#### /Doc/library/random.rst

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1 2:mod:`random` --- Generate pseudo-random numbers 3================================================ 4 5.. module:: random 6 :synopsis: Generate pseudo-random numbers with various common distributions. 7 8 9This module implements pseudo-random number generators for various 10distributions. 11 12For integers, uniform selection from a range. For sequences, uniform selection 13of a random element, a function to generate a random permutation of a list 14in-place, and a function for random sampling without replacement. 15 16On the real line, there are functions to compute uniform, normal (Gaussian), 17lognormal, negative exponential, gamma, and beta distributions. For generating 18distributions of angles, the von Mises distribution is available. 19 20Almost all module functions depend on the basic function :func:`random`, which 21generates a random float uniformly in the semi-open range [0.0, 1.0). Python 22uses the Mersenne Twister as the core generator. It produces 53-bit precision 23floats and has a period of 2\*\*19937-1. The underlying implementation in C is 24both fast and threadsafe. The Mersenne Twister is one of the most extensively 25tested random number generators in existence. However, being completely 26deterministic, it is not suitable for all purposes, and is completely unsuitable 27for cryptographic purposes. 28 29The functions supplied by this module are actually bound methods of a hidden 30instance of the :class:`random.Random` class. You can instantiate your own 31instances of :class:`Random` to get generators that don't share state. This is 32especially useful for multi-threaded programs, creating a different instance of 33:class:`Random` for each thread, and using the :meth:`jumpahead` method to make 34it likely that the generated sequences seen by each thread don't overlap. 35 36Class :class:`Random` can also be subclassed if you want to use a different 37basic generator of your own devising: in that case, override the :meth:`random`, 38:meth:`seed`, :meth:`getstate`, :meth:`setstate` and :meth:`jumpahead` methods. 39Optionally, a new generator can supply a :meth:`getrandbits` method --- this 40allows :meth:`randrange` to produce selections over an arbitrarily large range. 41 42.. versionadded:: 2.4 43 the :meth:`getrandbits` method. 44 45As an example of subclassing, the :mod:`random` module provides the 46:class:`WichmannHill` class that implements an alternative generator in pure 47Python. The class provides a backward compatible way to reproduce results from 48earlier versions of Python, which used the Wichmann-Hill algorithm as the core 49generator. Note that this Wichmann-Hill generator can no longer be recommended: 50its period is too short by contemporary standards, and the sequence generated is 51known to fail some stringent randomness tests. See the references below for a 52recent variant that repairs these flaws. 53 54.. versionchanged:: 2.3 55 Substituted MersenneTwister for Wichmann-Hill. 56 57Bookkeeping functions: 58 59 60.. function:: seed([x]) 61 62 Initialize the basic random number generator. Optional argument *x* can be any 63 :term:`hashable` object. If *x* is omitted or ``None``, current system time is used; 64 current system time is also used to initialize the generator when the module is 65 first imported. If randomness sources are provided by the operating system, 66 they are used instead of the system time (see the :func:`os.urandom` function 67 for details on availability). 68 69 .. versionchanged:: 2.4 70 formerly, operating system resources were not used. 71 72 If *x* is not ``None`` or an int or long, ``hash(x)`` is used instead. If *x* is 73 an int or long, *x* is used directly. 74 75 76.. function:: getstate() 77 78 Return an object capturing the current internal state of the generator. This 79 object can be passed to :func:`setstate` to restore the state. 80 81 .. versionadded:: 2.1 82 83 .. versionchanged:: 2.6 84 State values produced in Python 2.6 cannot be loaded into earlier versions. 85 86 87.. function:: setstate(state) 88 89 *state* should have been obtained from a previous call to :func:`getstate`, and 90 :func:`setstate` restores the internal state of the generator to what it was at 91 the time :func:`setstate` was called. 92 93 .. versionadded:: 2.1 94 95 96.. function:: jumpahead(n) 97 98 Change the internal state to one different from and likely far away from the 99 current state. *n* is a non-negative integer which is used to scramble the 100 current state vector. This is most useful in multi-threaded programs, in 101 conjunction with multiple instances of the :class:`Random` class: 102 :meth:`setstate` or :meth:`seed` can be used to force all instances into the 103 same internal state, and then :meth:`jumpahead` can be used to force the 104 instances' states far apart. 105 106 .. versionadded:: 2.1 107 108 .. versionchanged:: 2.3 109 Instead of jumping to a specific state, *n* steps ahead, ``jumpahead(n)`` 110 jumps to another state likely to be separated by many steps. 111 112 113.. function:: getrandbits(k) 114 115 Returns a python :class:`long` int with *k* random bits. This method is supplied 116 with the MersenneTwister generator and some other generators may also provide it 117 as an optional part of the API. When available, :meth:`getrandbits` enables 118 :meth:`randrange` to handle arbitrarily large ranges. 119 120 .. versionadded:: 2.4 121 122Functions for integers: 123 124 125.. function:: randrange([start,] stop[, step]) 126 127 Return a randomly selected element from ``range(start, stop, step)``. This is 128 equivalent to ``choice(range(start, stop, step))``, but doesn't actually build a 129 range object. 130 131 .. versionadded:: 1.5.2 132 133 134.. function:: randint(a, b) 135 136 Return a random integer *N* such that ``a <= N <= b``. 137 138Functions for sequences: 139 140 141.. function:: choice(seq) 142 143 Return a random element from the non-empty sequence *seq*. If *seq* is empty, 144 raises :exc:`IndexError`. 145 146 147.. function:: shuffle(x[, random]) 148 149 Shuffle the sequence *x* in place. The optional argument *random* is a 150 0-argument function returning a random float in [0.0, 1.0); by default, this is 151 the function :func:`random`. 152 153 Note that for even rather small ``len(x)``, the total number of permutations of 154 *x* is larger than the period of most random number generators; this implies 155 that most permutations of a long sequence can never be generated. 156 157 158.. function:: sample(population, k) 159 160 Return a *k* length list of unique elements chosen from the population sequence. 161 Used for random sampling without replacement. 162 163 .. versionadded:: 2.3 164 165 Returns a new list containing elements from the population while leaving the 166 original population unchanged. The resulting list is in selection order so that 167 all sub-slices will also be valid random samples. This allows raffle winners 168 (the sample) to be partitioned into grand prize and second place winners (the 169 subslices). 170 171 Members of the population need not be :term:`hashable` or unique. If the population 172 contains repeats, then each occurrence is a possible selection in the sample. 173 174 To choose a sample from a range of integers, use an :func:`xrange` object as an 175 argument. This is especially fast and space efficient for sampling from a large 176 population: ``sample(xrange(10000000), 60)``. 177 178The following functions generate specific real-valued distributions. Function 179parameters are named after the corresponding variables in the distribution's 180equation, as used in common mathematical practice; most of these equations can 181be found in any statistics text. 182 183 184.. function:: random() 185 186 Return the next random floating point number in the range [0.0, 1.0). 187 188 189.. function:: uniform(a, b) 190 191 Return a random floating point number *N* such that ``a <= N <= b`` for 192 ``a <= b`` and ``b <= N <= a`` for ``b < a``. 193 194 The end-point value ``b`` may or may not be included in the range 195 depending on floating-point rounding in the equation ``a + (b-a) * random()``. 196 197.. function:: triangular(low, high, mode) 198 199 Return a random floating point number *N* such that ``low <= N <= high`` and 200 with the specified *mode* between those bounds. The *low* and *high* bounds 201 default to zero and one. The *mode* argument defaults to the midpoint 202 between the bounds, giving a symmetric distribution. 203 204 .. versionadded:: 2.6 205 206 207.. function:: betavariate(alpha, beta) 208 209 Beta distribution. Conditions on the parameters are ``alpha > 0`` and 210 ``beta > 0``. Returned values range between 0 and 1. 211 212 213.. function:: expovariate(lambd) 214 215 Exponential distribution. *lambd* is 1.0 divided by the desired 216 mean. It should be nonzero. (The parameter would be called 217 "lambda", but that is a reserved word in Python.) Returned values 218 range from 0 to positive infinity if *lambd* is positive, and from 219 negative infinity to 0 if *lambd* is negative. 220 221 222.. function:: gammavariate(alpha, beta) 223 224 Gamma distribution. (*Not* the gamma function!) Conditions on the 225 parameters are ``alpha > 0`` and ``beta > 0``. 226 227 228.. function:: gauss(mu, sigma) 229 230 Gaussian distribution. *mu* is the mean, and *sigma* is the standard 231 deviation. This is slightly faster than the :func:`normalvariate` function 232 defined below. 233 234 235.. function:: lognormvariate(mu, sigma) 236 237 Log normal distribution. If you take the natural logarithm of this 238 distribution, you'll get a normal distribution with mean *mu* and standard 239 deviation *sigma*. *mu* can have any value, and *sigma* must be greater than 240 zero. 241 242 243.. function:: normalvariate(mu, sigma) 244 245 Normal distribution. *mu* is the mean, and *sigma* is the standard deviation. 246 247 248.. function:: vonmisesvariate(mu, kappa) 249 250 *mu* is the mean angle, expressed in radians between 0 and 2\*\ *pi*, and *kappa* 251 is the concentration parameter, which must be greater than or equal to zero. If 252 *kappa* is equal to zero, this distribution reduces to a uniform random angle 253 over the range 0 to 2\*\ *pi*. 254 255 256.. function:: paretovariate(alpha) 257 258 Pareto distribution. *alpha* is the shape parameter. 259 260 261.. function:: weibullvariate(alpha, beta) 262 263 Weibull distribution. *alpha* is the scale parameter and *beta* is the shape 264 parameter. 265 266 267Alternative Generators: 268 269.. class:: WichmannHill([seed]) 270 271 Class that implements the Wichmann-Hill algorithm as the core generator. Has all 272 of the same methods as :class:`Random` plus the :meth:`whseed` method described 273 below. Because this class is implemented in pure Python, it is not threadsafe 274 and may require locks between calls. The period of the generator is 275 6,953,607,871,644 which is small enough to require care that two independent 276 random sequences do not overlap. 277 278 279.. function:: whseed([x]) 280 281 This is obsolete, supplied for bit-level compatibility with versions of Python 282 prior to 2.1. See :func:`seed` for details. :func:`whseed` does not guarantee 283 that distinct integer arguments yield distinct internal states, and can yield no 284 more than about 2\*\*24 distinct internal states in all. 285 286 287.. class:: SystemRandom([seed]) 288 289 Class that uses the :func:`os.urandom` function for generating random numbers 290 from sources provided by the operating system. Not available on all systems. 291 Does not rely on software state and sequences are not reproducible. Accordingly, 292 the :meth:`seed` and :meth:`jumpahead` methods have no effect and are ignored. 293 The :meth:`getstate` and :meth:`setstate` methods raise 294 :exc:`NotImplementedError` if called. 295 296 .. versionadded:: 2.4 297 298Examples of basic usage:: 299 300 >>> random.random() # Random float x, 0.0 <= x < 1.0 301 0.37444887175646646 302 >>> random.uniform(1, 10) # Random float x, 1.0 <= x < 10.0 303 1.1800146073117523 304 >>> random.randint(1, 10) # Integer from 1 to 10, endpoints included 305 7 306 >>> random.randrange(0, 101, 2) # Even integer from 0 to 100 307 26 308 >>> random.choice('abcdefghij') # Choose a random element 309 'c' 310 311 >>> items = [1, 2, 3, 4, 5, 6, 7] 312 >>> random.shuffle(items) 313 >>> items 314 [7, 3, 2, 5, 6, 4, 1] 315 316 >>> random.sample([1, 2, 3, 4, 5], 3) # Choose 3 elements 317 [4, 1, 5] 318 319 320 321.. seealso:: 322 323 M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally 324 equidistributed uniform pseudorandom number generator", ACM Transactions on 325 Modeling and Computer Simulation Vol. 8, No. 1, January pp.3-30 1998. 326 327 Wichmann, B. A. & Hill, I. D., "Algorithm AS 183: An efficient and portable 328 pseudo-random number generator", Applied Statistics 31 (1982) 188-190. 329 330 `Complementary-Multiply-with-Carry recipe 331 <http://code.activestate.com/recipes/576707/>`_ for a compatible alternative 332 random number generator with a long period and comparatively simple update 333 operations.