randomstate 1.14.0

Introduction

This is a library and generic interface for alternative random generators in Python and NumPy.

Features

• Immediate drop in replacement for NumPy’s RandomState

# import numpy.random as rnd
import randomstate as rnd
x = rnd.standard_normal(100)
y = rnd.random_sample(100)
z = rnd.randn(10,10)

• Default random generator is identical to NumPy’s RandomState (i.e., same seed, same random numbers).

• Support for random number generators that support independent streams and jumping ahead so that sub-streams can be generated

• Faster random number generation, especially for normal, standard exponential and standard gamma using the Ziggurat method

import randomstate as rnd
w = rnd.standard_normal(10000, method='zig')
x = rnd.standard_exponential(10000, method='zig')
y = rnd.standard_gamma(5.5, 10000, method='zig')

• Support for 32-bit floating randoms for core generators. Currently supported:

  • Uniforms (random_sample)

  • Exponentials (standard_exponential, both Inverse CDF and Ziggurat)

  • Normals (standard_normal, both Box-Muller and Ziggurat)

  • Standard Gammas (via standard_gamma, both Inverse CDF and Ziggurat)

WARNING: The 32-bit generators are experimental and subject to change.

Note: There are no plans to extend the alternative precision generation to all random number types.

• Support for filling existing arrays using out keyword argument. Currently supported in (both 32- and 64-bit outputs)

  • Uniforms (random_sample)

  • Exponentials (standard_exponential)

  • Normals (standard_normal)

  • Standard Gammas (via standard_gamma)

Included Pseudo Random Number Generators

This modules includes a number of alternative random number generators in addition to the MT19937 that is included in NumPy. The RNGs include:

• MT19937, the NumPy rng

• dSFMT a SSE2-aware version of the MT19937 generator that is especially fast at generating doubles

• SFMT a SSE2-aware version of the MT19937 generator that is optimized for integer values

• xorshift128+, xoroshiro128+ and xorshift1024*

• PCG32 and PCG64

• MRG32K3A

• A multiplicative lagged fibonacci generator (LFG(63, 1279, 861, *))

Differences from numpy.random.RandomState

Status

• Complete drop-in replacement for numpy.random.RandomState. The mt19937 generator is identical to numpy.random.RandomState, and will produce an identical sequence of random numbers for a given seed.

• Builds and passes all tests on:

• Linux 32/64 bit, Python 2.7, 3.4, 3.5, 3.6 (probably works on 2.6 and 3.3)

• PC-BSD (FreeBSD) 64-bit, Python 2.7

• OSX 64-bit, Python 2.7

• Windows 32/64 bit (only tested on Python 2.7, 3.5 and 3.6, but should work on 3.3/3.4)

Version

The version matched the latest version of NumPy where randomstate.prng.mt19937 passes all NumPy test.

Documentation

An occasionally updated build of the documentation is available on my github pages.

Plans

This module is essentially complete. There are a few rough edges that need to be smoothed.

• Stream support for MLFG

• Creation of additional streams from a RandomState where supported (i.e. a next_stream() method)

Requirements

Building requires:

• Python (2.7, 3.4, 3.5, 3.6)

• NumPy (1.9, 1.10, 1.11, 1.12)

• Cython (0.22, not 0.23, 0.24, 0.25)

• tempita (0.5+), if not provided by Cython

Testing requires pytest (3.0+).

Note: it might work with other versions but only tested with these versions.

Development and Testing

Basic tests are in place for all RNGs. The MT19937 is tested against NumPy’s implementation for identical results. It also passes NumPy’s test suite.

Installing

python setup.py install

python setup.py install --no-sse2

Using

The separate generators are importable from randomstate.prng.

import randomstate
rs = randomstate.prng.xorshift128.RandomState()
rs.random_sample(100)

rs = randomstate.prng.pcg64.RandomState()
rs.random_sample(100)

# Identical to NumPy
rs = randomstate.prng.mt19937.RandomState()
rs.random_sample(100)

Like NumPy, randomstate also exposes a single instance of the mt19937 generator directly at the module level so that commands like

import randomstate
randomstate.standard_normal()
randomstate.exponential(1.0, 1.0, size=10)

will work.

License

Standard NCSA, plus sub licenses for components.

Performance

Performance is promising, and even the mt19937 seems to be faster than NumPy’s mt19937.

Speed-up relative to NumPy (Uniform Doubles)
************************************************************
randomstate.prng-dsfmt-random_sample               313.5%
randomstate.prng-mlfg_1279_861-random_sample       459.4%
randomstate.prng-mrg32k3a-random_sample            -57.6%
randomstate.prng-mt19937-random_sample              72.5%
randomstate.prng-pcg32-random_sample               232.8%
randomstate.prng-pcg64-random_sample               330.6%
randomstate.prng-xoroshiro128plus-random_sample    609.9%
randomstate.prng-xorshift1024-random_sample        348.8%
randomstate.prng-xorshift128-random_sample         489.7%

Speed-up relative to NumPy (Normals using Box-Muller)
************************************************************
randomstate.prng-dsfmt-standard_normal                26.8%
randomstate.prng-mlfg_1279_861-standard_normal        30.9%
randomstate.prng-mrg32k3a-standard_normal            -14.8%
randomstate.prng-mt19937-standard_normal              17.7%
randomstate.prng-pcg32-standard_normal                24.5%
randomstate.prng-pcg64-standard_normal                26.2%
randomstate.prng-xoroshiro128plus-standard_normal     31.4%
randomstate.prng-xorshift1024-standard_normal         27.4%
randomstate.prng-xorshift128-standard_normal          30.3%

Speed-up relative to NumPy (Normals using Ziggurat)
************************************************************
randomstate.prng-dsfmt-standard_normal               491.7%
randomstate.prng-mlfg_1279_861-standard_normal       439.6%
randomstate.prng-mrg32k3a-standard_normal            101.2%
randomstate.prng-mt19937-standard_normal             354.4%
randomstate.prng-pcg32-standard_normal               531.0%
randomstate.prng-pcg64-standard_normal               517.9%
randomstate.prng-xoroshiro128plus-standard_normal    674.0%
randomstate.prng-xorshift1024-standard_normal        486.7%
randomstate.prng-xorshift128-standard_normal         617.0%