Random sampling (numpy.random) — NumPy v2.0 Manual (2024)

Quick start#

The numpy.random module implements pseudo-random number generators(PRNGs or RNGs, for short) with the ability to draw samples from a variety ofprobability distributions. In general, users will create a Generator instancewith default_rng and call the various methods on it to obtain samples fromdifferent distributions.

>>> import numpy as np>>> rng = np.random.default_rng()# Generate one random float uniformly distributed over the range [0, 1)>>> rng.random() 0.06369197489564249 # may vary# Generate an array of 10 numbers according to a unit Gaussian distribution.>>> rng.standard_normal(10) array([-0.31018314, -1.8922078 , -0.3628523 , -0.63526532, 0.43181166, # may vary 0.51640373, 1.25693945, 0.07779185, 0.84090247, -2.13406828])# Generate an array of 5 integers uniformly over the range [0, 10).>>> rng.integers(low=0, high=10, size=5) array([8, 7, 6, 2, 0]) # may vary

Our RNGs are deterministic sequences and can be reproduced by specifying a seed integer toderive its initial state. By default, with no seed provided, default_rng willseed the RNG from nondeterministic data from the operating system and thereforegenerate different numbers each time. The pseudo-random sequences will beindependent for all practical purposes, at least those purposes for which ourpseudo-randomness was good for in the first place.

>>> rng1 = np.random.default_rng()>>> rng1.random() 0.6596288841243357 # may vary>>> rng2 = np.random.default_rng()>>> rng2.random() 0.11885628817151628 # may vary

Seeds should be large positive integers. default_rng can take positiveintegers of any size. We recommend using very large, unique numbers to ensurethat your seed is different from anyone else’s. This is good practice to ensurethat your results are statistically independent from theirs unless you areintentionally trying to reproduce their result. A convenient way to getsuch a seed number is to use secrets.randbits to get anarbitrary 128-bit integer.

>>> import secrets>>> import numpy as np>>> secrets.randbits(128) 122807528840384100672342137672332424406 # may vary>>> rng1 = np.random.default_rng(122807528840384100672342137672332424406)>>> rng1.random()0.5363922081269535>>> rng2 = np.random.default_rng(122807528840384100672342137672332424406)>>> rng2.random()0.5363922081269535

See the documentation on default_rng and SeedSequence for more advancedoptions for controlling the seed in specialized scenarios.

Generator and its associated infrastructure was introduced in NumPy version1.17.0. There is still a lot of code that uses the older RandomState and thefunctions in numpy.random. While there are no plans to remove them at thistime, we do recommend transitioning to Generator as you can. The algorithmsare faster, more flexible, and will receive more improvements in the future.For the most part, Generator can be used as a replacement for RandomState.See Legacy random generation for information on the legacy infrastructure,What’s new or different for information on transitioning, and NEP 19 for some of the reasoning for the transition.

Design#

Users primarily interact with Generator instances. Each Generator instanceowns a BitGenerator instance that implements the core RNG algorithm. TheBitGenerator has a limited set of responsibilities. It manages state andprovides functions to produce random doubles and random unsigned 32- and 64-bitvalues.

The Generator takes the bit generator-provided stream and transforms theminto more useful distributions, e.g., simulated normal random values. Thisstructure allows alternative bit generators to be used with little codeduplication.

NumPy implements several different BitGenerator classes implementingdifferent RNG algorithms. default_rng currently uses PCG64 as thedefault BitGenerator. It has better statistical properties and performancethan the MT19937 algorithm used in the legacy RandomState. SeeBit generators for more details on the supported BitGenerators.

default_rng and BitGenerators delegate the conversion of seeds into RNGstates to SeedSequence internally. SeedSequence implements a sophisticatedalgorithm that intermediates between the user’s input and the internalimplementation details of each BitGenerator algorithm, each of which canrequire different amounts of bits for its state. Importantly, it lets you usearbitrary-sized integers and arbitrary sequences of such integers to mixtogether into the RNG state. This is a useful primitive for constructinga flexible pattern for parallel RNG streams.

For backward compatibility, we still maintain the legacy RandomState class.It continues to use the MT19937 algorithm by default, and old seeds continueto reproduce the same results. The convenience Functions in numpy.randomare still aliases to the methods on a single global RandomState instance. SeeLegacy random generation for the complete details. See What’s new or different fora detailed comparison between Generator and RandomState.

Concepts#

Features#