This module implements pseudo-random number generators for various distributions.
For integers, uniform selection from a range. For sequences, uniform selection of a random element, a function to generate a random permutation of a list in-place, and a function for random sampling without replacement.
On the real line, there are functions to compute uniform, normal (Gaussian), lognormal, negative exponential, gamma, and beta distributions. For generating distributions of angles, the von Mises distribution is available.
Almost all module functions depend on the basic function random(), which generates a random float uniformly in the semi-open range [0.0, 1.0). Python uses the Mersenne Twister as the core generator. It produces 53-bit precision floats and has a period of 2**19937-1. The underlying implementation in C is both fast and threadsafe. The Mersenne Twister is one of the most extensively tested random number generators in existence. However, being completely deterministic, it is not suitable for all purposes, and is completely unsuitable for cryptographic purposes.
The functions supplied by this module are actually bound methods of a hidden instance of the random.Random class. You can instantiate your own instances of Random to get generators that don't share state. This is especially useful for multi-threaded programs, creating a different instance of Random for each thread, and using the jumpahead() method to make it likely that the generated sequences seen by each thread don't overlap.
Class Random can also be subclassed if you want to use a different basic generator of your own devising: in that case, override the random(), seed(), getstate(), setstate() and jumpahead() methods. Optionally, a new generator can supply a getrandombits() method -- this allows randrange() to produce selections over an arbitrarily large range. New in version 2.4: the getrandombits() method.
As an example of subclassing, the random module provides the WichmannHill class that implements an alternative generator in pure Python. The class provides a backward compatible way to reproduce results from earlier versions of Python, which used the Wichmann-Hill algorithm as the core generator. Note that this Wichmann-Hill generator can no longer be recommended: its period is too short by contemporary standards, and the sequence generated is known to fail some stringent randomness tests. See the references below for a recent variant that repairs these flaws. Changed in version 2.3: Substituted MersenneTwister for Wichmann-Hill.
None, current system time is used; current system time is also used to initialize the generator when the module is first imported. If randomness sources are provided by the operating system, they are used instead of the system time (see the os.urandom() function for details on availability). Changed in version 2.4: formerly, operating system resources were not used. If x is not
Noneor an int or long,
hash(x)is used instead. If x is an int or long, x is used directly.
Functions for integers:
|[start,] stop[, step])|
range(start, stop, step). This is equivalent to
choice(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 small
len(x), the total
number of permutations of x is larger than the period of most
random number generators; this implies that most permutations of a
long sequence can never be generated.
Returns a new list containing elements from the population while leaving the original population unchanged. The resulting list is in selection order so that all sub-slices will also be valid random samples. This allows raffle winners (the sample) to be partitioned into grand prize and second place winners (the subslices).
Members of the population need not be hashable or unique. If the population contains repeats, then each occurrence is a possible selection in the sample.
To choose a sample from a range of integers, use an xrange()
object as an argument. This is especially fast and space efficient for
sampling from a large population:
The following functions generate specific real-valued distributions. Function parameters are named after the corresponding variables in the distribution's equation, as used in common mathematical practice; most of these equations can be found in any statistics text.
a <= N < b.
alpha > 0and
beta > 0. Returned values range between 0 and 1.
alpha > 0and
beta > 0.
Examples of basic usage:
>>> random.random() # Random float x, 0.0 <= x < 1.0 0.37444887175646646 >>> random.uniform(1, 10) # Random float x, 1.0 <= x < 10.0 1.1800146073117523 >>> random.randint(1, 10) # Integer from 1 to 10, endpoints included 7 >>> random.randrange(0, 101, 2) # Even integer from 0 to 100 26 >>> random.choice('abcdefghij') # Choose a random element 'c' >>> items = [1, 2, 3, 4, 5, 6, 7] >>> random.shuffle(items) >>> items [7, 3, 2, 5, 6, 4, 1] >>> random.sample([1, 2, 3, 4, 5], 3) # Choose 3 elements [4, 1, 5]
M. Matsumoto and T. Nishimura, ``Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator'', ACM Transactions on Modeling and Computer Simulation Vol. 8, No. 1, January pp.3-30 1998.
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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