| :mod:`random` --- Generate pseudo-random numbers |
| ================================================ |
| |
| .. module:: random |
| :synopsis: Generate pseudo-random numbers with various common distributions. |
| |
| **Source code:** :source:`Lib/random.py` |
| |
| -------------- |
| |
| This module implements pseudo-random number generators for various |
| distributions. |
| |
| For integers, there is uniform selection from a range. For sequences, there is |
| 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 :func:`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 :class:`random.Random` class. You can instantiate your own |
| instances of :class:`Random` to get generators that don't share state. |
| |
| Class :class:`Random` can also be subclassed if you want to use a different |
| basic generator of your own devising: in that case, override the :meth:`random`, |
| :meth:`seed`, :meth:`getstate`, and :meth:`setstate` methods. |
| Optionally, a new generator can supply a :meth:`getrandbits` method --- this |
| allows :meth:`randrange` to produce selections over an arbitrarily large range. |
| |
| The :mod:`random` module also provides the :class:`SystemRandom` class which |
| uses the system function :func:`os.urandom` to generate random numbers |
| from sources provided by the operating system. |
| |
| |
| Bookkeeping functions: |
| |
| .. function:: seed([x], version=2) |
| |
| Initialize the random number generator. |
| |
| If *x* 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 :func:`os.urandom` function for details |
| on availability). |
| |
| If *x* is an int, it is used directly. |
| |
| With version 2 (the default), a :class:`str`, :class:`bytes`, or :class:`bytearray` |
| object gets converted to an :class:`int` and all of its bits are used. With version 1, |
| the :func:`hash` of *x* is used instead. |
| |
| .. versionchanged:: 3.2 |
| Moved to the version 2 scheme which uses all of the bits in a string seed. |
| |
| .. function:: getstate() |
| |
| Return an object capturing the current internal state of the generator. This |
| object can be passed to :func:`setstate` to restore the state. |
| |
| |
| .. function:: setstate(state) |
| |
| *state* should have been obtained from a previous call to :func:`getstate`, and |
| :func:`setstate` restores the internal state of the generator to what it was at |
| the time :func:`getstate` was called. |
| |
| |
| .. function:: 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, :meth:`getrandbits` enables |
| :meth:`randrange` to handle arbitrarily large ranges. |
| |
| |
| Functions for integers: |
| |
| .. function:: 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 :func:`range`. Keyword arguments |
| should not be used because the function may use them in unexpected ways. |
| |
| .. versionchanged:: 3.2 |
| :meth:`randrange` is more sophisticated about producing equally distributed |
| values. Formerly it used a style like ``int(random()*n)`` which could produce |
| slightly uneven distributions. |
| |
| .. function:: randint(a, b) |
| |
| Return a random integer *N* such that ``a <= N <= b``. Alias for |
| ``randrange(a, b+1)``. |
| |
| |
| Functions for sequences: |
| |
| .. function:: choice(seq) |
| |
| Return a random element from the non-empty sequence *seq*. If *seq* is empty, |
| raises :exc:`IndexError`. |
| |
| |
| .. function:: 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 :func:`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. |
| |
| |
| .. function:: 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 :term:`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 :func:`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. |
| |
| |
| .. function:: random() |
| |
| Return the next random floating point number in the range [0.0, 1.0). |
| |
| |
| .. function:: 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()``. |
| |
| |
| .. function:: 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. |
| |
| |
| .. function:: betavariate(alpha, beta) |
| |
| Beta distribution. Conditions on the parameters are ``alpha > 0`` and |
| ``beta > 0``. Returned values range between 0 and 1. |
| |
| |
| .. function:: 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. |
| |
| |
| .. function:: 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 |
| |
| |
| .. function:: gauss(mu, sigma) |
| |
| Gaussian distribution. *mu* is the mean, and *sigma* is the standard |
| deviation. This is slightly faster than the :func:`normalvariate` function |
| defined below. |
| |
| |
| .. function:: 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. |
| |
| |
| .. function:: normalvariate(mu, sigma) |
| |
| Normal distribution. *mu* is the mean, and *sigma* is the standard deviation. |
| |
| |
| .. function:: 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*. |
| |
| |
| .. function:: paretovariate(alpha) |
| |
| Pareto distribution. *alpha* is the shape parameter. |
| |
| |
| .. function:: weibullvariate(alpha, beta) |
| |
| Weibull distribution. *alpha* is the scale parameter and *beta* is the shape |
| parameter. |
| |
| |
| Alternative Generator: |
| |
| .. class:: SystemRandom([seed]) |
| |
| Class that uses the :func:`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 :meth:`seed` method has no effect and is ignored. |
| The :meth:`getstate` and :meth:`setstate` methods raise |
| :exc:`NotImplementedError` if called. |
| |
| |
| .. seealso:: |
| |
| 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 |
| <http://code.activestate.com/recipes/576707/>`_ for a compatible alternative |
| random number generator with a long period and comparatively simple update |
| operations. |
| |
| |
| 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 :meth:`random` method will continue to produce the same |
| sequence when the compatible seeder is given the same seed. |
| |
| .. _random-examples: |
| |
| Examples and Recipes |
| -------------------- |
| |
| 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.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 :func:`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)] |
| >>> random.choice(population) |
| 'Green' |
| |
| A more general approach is to arrange the weights in a cumulative distribution |
| with :func:`itertools.accumulate`, and then locate the random value with |
| :func:`bisect.bisect`:: |
| |
| >>> choices, weights = zip(*weighted_choices) |
| >>> cumdist = list(itertools.accumulate(weights)) |
| >>> x = random.random() * cumdist[-1] |
| >>> choices[bisect.bisect(cumdist, x)] |
| 'Blue' |