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# 9.6. `random` — Generate pseudo-random numbers

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.

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()`, and `setstate()` methods. Optionally, a new generator can supply a `getrandbits()` method — this allows `randrange()` to produce selections over an arbitrarily large range.

Bookkeeping functions:

`random.``seed`([x])

  Initialize the basic random number generator. Optional argument x can be any hashable object. If x is omitted or `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).

  If x is not `None` or an int, `hash(x)` is used instead. If x is an int, x is used directly.

`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 `setstate()` 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`([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.

`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)`.

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`.

`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.``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.

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]

See also

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.

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