Random sampling (numpy.random)

Numpy’s random number routines produce pseudo random numbers using combinations of a BitGenerator to create sequences and a Generator to use those sequences to sample from different statistical distributions:

• BitGenerators: Objects that generate random numbers. These are typically unsigned integer words filled with sequences of either 32 or 64 random bits.
• Generators: Objects that transform sequences of random bits from a BitGenerator into sequences of numbers that follow a specific probability distribution (such as uniform, Normal or Binomial) within a specified interval.

Since Numpy version 1.17.0 the Generator can be initialized with a number of different BitGenerators. It exposes many different probability distributions. See NEP 19 for context on the updated random Numpy number routines. The legacy RandomState random number routines are still available, but limited to a single BitGenerator.

For convenience and backward compatibility, a single RandomState instance’s methods are imported into the numpy.random namespace, see Legacy Random Generation for the complete list.

Quick Start

By default, Generator uses bits provided by PCG64 which has better statistical properties than the legacy mt19937 random number generator in RandomState.

# Uses the old numpy.random.RandomState
from numpy import random
random.standard_normal()

Generator can be used as a direct replacement for RandomState, although the random values are generated by PCG64. The Generator holds an instance of a BitGenerator. It is accessible as gen.bit_generator.

# As replacement for RandomState(); default_rng() instantiates Generator with
# the default PCG64 BitGenerator.
from numpy.random import default_rng
rg = default_rng()
rg.standard_normal()
rg.bit_generator

Seeds can be passed to any of the BitGenerators. The provided value is mixed via SeedSequence to spread a possible sequence of seeds across a wider range of initialization states for the BitGenerator. Here PCG64 is used and is wrapped with a Generator.

from numpy.random import Generator, PCG64
rg = Generator(PCG64(12345))
rg.standard_normal()

Introduction

The new infrastructure takes a different approach to producing random numbers from the RandomState object. Random number generation is separated into two components, a bit generator and a random generator.

The BitGenerator has a limited set of responsibilities. It manages state and provides functions to produce random doubles and random unsigned 32- and 64-bit values.

The random generator takes the bit generator-provided stream and transforms them into more useful distributions, e.g., simulated normal random values. This structure allows alternative bit generators to be used with little code duplication.

The Generator is the user-facing object that is nearly identical to RandomState. The canonical method to initialize a generator passes a PCG64 bit generator as the sole argument.

from numpy.random import default_rng
rg = default_rng(12345)
rg.random()

One can also instantiate Generator directly with a BitGenerator instance. To use the older MT19937 algorithm, one can instantiate it directly and pass it to Generator.

from numpy.random import Generator, MT19937
rg = Generator(MT19937(12345))
rg.random()

What’s New or Different

Warning

The Box-Muller method used to produce NumPy’s normals is no longer available in Generator. It is not possible to reproduce the exact random values using Generator for the normal distribution or any other distribution that relies on the normal such as the RandomState.gamma or RandomState.standard_t. If you require bitwise backward compatible streams, use RandomState.

• The Generator’s normal, exponential and gamma functions use 256-step Ziggurat methods which are 2-10 times faster than NumPy’s Box-Muller or inverse CDF implementations.
• Optional dtype argument that accepts np.float32 or np.float64 to produce either single or double prevision uniform random variables for select distributions
• Optional out argument that allows existing arrays to be filled for select distributions
• random_entropy provides access to the system source of randomness that is used in cryptographic applications (e.g., /dev/urandom on Unix).
• All BitGenerators can produce doubles, uint64s and uint32s via CTypes (ctypes) and CFFI (cffi). This allows the bit generators to be used in numba.
• The bit generators can be used in downstream projects via Cython.
• integers is now the canonical way to generate integer random numbers from a discrete uniform distribution. The rand and randn methods are only available through the legacy RandomState. The endpoint keyword can be used to specify open or closed intervals. This replaces both randint and the deprecated random_integers.
• random is now the canonical way to generate floating-point random numbers, which replaces RandomState.random_sample, RandomState.sample, and RandomState.ranf. This is consistent with Python’s random.random.
• All BitGenerators in numpy use SeedSequence to convert seeds into initialized states.

See What’s New or Different for a complete list of improvements and differences from the traditional Randomstate.

Parallel Generation

The included generators can be used in parallel, distributed applications in one of three ways:

• SeedSequence spawning
• Independent Streams
• Jumping the BitGenerator state

Concepts

• Random Generator
• legacy mtrand
• Bit Generators
• Seeding and Entropy

Features

• Parallel Applications
  • SeedSequence spawning
  • Independent Streams
  • Jumping the BitGenerator state
• Multithreaded Generation
• What’s New or Different
• Comparing Performance
  • Recommendation
  • Timings
  • Performance on different Operating Systems
• Extending
  • Numba
  • Cython
  • New Basic RNGs
• Reading System Entropy

Original Source

This package was developed independently of NumPy and was integrated in version 1.17.0. The original repo is at https://github.com/bashtage/randomgen.