9.6. random — Génère des nombres pseudo-aléatoires

Code source : Lib/random.py

Ce module implémente des générateurs de nombres pseudo-aléatoires pour différentes 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.

Pour l’ensemble des réels, il y a des fonctions pour calculer des distributions uniformes, normales (gaussiennes), log-normales, exponentielles négatives, gamma et bêta. Pour générer des distributions d’angles, la distribution de von Mises est disponible.

Presque toutes les fonctions du module dépendent de la fonction de base random(), qui génère un nombre à virgule flottante aléatoire de façon uniforme dans la plage semi-ouverte [0.0, 1.0). Python utilise l’algorithme Mersenne Twister comme générateur de base. Il produit des flottants de précision de 53 bits et a une période de 2***19937-1. L’implémentation sous-jacente en C est à la fois rapide et compatible avec les programmes ayant de multiples fils d’exécution. Le Mersenne Twister est l’un des générateurs de nombres aléatoires les plus largement testés qui existent. Cependant, étant complètement déterministe, il n’est pas adapté à tous les usages et est totalement inadapté à des fins cryptographiques.

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 getrandbits() method — this allows randrange() to produce selections over an arbitrarily large range.

Nouveau dans la version 2.4: the getrandbits() 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.

Modifié dans la version 2.3: MersenneTwister replaced Wichmann-Hill as the default generator.

The random module also provides the SystemRandom class which uses the system function os.urandom() to generate random numbers from sources provided by the operating system.

Avertissement

The pseudo-random generators of this module should not be used for security purposes. Use os.urandom() or SystemRandom if you require a cryptographically secure pseudo-random number generator.

Bookkeeping functions:

random.seed(a=None)

Initialize internal state of the random number generator.

None or no argument seeds from current time or from an operating system specific randomness source if available (see the os.urandom() function for details on availability).

If a is not None or an int or a long, then hash(a) is used instead. Note that the hash values for some types are nondeterministic when PYTHONHASHSEED is enabled.

Modifié dans la version 2.4: formerly, operating system resources were not used.

random.getstate()

Return an object capturing the current internal state of the generator. This object can be passed to setstate() to restore the state.

Nouveau dans la version 2.1.

Modifié dans la version 2.6: State values produced in Python 2.6 cannot be loaded into earlier versions.

random.setstate(state)

state should have been obtained from a previous call to getstate(), and setstate() restores the internal state of the generator to what it was at the time getstate() was called.

Nouveau dans la version 2.1.

random.jumpahead(n)

Change the internal state to one different from and likely far away from the current state. n is a non-negative integer which is used to scramble the current state vector. This is most useful in multi-threaded programs, in conjunction with multiple instances of the Random class: setstate() or seed() can be used to force all instances into the same internal state, and then jumpahead() can be used to force the instances” states far apart.

Nouveau dans la version 2.1.

Modifié dans la version 2.3: Instead of jumping to a specific state, n steps ahead, jumpahead(n) jumps to another state likely to be separated by many steps.

random.getrandbits(k)

Returns a python long int with k random bits. This method is supplied with the MersenneTwister generator and some other generators may also provide it as an optional part of the API. When available, getrandbits() enables randrange() to handle arbitrarily large ranges.

Nouveau dans la version 2.4.

Functions for integers:

random.randrange(stop)
random.randrange(start, stop[, step])

Return a randomly selected element from range(start, stop, step). This is equivalent to choice(range(start, stop, step)), but doesn’t actually build a range object.

Nouveau dans la version 1.5.2.

random.randint(a, b)

Return a random integer N such that a <= N <= b.

Functions for sequences:

random.choice(seq)

Return a random element from the non-empty sequence seq. If seq is empty, raises IndexError.

random.shuffle(x[, random])

Shuffle the sequence x in place. The optional argument random is a 0-argument function returning a random float in [0.0, 1.0); by default, this is the function random().

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.

random.sample(population, k)

Return a k length list of unique elements chosen from the population sequence. Used for random sampling without replacement.

Nouveau dans la version 2.3.

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: sample(xrange(10000000), 60).

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.

random.random()

Return the next random floating point number in the range [0.0, 1.0).

random.uniform(a, b)

Return a random floating point number N such that a <= N <= b for a <= b and b <= N <= a for b < a.

The end-point value b may or may not be included in the range depending on floating-point rounding in the equation a + (b-a) * random().

random.triangular(low, high, mode)

Return a random floating point number N such that low <= N <= high and with the specified mode between those bounds. The low and high bounds default to zero and one. The mode argument defaults to the midpoint between the bounds, giving a symmetric distribution.

Nouveau dans la version 2.6.

random.betavariate(alpha, beta)

Beta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1.

random.expovariate(lambd)

Exponential distribution. lambd is 1.0 divided by the desired mean. It should be nonzero. (The parameter would be called « lambda », but that is a reserved word in Python.) Returned values range from 0 to positive infinity if lambd is positive, and from negative infinity to 0 if lambd is negative.

random.gammavariate(alpha, beta)

Gamma distribution. (Not the gamma function!) Conditions on the parameters are alpha > 0 and beta > 0.

The probability distribution function is:

          x ** (alpha - 1) * math.exp(-x / beta)
pdf(x) =  --------------------------------------
            math.gamma(alpha) * beta ** alpha
random.gauss(mu, sigma)

Gaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function defined below.

random.lognormvariate(mu, sigma)

Log normal distribution. If you take the natural logarithm of this distribution, you’ll get a normal distribution with mean mu and standard deviation sigma. mu can have any value, and sigma must be greater than zero.

random.normalvariate(mu, sigma)

Normal distribution. mu is the mean, and sigma is the standard deviation.

random.vonmisesvariate(mu, kappa)

mu is the mean angle, expressed in radians between 0 and 2*pi, and kappa is the concentration parameter, which must be greater than or equal to zero. If kappa is equal to zero, this distribution reduces to a uniform random angle over the range 0 to 2*pi.

random.paretovariate(alpha)

Pareto distribution. alpha is the shape parameter.

random.weibullvariate(alpha, beta)

Weibull distribution. alpha is the scale parameter and beta is the shape parameter.

Alternative Generators:

class random.WichmannHill([seed])

Class that implements the Wichmann-Hill algorithm as the core generator. Has all of the same methods as Random plus the whseed() method described below. Because this class is implemented in pure Python, it is not threadsafe and may require locks between calls. The period of the generator is 6,953,607,871,644 which is small enough to require care that two independent random sequences do not overlap.

random.whseed([x])

This is obsolete, supplied for bit-level compatibility with versions of Python prior to 2.1. See seed() for details. whseed() does not guarantee that distinct integer arguments yield distinct internal states, and can yield no more than about 2**24 distinct internal states in all.

class random.SystemRandom([seed])

Class that uses the os.urandom() function for generating random numbers from sources provided by the operating system. Not available on all systems. Does not rely on software state and sequences are not reproducible. Accordingly, the seed() and jumpahead() methods have no effect and are ignored. The getstate() and setstate() methods raise NotImplementedError if called.

Nouveau dans la version 2.4.

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]

Voir aussi

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.

Complementary-Multiply-with-Carry recipe for a compatible alternative random number generator with a long period and comparatively simple update operations.