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This module implements pseudo-random number generators for variousdistributions.For integers, uniform selection from a range.For sequences, uniform selection of a random element, and a function togenerate a random permutation of a list in-place.On the real line, there are functions to compute uniform, normal (Gaussian),lognormal, negative exponential, gamma, and beta distributions.For generating distribution of angles, the circular uniform andvon Mises distributions are available.
Almost all module functions depend on the basic functionrandom(), which generates a random float uniformly inthe semi-open range [0.0, 1.0). Python uses the standard Wichmann-Hillgenerator, combining three pure multiplicative congruentialgenerators of modulus 30269, 30307 and 30323. Its period (how manynumbers it generates before repeating the sequence exactly) is6,953,607,871,644. While of much higher quality than therand()function supplied by most C libraries, the theoretical propertiesare much the same as for a single linear congruential generator oflarge modulus. It is not suitable for all purposes, and is completelyunsuitable for cryptographic purposes.
The functions in this module are not threadsafe: if you want to call thesefunctions from multiple threads, you should explicitly serialize the calls.Else, because no critical sections are implemented internally, callsfrom different threads may see the same return values.
The functions supplied by this module are actually bound methods of ahidden instance of therandom.Random class. You caninstantiate your own instances ofRandom to get generatorsthat don't share state. This is especially useful for multi-threadedprograms, creating a different instance ofRandom for eachthread, and using thejumpahead() method to ensure that thegenerated sequences seen by each thread don't overlap (see examplebelow).
ClassRandom can also be subclassed if you want to use adifferent basic generator of your own devising: in that case, overridetherandom(),seed(),getstate(),setstate() andjumpahead() methods.
Here's one way to create threadsafe distinct and non-overlapping generators:
def create_generators(num, delta, firstseed=None): """Return list of num distinct generators. Each generator has its own unique segment of delta elements from Random.random()'s full period. Seed the first generator with optional arg firstseed (default is None, to seed from current time). """ from random import Random g = Random(firstseed) result = [g] for i in range(num - 1): laststate = g.getstate() g = Random() g.setstate(laststate) g.jumpahead(delta) result.append(g) return resultgens = create_generators(10, 1000000)
That creates 10 distinct generators, which can be passed out to 10distinct threads. The generators don't share state so can be calledsafely in parallel. So long as no thread calls itsg.random()more than a million times (the second argument tocreate_generators()), the sequences seen by each thread willnot overlap. The period of the underlying Wichmann-Hill generatorlimits how far this technique can be pushed.
Just for fun, note that since we know the period,jumpahead()can also be used to ``move backward in time:''
>>> g = Random(42) # arbitrary>>> g.random()0.25420336316883324>>> g.jumpahead(6953607871644L - 1) # move *back* one>>> g.random()0.25420336316883324
Bookkeeping functions:
None, current system time is used; current system time is also used to initialize the generator when the module is first imported. Ifx is notNone or an int or long,hash(x) is used instead. Ifx is an int or long,x is used directly. Distinct values between 0 and 27814431486575L inclusive are guaranteed to yield distinct internal states (this guarantee is specific to the default Wichmann-Hill generator, and may not apply to subclasses supplying their own basic generator).Functions for integers:
range(start,stop,step). This is equivalent tochoice(range(start,stop,step)), but doesn't actually build a range object.New in version 1.5.2.a <=N <=b.Functions for sequences:
Note that for even rather smalllen(x), the total number of permutations ofx is larger than the period of most random number generators; this implies that most permutations of a long sequence can never be generated.
The following functions generate specific real-valued distributions.Function parameters are named after the corresponding variables in thedistribution's equation, as used in common mathematical practice; most ofthese equations can be found in any statistics text.
a <=N <b.alpha > -1 andbeta > -1. Returned values range between 0 and 1.mean -arc/2 andmean +arc/2 and are normalized to between 0 andpi.(mean +arc * (random.random() - 0.5)) % math.pi.alpha > 0 andbeta > 0.See Also:
Wichmann, B. A. & Hill, I. D., ``Algorithm AS 183: An efficient and portable pseudo-random number generator'',Applied Statistics 31 (1982) 188-190.
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