation of the mrg32k3a pseudo-random number generator.

Project description


This package provides a Python implementation of the mrg32k3a pseudo-random number generator of L'Ecuyer (1999) and L'Ecuyer et al. (2002). It extends the implementation used in PyMOSO to handle streams, substreams, and subsubstreams. The generator's period of ~2191 is split into ~250 streams of length 2141, each containing 247 substreams of length 294, each containing 247 subsubstreams of length 247.


The mrg32k3a module includes the MRG32k3a class and several useful functions for controlling the generators.

  • The MRG32k3a class is a subclass of Python's random.Random class and therefore inherits easy-to-use methods for generating random variates. E.g., if rng is an instance of the MRG32k3a class, the command rng.normalvariate(mu=2, sigma=5) generates a normal random variate with mean 2 and standard deviation 5. Normal random variates are generated via inversion using the Beasley-Springer-Moro algorithm.
  • The MRG32k3a class expands the suite of functions for random-variate generation available in random.Random to include lognormalvariate, mvnormalvariate, poissonvariate, gumbelvariate, binomialvariate. Additionally, the methods integer_random_vector_from_simplex and continuous_random_vector_from_simplex generate discrete and continuous vectors from a symmetric non-negative simplex.
  • The advance_stream, advance_substream, and advance_subsubstream functions advance the generator to the start of the next stream, substream, or subsubstream, respectively. They make use of techniques for efficiently "jumping ahead," as outlined by L'Ecuyer (1990).
  • The reset_stream, reset_substream, and reset_subsubstream functions reset the generator to the start of the current stream, substream, or subsubstream, respectively.

The matmodops module includes basic matrix/modulus operations used by the mrg32k3a module.


The mrg32k3a package is available to download through the Python Packaging Index (PyPI) and can be installed from the terminal with the following command:

python -m pip install mrg32k3a

Basic Example

After installing mrg32k3a, the package's main class (MRG32k3a) can be imported from the Python console (or in code):

from mrg32k3a.mrg32k3a import MRG32k3a

One can instantiate a random number generator set at a given stream, substream, and subsubstream triplet or seed. For example, the command

rng = MRG32k3a(s_ss_sss_index=[1, 2, 3])

creates a object of the MRG32k3a class called rng that it initialized at the start of subsubstream 3 of substream 2 of stream 1. If the argument s_ss_sss_index is not provided, the random number generator is initialized at stream-substream-subsubstream 0-0-0. (We adopt the Python convention of indexing from 0.) Alternatively, the command

rng = MRG32k3a(ref_seed=(12345, 12345, 12345, 12345, 12345, 12345))

initializes the random number generator at the state described by the length-6 tuple (12345, 12345, 12345, 12345, 12345, 12345). Streams, substreams, and subsubstreams are indexed using ref_seed as a point of reference.

After instantiating a random number generator, its methods can be invoked to generate (scalar or vector) random variates from a particular probability distribution. For example,

x = rng.normalvariate(mu=2, sigma=5)

returns a normally distributed random variate x with mean 2 and standard deviation 5.


x = rng.poissonvariate(lmdba=50)

returns a Poisson distributed random variate x with rate parameter (mean) 50.


v = rng.integer_random_vector_from_simplex(n_elements=3, summation=10, with_zero=False))

returns a random length-3 vector v of positive integers summing to 10. The vector v is uniformly distributed over the set of such vectors.


Full documentation for the mrg32k3a source code can be found here.


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