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.

Pour les entiers, il existe une sélection uniforme à partir d’une plage. Pour les séquences, il existe une sélection uniforme d’un élément aléatoire, une fonction pour générer une permutation aléatoire d’une liste sur place et une fonction pour un échantillonnage aléatoire sans remplacement.

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.

Les fonctions fournies par ce module dépendent en réalité de méthodes d’une instance cachée de la classe random.Random. Vous pouvez créer vos propres instances de Random pour obtenir des générateurs sans états partagés.

La classe Random peut également être sous-classée si vous voulez utiliser un générateur de base différent, de votre propre conception. Dans ce cas, remplacez les méthodes random(), seed(), gettsate() et setstate(). En option, un nouveau générateur peut fournir une méthode getrandbits() — ce qui permet à randrange() de produire des sélections sur une plage de taille arbitraire.

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.

Bookkeeping functions:

random.seed(a=None, version=2)

Initialize the random number generator.

If a is omitted or None, the current system time is used. 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).

If a is an int, it is used directly.

With version 2 (the default), a str, bytes, or bytearray object gets converted to an int and all of its bits are used.

With version 1 (provided for reproducing random sequences from older versions of Python), the algorithm for str and bytes generates a narrower range of seeds.

Modifié dans la version 3.2: Moved to the version 2 scheme which uses all of the bits in a string seed.

random.getstate()

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

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.

random.getrandbits(k)

Returns a Python integer 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.

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.

The positional argument pattern matches that of range(). Keyword arguments should not be used because the function may use them in unexpected ways.

Modifié dans la version 3.2: randrange() is more sophisticated about producing equally distributed values. Formerly it used a style like int(random()*n) which could produce slightly uneven distributions.

random.randint(a, b)

Return a random integer N such that a <= N <= b. Alias for randrange(a, b+1).

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 or set. Used for random sampling without replacement.

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 range() object as an argument. This is especially fast and space efficient for sampling from a large population: sample(range(10000000), 60).

If the sample size is larger than the population size, a ValueError is raised.

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.

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 Generator:

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() method has no effect and is ignored. The getstate() and setstate() methods raise NotImplementedError if called.

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.

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

9.6.1. Notes on Reproducibility

Sometimes it is useful to be able to reproduce the sequences given by a pseudo random number generator. By re-using a seed value, the same sequence should be reproducible from run to run as long as multiple threads are not running.

Most of the random module’s algorithms and seeding functions are subject to change across Python versions, but two aspects are guaranteed not to change:

  • If a new seeding method is added, then a backward compatible seeder will be offered.
  • The generator’s random() method will continue to produce the same sequence when the compatible seeder is given the same seed.

9.6.2. Exemples et Recettes

Utilisation basique :

>>> 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.randrange(10)                 # Integer from 0 to 9
7

>>> random.randrange(0, 101, 2)          # Even integer from 0 to 100
26

>>> random.choice('abcdefghij')          # Single 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)   # Three samples without replacement
[4, 1, 5]

A common task is to make a random.choice() with weighted probabilities.

If the weights are small integer ratios, a simple technique is to build a sample population with repeats:

>>> weighted_choices = [('Red', 3), ('Blue', 2), ('Yellow', 1), ('Green', 4)]
>>> population = [val for val, cnt in weighted_choices for i in range(cnt)]
>>> population
['Red', 'Red', 'Red', 'Blue', 'Blue', 'Yellow', 'Green', 'Green', 'Green', 'Green']

>>> random.choice(population)
'Green'

A more general approach is to arrange the weights in a cumulative distribution with itertools.accumulate(), and then locate the random value with bisect.bisect():

>>> choices, weights = zip(*weighted_choices)
>>> cumdist = list(itertools.accumulate(weights))
>>> cumdist            # [3, 3+2, 3+2+1, 3+2+1+4]
[3, 5, 6, 10]

>>> x = random.random() * cumdist[-1]
>>> choices[bisect.bisect(cumdist, x)]
'Blue'