1 :mod:`random` --- Generate pseudo-random numbers 2 ================================================ 3 4 .. module:: random 5 :synopsis: Generate pseudo-random numbers with various common distributions. 6 7 **Source code:** :source:`Lib/random.py` 8 9 -------------- 10 11 This module implements pseudo-random number generators for various 12 distributions. 13 14 For integers, uniform selection from a range. For sequences, uniform selection 15 of a random element, a function to generate a random permutation of a list 16 in-place, and a function for random sampling without replacement. 17 18 On the real line, there are functions to compute uniform, normal (Gaussian), 19 lognormal, negative exponential, gamma, and beta distributions. For generating 20 distributions of angles, the von Mises distribution is available. 21 22 Almost all module functions depend on the basic function :func:`.random`, which 23 generates a random float uniformly in the semi-open range [0.0, 1.0). Python 24 uses the Mersenne Twister as the core generator. It produces 53-bit precision 25 floats and has a period of 2\*\*19937-1. The underlying implementation in C is 26 both fast and threadsafe. The Mersenne Twister is one of the most extensively 27 tested random number generators in existence. However, being completely 28 deterministic, it is not suitable for all purposes, and is completely unsuitable 29 for cryptographic purposes. 30 31 The functions supplied by this module are actually bound methods of a hidden 32 instance of the :class:`random.Random` class. You can instantiate your own 33 instances of :class:`Random` to get generators that don't share state. This is 34 especially useful for multi-threaded programs, creating a different instance of 35 :class:`Random` for each thread, and using the :meth:`jumpahead` method to make 36 it likely that the generated sequences seen by each thread don't overlap. 37 38 Class :class:`Random` can also be subclassed if you want to use a different 39 basic generator of your own devising: in that case, override the :meth:`~Random.random`, 40 :meth:`~Random.seed`, :meth:`~Random.getstate`, :meth:`~Random.setstate` and 41 :meth:`~Random.jumpahead` methods. Optionally, a new generator can supply a 42 :meth:`~Random.getrandbits` method --- this 43 allows :meth:`randrange` to produce selections over an arbitrarily large range. 44 45 .. versionadded:: 2.4 46 the :meth:`getrandbits` method. 47 48 As an example of subclassing, the :mod:`random` module provides the 49 :class:`WichmannHill` class that implements an alternative generator in pure 50 Python. The class provides a backward compatible way to reproduce results from 51 earlier versions of Python, which used the Wichmann-Hill algorithm as the core 52 generator. Note that this Wichmann-Hill generator can no longer be recommended: 53 its period is too short by contemporary standards, and the sequence generated is 54 known to fail some stringent randomness tests. See the references below for a 55 recent variant that repairs these flaws. 56 57 .. versionchanged:: 2.3 58 MersenneTwister replaced Wichmann-Hill as the default generator. 59 60 The :mod:`random` module also provides the :class:`SystemRandom` class which 61 uses the system function :func:`os.urandom` to generate random numbers 62 from sources provided by the operating system. 63 64 .. warning:: 65 66 The pseudo-random generators of this module should not be used for 67 security purposes. Use :func:`os.urandom` or :class:`SystemRandom` if 68 you require a cryptographically secure pseudo-random number generator. 69 70 71 Bookkeeping functions: 72 73 74 .. function:: seed([x]) 75 76 Initialize the basic random number generator. Optional argument *x* can be any 77 :term:`hashable` object. If *x* is omitted or ``None``, current system time is used; 78 current system time is also used to initialize the generator when the module is 79 first imported. If randomness sources are provided by the operating system, 80 they are used instead of the system time (see the :func:`os.urandom` function 81 for details on availability). 82 83 If a :term:`hashable` object is given, deterministic results are only assured 84 when :envvar:`PYTHONHASHSEED` is disabled. 85 86 .. versionchanged:: 2.4 87 formerly, operating system resources were not used. 88 89 .. function:: getstate() 90 91 Return an object capturing the current internal state of the generator. This 92 object can be passed to :func:`setstate` to restore the state. 93 94 .. versionadded:: 2.1 95 96 .. versionchanged:: 2.6 97 State values produced in Python 2.6 cannot be loaded into earlier versions. 98 99 100 .. function:: setstate(state) 101 102 *state* should have been obtained from a previous call to :func:`getstate`, and 103 :func:`setstate` restores the internal state of the generator to what it was at 104 the time :func:`getstate` was called. 105 106 .. versionadded:: 2.1 107 108 109 .. function:: jumpahead(n) 110 111 Change the internal state to one different from and likely far away from the 112 current state. *n* is a non-negative integer which is used to scramble the 113 current state vector. This is most useful in multi-threaded programs, in 114 conjunction with multiple instances of the :class:`Random` class: 115 :meth:`setstate` or :meth:`seed` can be used to force all instances into the 116 same internal state, and then :meth:`jumpahead` can be used to force the 117 instances' states far apart. 118 119 .. versionadded:: 2.1 120 121 .. versionchanged:: 2.3 122 Instead of jumping to a specific state, *n* steps ahead, ``jumpahead(n)`` 123 jumps to another state likely to be separated by many steps. 124 125 126 .. function:: getrandbits(k) 127 128 Returns a python :class:`long` int with *k* random bits. This method is supplied 129 with the MersenneTwister generator and some other generators may also provide it 130 as an optional part of the API. When available, :meth:`getrandbits` enables 131 :meth:`randrange` to handle arbitrarily large ranges. 132 133 .. versionadded:: 2.4 134 135 Functions for integers: 136 137 138 .. function:: randrange(stop) 139 randrange(start, stop[, step]) 140 141 Return a randomly selected element from ``range(start, stop, step)``. This is 142 equivalent to ``choice(range(start, stop, step))``, but doesn't actually build a 143 range object. 144 145 .. versionadded:: 1.5.2 146 147 148 .. function:: randint(a, b) 149 150 Return a random integer *N* such that ``a <= N <= b``. 151 152 Functions for sequences: 153 154 155 .. function:: choice(seq) 156 157 Return a random element from the non-empty sequence *seq*. If *seq* is empty, 158 raises :exc:`IndexError`. 159 160 161 .. function:: shuffle(x[, random]) 162 163 Shuffle the sequence *x* in place. The optional argument *random* is a 164 0-argument function returning a random float in [0.0, 1.0); by default, this is 165 the function :func:`.random`. 166 167 Note that for even rather small ``len(x)``, the total number of permutations of 168 *x* is larger than the period of most random number generators; this implies 169 that most permutations of a long sequence can never be generated. 170 171 172 .. function:: sample(population, k) 173 174 Return a *k* length list of unique elements chosen from the population sequence. 175 Used for random sampling without replacement. 176 177 .. versionadded:: 2.3 178 179 Returns a new list containing elements from the population while leaving the 180 original population unchanged. The resulting list is in selection order so that 181 all sub-slices will also be valid random samples. This allows raffle winners 182 (the sample) to be partitioned into grand prize and second place winners (the 183 subslices). 184 185 Members of the population need not be :term:`hashable` or unique. If the population 186 contains repeats, then each occurrence is a possible selection in the sample. 187 188 To choose a sample from a range of integers, use an :func:`xrange` object as an 189 argument. This is especially fast and space efficient for sampling from a large 190 population: ``sample(xrange(10000000), 60)``. 191 192 The following functions generate specific real-valued distributions. Function 193 parameters are named after the corresponding variables in the distribution's 194 equation, as used in common mathematical practice; most of these equations can 195 be found in any statistics text. 196 197 198 .. function:: random() 199 200 Return the next random floating point number in the range [0.0, 1.0). 201 202 203 .. function:: uniform(a, b) 204 205 Return a random floating point number *N* such that ``a <= N <= b`` for 206 ``a <= b`` and ``b <= N <= a`` for ``b < a``. 207 208 The end-point value ``b`` may or may not be included in the range 209 depending on floating-point rounding in the equation ``a + (b-a) * random()``. 210 211 212 .. function:: triangular(low, high, mode) 213 214 Return a random floating point number *N* such that ``low <= N <= high`` and 215 with the specified *mode* between those bounds. The *low* and *high* bounds 216 default to zero and one. The *mode* argument defaults to the midpoint 217 between the bounds, giving a symmetric distribution. 218 219 .. versionadded:: 2.6 220 221 222 .. function:: betavariate(alpha, beta) 223 224 Beta distribution. Conditions on the parameters are ``alpha > 0`` and 225 ``beta > 0``. Returned values range between 0 and 1. 226 227 228 .. function:: expovariate(lambd) 229 230 Exponential distribution. *lambd* is 1.0 divided by the desired 231 mean. It should be nonzero. (The parameter would be called 232 "lambda", but that is a reserved word in Python.) Returned values 233 range from 0 to positive infinity if *lambd* is positive, and from 234 negative infinity to 0 if *lambd* is negative. 235 236 237 .. function:: gammavariate(alpha, beta) 238 239 Gamma distribution. (*Not* the gamma function!) Conditions on the 240 parameters are ``alpha > 0`` and ``beta > 0``. 241 242 The probability distribution function is:: 243 244 x ** (alpha - 1) * math.exp(-x / beta) 245 pdf(x) = -------------------------------------- 246 math.gamma(alpha) * beta ** alpha 247 248 249 .. function:: gauss(mu, sigma) 250 251 Gaussian distribution. *mu* is the mean, and *sigma* is the standard 252 deviation. This is slightly faster than the :func:`normalvariate` function 253 defined below. 254 255 256 .. function:: lognormvariate(mu, sigma) 257 258 Log normal distribution. If you take the natural logarithm of this 259 distribution, you'll get a normal distribution with mean *mu* and standard 260 deviation *sigma*. *mu* can have any value, and *sigma* must be greater than 261 zero. 262 263 264 .. function:: normalvariate(mu, sigma) 265 266 Normal distribution. *mu* is the mean, and *sigma* is the standard deviation. 267 268 269 .. function:: vonmisesvariate(mu, kappa) 270 271 *mu* is the mean angle, expressed in radians between 0 and 2\*\ *pi*, and *kappa* 272 is the concentration parameter, which must be greater than or equal to zero. If 273 *kappa* is equal to zero, this distribution reduces to a uniform random angle 274 over the range 0 to 2\*\ *pi*. 275 276 277 .. function:: paretovariate(alpha) 278 279 Pareto distribution. *alpha* is the shape parameter. 280 281 282 .. function:: weibullvariate(alpha, beta) 283 284 Weibull distribution. *alpha* is the scale parameter and *beta* is the shape 285 parameter. 286 287 288 Alternative Generators: 289 290 .. class:: WichmannHill([seed]) 291 292 Class that implements the Wichmann-Hill algorithm as the core generator. Has all 293 of the same methods as :class:`Random` plus the :meth:`whseed` method described 294 below. Because this class is implemented in pure Python, it is not threadsafe 295 and may require locks between calls. The period of the generator is 296 6,953,607,871,644 which is small enough to require care that two independent 297 random sequences do not overlap. 298 299 300 .. function:: whseed([x]) 301 302 This is obsolete, supplied for bit-level compatibility with versions of Python 303 prior to 2.1. See :func:`seed` for details. :func:`whseed` does not guarantee 304 that distinct integer arguments yield distinct internal states, and can yield no 305 more than about 2\*\*24 distinct internal states in all. 306 307 308 .. class:: SystemRandom([seed]) 309 310 Class that uses the :func:`os.urandom` function for generating random numbers 311 from sources provided by the operating system. Not available on all systems. 312 Does not rely on software state and sequences are not reproducible. Accordingly, 313 the :meth:`seed` and :meth:`jumpahead` methods have no effect and are ignored. 314 The :meth:`getstate` and :meth:`setstate` methods raise 315 :exc:`NotImplementedError` if called. 316 317 .. versionadded:: 2.4 318 319 Examples of basic usage:: 320 321 >>> random.random() # Random float x, 0.0 <= x < 1.0 322 0.37444887175646646 323 >>> random.uniform(1, 10) # Random float x, 1.0 <= x < 10.0 324 1.1800146073117523 325 >>> random.randint(1, 10) # Integer from 1 to 10, endpoints included 326 7 327 >>> random.randrange(0, 101, 2) # Even integer from 0 to 100 328 26 329 >>> random.choice('abcdefghij') # Choose a random element 330 'c' 331 332 >>> items = [1, 2, 3, 4, 5, 6, 7] 333 >>> random.shuffle(items) 334 >>> items 335 [7, 3, 2, 5, 6, 4, 1] 336 337 >>> random.sample([1, 2, 3, 4, 5], 3) # Choose 3 elements 338 [4, 1, 5] 339 340 341 342 .. seealso:: 343 344 M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally 345 equidistributed uniform pseudorandom number generator", ACM Transactions on 346 Modeling and Computer Simulation Vol. 8, No. 1, January pp.3--30 1998. 347 348 Wichmann, B. A. & Hill, I. D., "Algorithm AS 183: An efficient and portable 349 pseudo-random number generator", Applied Statistics 31 (1982) 188-190. 350 351 `Complementary-Multiply-with-Carry recipe 352 <http://code.activestate.com/recipes/576707/>`_ for a compatible alternative 353 random number generator with a long period and comparatively simple update 354 operations. 355
