/Doc/library/random.rst

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  1. :mod:`random` --- Generate pseudo-random numbers
  2. ================================================
  3. .. module:: random
  4. :synopsis: Generate pseudo-random numbers with various common distributions.
  5. This module implements pseudo-random number generators for various
  6. distributions.
  7. For integers, uniform selection from a range. For sequences, uniform selection
  8. of a random element, a function to generate a random permutation of a list
  9. in-place, and a function for random sampling without replacement.
  10. On the real line, there are functions to compute uniform, normal (Gaussian),
  11. lognormal, negative exponential, gamma, and beta distributions. For generating
  12. distributions of angles, the von Mises distribution is available.
  13. Almost all module functions depend on the basic function :func:`random`, which
  14. generates a random float uniformly in the semi-open range [0.0, 1.0). Python
  15. uses the Mersenne Twister as the core generator. It produces 53-bit precision
  16. floats and has a period of 2\*\*19937-1. The underlying implementation in C is
  17. both fast and threadsafe. The Mersenne Twister is one of the most extensively
  18. tested random number generators in existence. However, being completely
  19. deterministic, it is not suitable for all purposes, and is completely unsuitable
  20. for cryptographic purposes.
  21. The functions supplied by this module are actually bound methods of a hidden
  22. instance of the :class:`random.Random` class. You can instantiate your own
  23. instances of :class:`Random` to get generators that don't share state. This is
  24. especially useful for multi-threaded programs, creating a different instance of
  25. :class:`Random` for each thread, and using the :meth:`jumpahead` method to make
  26. it likely that the generated sequences seen by each thread don't overlap.
  27. Class :class:`Random` can also be subclassed if you want to use a different
  28. basic generator of your own devising: in that case, override the :meth:`random`,
  29. :meth:`seed`, :meth:`getstate`, :meth:`setstate` and :meth:`jumpahead` methods.
  30. Optionally, a new generator can supply a :meth:`getrandbits` method --- this
  31. allows :meth:`randrange` to produce selections over an arbitrarily large range.
  32. .. versionadded:: 2.4
  33. the :meth:`getrandbits` method.
  34. As an example of subclassing, the :mod:`random` module provides the
  35. :class:`WichmannHill` class that implements an alternative generator in pure
  36. Python. The class provides a backward compatible way to reproduce results from
  37. earlier versions of Python, which used the Wichmann-Hill algorithm as the core
  38. generator. Note that this Wichmann-Hill generator can no longer be recommended:
  39. its period is too short by contemporary standards, and the sequence generated is
  40. known to fail some stringent randomness tests. See the references below for a
  41. recent variant that repairs these flaws.
  42. .. versionchanged:: 2.3
  43. Substituted MersenneTwister for Wichmann-Hill.
  44. Bookkeeping functions:
  45. .. function:: seed([x])
  46. Initialize the basic random number generator. Optional argument *x* can be any
  47. :term:`hashable` object. If *x* is omitted or ``None``, current system time is used;
  48. current system time is also used to initialize the generator when the module is
  49. first imported. If randomness sources are provided by the operating system,
  50. they are used instead of the system time (see the :func:`os.urandom` function
  51. for details on availability).
  52. .. versionchanged:: 2.4
  53. formerly, operating system resources were not used.
  54. If *x* is not ``None`` or an int or long, ``hash(x)`` is used instead. If *x* is
  55. an int or long, *x* is used directly.
  56. .. function:: getstate()
  57. Return an object capturing the current internal state of the generator. This
  58. object can be passed to :func:`setstate` to restore the state.
  59. .. versionadded:: 2.1
  60. .. versionchanged:: 2.6
  61. State values produced in Python 2.6 cannot be loaded into earlier versions.
  62. .. function:: setstate(state)
  63. *state* should have been obtained from a previous call to :func:`getstate`, and
  64. :func:`setstate` restores the internal state of the generator to what it was at
  65. the time :func:`setstate` was called.
  66. .. versionadded:: 2.1
  67. .. function:: jumpahead(n)
  68. Change the internal state to one different from and likely far away from the
  69. current state. *n* is a non-negative integer which is used to scramble the
  70. current state vector. This is most useful in multi-threaded programs, in
  71. conjunction with multiple instances of the :class:`Random` class:
  72. :meth:`setstate` or :meth:`seed` can be used to force all instances into the
  73. same internal state, and then :meth:`jumpahead` can be used to force the
  74. instances' states far apart.
  75. .. versionadded:: 2.1
  76. .. versionchanged:: 2.3
  77. Instead of jumping to a specific state, *n* steps ahead, ``jumpahead(n)``
  78. jumps to another state likely to be separated by many steps.
  79. .. function:: getrandbits(k)
  80. Returns a python :class:`long` int with *k* random bits. This method is supplied
  81. with the MersenneTwister generator and some other generators may also provide it
  82. as an optional part of the API. When available, :meth:`getrandbits` enables
  83. :meth:`randrange` to handle arbitrarily large ranges.
  84. .. versionadded:: 2.4
  85. Functions for integers:
  86. .. function:: randrange([start,] stop[, step])
  87. Return a randomly selected element from ``range(start, stop, step)``. This is
  88. equivalent to ``choice(range(start, stop, step))``, but doesn't actually build a
  89. range object.
  90. .. versionadded:: 1.5.2
  91. .. function:: randint(a, b)
  92. Return a random integer *N* such that ``a <= N <= b``.
  93. Functions for sequences:
  94. .. function:: choice(seq)
  95. Return a random element from the non-empty sequence *seq*. If *seq* is empty,
  96. raises :exc:`IndexError`.
  97. .. function:: shuffle(x[, random])
  98. Shuffle the sequence *x* in place. The optional argument *random* is a
  99. 0-argument function returning a random float in [0.0, 1.0); by default, this is
  100. the function :func:`random`.
  101. Note that for even rather small ``len(x)``, the total number of permutations of
  102. *x* is larger than the period of most random number generators; this implies
  103. that most permutations of a long sequence can never be generated.
  104. .. function:: sample(population, k)
  105. Return a *k* length list of unique elements chosen from the population sequence.
  106. Used for random sampling without replacement.
  107. .. versionadded:: 2.3
  108. Returns a new list containing elements from the population while leaving the
  109. original population unchanged. The resulting list is in selection order so that
  110. all sub-slices will also be valid random samples. This allows raffle winners
  111. (the sample) to be partitioned into grand prize and second place winners (the
  112. subslices).
  113. Members of the population need not be :term:`hashable` or unique. If the population
  114. contains repeats, then each occurrence is a possible selection in the sample.
  115. To choose a sample from a range of integers, use an :func:`xrange` object as an
  116. argument. This is especially fast and space efficient for sampling from a large
  117. population: ``sample(xrange(10000000), 60)``.
  118. The following functions generate specific real-valued distributions. Function
  119. parameters are named after the corresponding variables in the distribution's
  120. equation, as used in common mathematical practice; most of these equations can
  121. be found in any statistics text.
  122. .. function:: random()
  123. Return the next random floating point number in the range [0.0, 1.0).
  124. .. function:: uniform(a, b)
  125. Return a random floating point number *N* such that ``a <= N <= b`` for
  126. ``a <= b`` and ``b <= N <= a`` for ``b < a``.
  127. The end-point value ``b`` may or may not be included in the range
  128. depending on floating-point rounding in the equation ``a + (b-a) * random()``.
  129. .. function:: triangular(low, high, mode)
  130. Return a random floating point number *N* such that ``low <= N <= high`` and
  131. with the specified *mode* between those bounds. The *low* and *high* bounds
  132. default to zero and one. The *mode* argument defaults to the midpoint
  133. between the bounds, giving a symmetric distribution.
  134. .. versionadded:: 2.6
  135. .. function:: betavariate(alpha, beta)
  136. Beta distribution. Conditions on the parameters are ``alpha > 0`` and
  137. ``beta > 0``. Returned values range between 0 and 1.
  138. .. function:: expovariate(lambd)
  139. Exponential distribution. *lambd* is 1.0 divided by the desired
  140. mean. It should be nonzero. (The parameter would be called
  141. "lambda", but that is a reserved word in Python.) Returned values
  142. range from 0 to positive infinity if *lambd* is positive, and from
  143. negative infinity to 0 if *lambd* is negative.
  144. .. function:: gammavariate(alpha, beta)
  145. Gamma distribution. (*Not* the gamma function!) Conditions on the
  146. parameters are ``alpha > 0`` and ``beta > 0``.
  147. .. function:: gauss(mu, sigma)
  148. Gaussian distribution. *mu* is the mean, and *sigma* is the standard
  149. deviation. This is slightly faster than the :func:`normalvariate` function
  150. defined below.
  151. .. function:: lognormvariate(mu, sigma)
  152. Log normal distribution. If you take the natural logarithm of this
  153. distribution, you'll get a normal distribution with mean *mu* and standard
  154. deviation *sigma*. *mu* can have any value, and *sigma* must be greater than
  155. zero.
  156. .. function:: normalvariate(mu, sigma)
  157. Normal distribution. *mu* is the mean, and *sigma* is the standard deviation.
  158. .. function:: vonmisesvariate(mu, kappa)
  159. *mu* is the mean angle, expressed in radians between 0 and 2\*\ *pi*, and *kappa*
  160. is the concentration parameter, which must be greater than or equal to zero. If
  161. *kappa* is equal to zero, this distribution reduces to a uniform random angle
  162. over the range 0 to 2\*\ *pi*.
  163. .. function:: paretovariate(alpha)
  164. Pareto distribution. *alpha* is the shape parameter.
  165. .. function:: weibullvariate(alpha, beta)
  166. Weibull distribution. *alpha* is the scale parameter and *beta* is the shape
  167. parameter.
  168. Alternative Generators:
  169. .. class:: WichmannHill([seed])
  170. Class that implements the Wichmann-Hill algorithm as the core generator. Has all
  171. of the same methods as :class:`Random` plus the :meth:`whseed` method described
  172. below. Because this class is implemented in pure Python, it is not threadsafe
  173. and may require locks between calls. The period of the generator is
  174. 6,953,607,871,644 which is small enough to require care that two independent
  175. random sequences do not overlap.
  176. .. function:: whseed([x])
  177. This is obsolete, supplied for bit-level compatibility with versions of Python
  178. prior to 2.1. See :func:`seed` for details. :func:`whseed` does not guarantee
  179. that distinct integer arguments yield distinct internal states, and can yield no
  180. more than about 2\*\*24 distinct internal states in all.
  181. .. class:: SystemRandom([seed])
  182. Class that uses the :func:`os.urandom` function for generating random numbers
  183. from sources provided by the operating system. Not available on all systems.
  184. Does not rely on software state and sequences are not reproducible. Accordingly,
  185. the :meth:`seed` and :meth:`jumpahead` methods have no effect and are ignored.
  186. The :meth:`getstate` and :meth:`setstate` methods raise
  187. :exc:`NotImplementedError` if called.
  188. .. versionadded:: 2.4
  189. Examples of basic usage::
  190. >>> random.random() # Random float x, 0.0 <= x < 1.0
  191. 0.37444887175646646
  192. >>> random.uniform(1, 10) # Random float x, 1.0 <= x < 10.0
  193. 1.1800146073117523
  194. >>> random.randint(1, 10) # Integer from 1 to 10, endpoints included
  195. 7
  196. >>> random.randrange(0, 101, 2) # Even integer from 0 to 100
  197. 26
  198. >>> random.choice('abcdefghij') # Choose a random element
  199. 'c'
  200. >>> items = [1, 2, 3, 4, 5, 6, 7]
  201. >>> random.shuffle(items)
  202. >>> items
  203. [7, 3, 2, 5, 6, 4, 1]
  204. >>> random.sample([1, 2, 3, 4, 5], 3) # Choose 3 elements
  205. [4, 1, 5]
  206. .. seealso::
  207. M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally
  208. equidistributed uniform pseudorandom number generator", ACM Transactions on
  209. Modeling and Computer Simulation Vol. 8, No. 1, January pp.3-30 1998.
  210. Wichmann, B. A. & Hill, I. D., "Algorithm AS 183: An efficient and portable
  211. pseudo-random number generator", Applied Statistics 31 (1982) 188-190.
  212. `Complementary-Multiply-with-Carry recipe
  213. <http://code.activestate.com/recipes/576707/>`_ for a compatible alternative
  214. random number generator with a long period and comparatively simple update
  215. operations.