Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 1 | """Random variable generators. |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 2 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 3 | integers |
| 4 | -------- |
| 5 | uniform within range |
| 6 | |
| 7 | sequences |
| 8 | --------- |
| 9 | pick random element |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 10 | pick random sample |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 11 | generate random permutation |
| 12 | |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 13 | distributions on the real line: |
| 14 | ------------------------------ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 15 | uniform |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 16 | triangular |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 17 | normal (Gaussian) |
| 18 | lognormal |
| 19 | negative exponential |
| 20 | gamma |
| 21 | beta |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 22 | pareto |
| 23 | Weibull |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 24 | |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 25 | distributions on the circle (angles 0 to 2pi) |
| 26 | --------------------------------------------- |
| 27 | circular uniform |
| 28 | von Mises |
| 29 | |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 30 | General notes on the underlying Mersenne Twister core generator: |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 31 | |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 32 | * The period is 2**19937-1. |
Thomas Wouters | 0e3f591 | 2006-08-11 14:57:12 +0000 | [diff] [blame] | 33 | * It is one of the most extensively tested generators in existence. |
Thomas Wouters | 0e3f591 | 2006-08-11 14:57:12 +0000 | [diff] [blame] | 34 | * The random() method is implemented in C, executes in a single Python step, |
| 35 | and is, therefore, threadsafe. |
Tim Peters | e360d95 | 2001-01-26 10:00:39 +0000 | [diff] [blame] | 36 | |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 37 | """ |
Guido van Rossum | d03e119 | 1998-05-29 17:51:31 +0000 | [diff] [blame] | 38 | |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 39 | from __future__ import division |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 40 | from warnings import warn as _warn |
| 41 | from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 42 | from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 43 | from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin |
Raymond Hettinger | c1c43ca | 2004-09-05 00:00:42 +0000 | [diff] [blame] | 44 | from os import urandom as _urandom |
Raymond Hettinger | 57d1a88 | 2011-02-23 00:46:28 +0000 | [diff] [blame] | 45 | from collections.abc import Set as _Set, Sequence as _Sequence |
Raymond Hettinger | 3fcf002 | 2010-12-08 01:13:53 +0000 | [diff] [blame] | 46 | from hashlib import sha512 as _sha512 |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 47 | |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 48 | __all__ = ["Random","seed","random","uniform","randint","choice","sample", |
Skip Montanaro | 0de6580 | 2001-02-15 22:15:14 +0000 | [diff] [blame] | 49 | "randrange","shuffle","normalvariate","lognormvariate", |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 50 | "expovariate","vonmisesvariate","gammavariate","triangular", |
Raymond Hettinger | f8a52d3 | 2003-08-05 12:23:19 +0000 | [diff] [blame] | 51 | "gauss","betavariate","paretovariate","weibullvariate", |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame] | 52 | "getstate","setstate", "getrandbits", |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 53 | "SystemRandom"] |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 54 | |
| 55 | NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 56 | TWOPI = 2.0*_pi |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 57 | LOG4 = _log(4.0) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 58 | SG_MAGICCONST = 1.0 + _log(4.5) |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 59 | BPF = 53 # Number of bits in a float |
Tim Peters | 7c2a85b | 2004-08-31 02:19:55 +0000 | [diff] [blame] | 60 | RECIP_BPF = 2**-BPF |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 61 | |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 62 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 63 | # Translated by Guido van Rossum from C source provided by |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 64 | # Adrian Baddeley. Adapted by Raymond Hettinger for use with |
Raymond Hettinger | 3fa19d7 | 2004-08-31 01:05:15 +0000 | [diff] [blame] | 65 | # the Mersenne Twister and os.urandom() core generators. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 66 | |
Raymond Hettinger | 145a4a0 | 2003-01-07 10:25:55 +0000 | [diff] [blame] | 67 | import _random |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 68 | |
Raymond Hettinger | 145a4a0 | 2003-01-07 10:25:55 +0000 | [diff] [blame] | 69 | class Random(_random.Random): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 70 | """Random number generator base class used by bound module functions. |
| 71 | |
| 72 | Used to instantiate instances of Random to get generators that don't |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame] | 73 | share state. |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 74 | |
| 75 | Class Random can also be subclassed if you want to use a different basic |
| 76 | generator of your own devising: in that case, override the following |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame] | 77 | methods: random(), seed(), getstate(), and setstate(). |
Benjamin Peterson | d18de0e | 2008-07-31 20:21:46 +0000 | [diff] [blame] | 78 | Optionally, implement a getrandbits() method so that randrange() |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 79 | can cover arbitrarily large ranges. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 80 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 81 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 82 | |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 83 | VERSION = 3 # used by getstate/setstate |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 84 | |
| 85 | def __init__(self, x=None): |
| 86 | """Initialize an instance. |
| 87 | |
| 88 | Optional argument x controls seeding, as for Random.seed(). |
| 89 | """ |
| 90 | |
| 91 | self.seed(x) |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 92 | self.gauss_next = None |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 93 | |
Raymond Hettinger | f763a72 | 2010-09-07 00:38:15 +0000 | [diff] [blame] | 94 | def seed(self, a=None, version=2): |
Tim Peters | 0de88fc | 2001-02-01 04:59:18 +0000 | [diff] [blame] | 95 | """Initialize internal state from hashable object. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 96 | |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 97 | None or no argument seeds from current time or from an operating |
| 98 | system specific randomness source if available. |
Tim Peters | 0de88fc | 2001-02-01 04:59:18 +0000 | [diff] [blame] | 99 | |
Raymond Hettinger | 183cd1f | 2010-09-08 18:48:21 +0000 | [diff] [blame] | 100 | For version 2 (the default), all of the bits are used if *a *is a str, |
| 101 | bytes, or bytearray. For version 1, the hash() of *a* is used instead. |
Raymond Hettinger | f763a72 | 2010-09-07 00:38:15 +0000 | [diff] [blame] | 102 | |
Raymond Hettinger | 183cd1f | 2010-09-08 18:48:21 +0000 | [diff] [blame] | 103 | If *a* is an int, all bits are used. |
Raymond Hettinger | f763a72 | 2010-09-07 00:38:15 +0000 | [diff] [blame] | 104 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 105 | """ |
| 106 | |
Raymond Hettinger | 3081d59 | 2003-08-09 18:30:57 +0000 | [diff] [blame] | 107 | if a is None: |
Raymond Hettinger | c1c43ca | 2004-09-05 00:00:42 +0000 | [diff] [blame] | 108 | try: |
Raymond Hettinger | 183cd1f | 2010-09-08 18:48:21 +0000 | [diff] [blame] | 109 | a = int.from_bytes(_urandom(32), 'big') |
Raymond Hettinger | c1c43ca | 2004-09-05 00:00:42 +0000 | [diff] [blame] | 110 | except NotImplementedError: |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 111 | import time |
Guido van Rossum | e2a383d | 2007-01-15 16:59:06 +0000 | [diff] [blame] | 112 | a = int(time.time() * 256) # use fractional seconds |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 113 | |
Raymond Hettinger | 3fcf002 | 2010-12-08 01:13:53 +0000 | [diff] [blame] | 114 | if version == 2: |
| 115 | if isinstance(a, (str, bytes, bytearray)): |
| 116 | if isinstance(a, str): |
Raymond Hettinger | f90ba8a | 2011-05-05 11:35:50 -0700 | [diff] [blame] | 117 | a = a.encode() |
Raymond Hettinger | 3fcf002 | 2010-12-08 01:13:53 +0000 | [diff] [blame] | 118 | a += _sha512(a).digest() |
| 119 | a = int.from_bytes(a, 'big') |
Raymond Hettinger | f763a72 | 2010-09-07 00:38:15 +0000 | [diff] [blame] | 120 | |
Guido van Rossum | cd16bf6 | 2007-06-13 18:07:49 +0000 | [diff] [blame] | 121 | super().seed(a) |
Tim Peters | 46c04e1 | 2002-05-05 20:40:00 +0000 | [diff] [blame] | 122 | self.gauss_next = None |
| 123 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 124 | def getstate(self): |
| 125 | """Return internal state; can be passed to setstate() later.""" |
Guido van Rossum | cd16bf6 | 2007-06-13 18:07:49 +0000 | [diff] [blame] | 126 | return self.VERSION, super().getstate(), self.gauss_next |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 127 | |
| 128 | def setstate(self, state): |
| 129 | """Restore internal state from object returned by getstate().""" |
| 130 | version = state[0] |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 131 | if version == 3: |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 132 | version, internalstate, self.gauss_next = state |
Guido van Rossum | cd16bf6 | 2007-06-13 18:07:49 +0000 | [diff] [blame] | 133 | super().setstate(internalstate) |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 134 | elif version == 2: |
| 135 | version, internalstate, self.gauss_next = state |
| 136 | # In version 2, the state was saved as signed ints, which causes |
| 137 | # inconsistencies between 32/64-bit systems. The state is |
| 138 | # really unsigned 32-bit ints, so we convert negative ints from |
| 139 | # version 2 to positive longs for version 3. |
| 140 | try: |
Raymond Hettinger | c585eec | 2010-09-07 15:00:15 +0000 | [diff] [blame] | 141 | internalstate = tuple(x % (2**32) for x in internalstate) |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 142 | except ValueError as e: |
| 143 | raise TypeError from e |
Raymond Hettinger | 183cd1f | 2010-09-08 18:48:21 +0000 | [diff] [blame] | 144 | super().setstate(internalstate) |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 145 | else: |
| 146 | raise ValueError("state with version %s passed to " |
| 147 | "Random.setstate() of version %s" % |
| 148 | (version, self.VERSION)) |
| 149 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 150 | ## ---- Methods below this point do not need to be overridden when |
| 151 | ## ---- subclassing for the purpose of using a different core generator. |
| 152 | |
| 153 | ## -------------------- pickle support ------------------- |
| 154 | |
| 155 | def __getstate__(self): # for pickle |
| 156 | return self.getstate() |
| 157 | |
| 158 | def __setstate__(self, state): # for pickle |
| 159 | self.setstate(state) |
| 160 | |
Raymond Hettinger | 5f078ff | 2003-06-24 20:29:04 +0000 | [diff] [blame] | 161 | def __reduce__(self): |
| 162 | return self.__class__, (), self.getstate() |
| 163 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 164 | ## -------------------- integer methods ------------------- |
| 165 | |
Raymond Hettinger | 0515661 | 2010-09-07 04:44:52 +0000 | [diff] [blame] | 166 | def randrange(self, start, stop=None, step=1, int=int): |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 167 | """Choose a random item from range(start, stop[, step]). |
| 168 | |
| 169 | This fixes the problem with randint() which includes the |
| 170 | endpoint; in Python this is usually not what you want. |
Raymond Hettinger | 3051cc3 | 2010-09-07 00:48:40 +0000 | [diff] [blame] | 171 | |
Raymond Hettinger | c324697 | 2010-09-07 09:32:57 +0000 | [diff] [blame] | 172 | Do not supply the 'int' argument. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 173 | """ |
| 174 | |
| 175 | # This code is a bit messy to make it fast for the |
Tim Peters | 9146f27 | 2002-08-16 03:41:39 +0000 | [diff] [blame] | 176 | # common case while still doing adequate error checking. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 177 | istart = int(start) |
| 178 | if istart != start: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 179 | raise ValueError("non-integer arg 1 for randrange()") |
Raymond Hettinger | 3051cc3 | 2010-09-07 00:48:40 +0000 | [diff] [blame] | 180 | if stop is None: |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 181 | if istart > 0: |
Raymond Hettinger | 0515661 | 2010-09-07 04:44:52 +0000 | [diff] [blame] | 182 | return self._randbelow(istart) |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 183 | raise ValueError("empty range for randrange()") |
Tim Peters | 9146f27 | 2002-08-16 03:41:39 +0000 | [diff] [blame] | 184 | |
| 185 | # stop argument supplied. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 186 | istop = int(stop) |
| 187 | if istop != stop: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 188 | raise ValueError("non-integer stop for randrange()") |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 189 | width = istop - istart |
| 190 | if step == 1 and width > 0: |
Raymond Hettinger | c324697 | 2010-09-07 09:32:57 +0000 | [diff] [blame] | 191 | return istart + self._randbelow(width) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 192 | if step == 1: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 193 | raise ValueError("empty range for randrange() (%d,%d, %d)" % (istart, istop, width)) |
Tim Peters | 9146f27 | 2002-08-16 03:41:39 +0000 | [diff] [blame] | 194 | |
| 195 | # Non-unit step argument supplied. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 196 | istep = int(step) |
| 197 | if istep != step: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 198 | raise ValueError("non-integer step for randrange()") |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 199 | if istep > 0: |
Raymond Hettinger | ffdb8bb | 2004-09-27 15:29:05 +0000 | [diff] [blame] | 200 | n = (width + istep - 1) // istep |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 201 | elif istep < 0: |
Raymond Hettinger | ffdb8bb | 2004-09-27 15:29:05 +0000 | [diff] [blame] | 202 | n = (width + istep + 1) // istep |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 203 | else: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 204 | raise ValueError("zero step for randrange()") |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 205 | |
| 206 | if n <= 0: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 207 | raise ValueError("empty range for randrange()") |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 208 | |
Raymond Hettinger | 0515661 | 2010-09-07 04:44:52 +0000 | [diff] [blame] | 209 | return istart + istep*self._randbelow(n) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 210 | |
| 211 | def randint(self, a, b): |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 212 | """Return random integer in range [a, b], including both end points. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 213 | """ |
| 214 | |
| 215 | return self.randrange(a, b+1) |
| 216 | |
Raymond Hettinger | e4a3e99 | 2010-09-08 00:30:28 +0000 | [diff] [blame] | 217 | def _randbelow(self, n, int=int, maxsize=1<<BPF, type=type, |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 218 | Method=_MethodType, BuiltinMethod=_BuiltinMethodType): |
Raymond Hettinger | e4a3e99 | 2010-09-08 00:30:28 +0000 | [diff] [blame] | 219 | "Return a random int in the range [0,n). Raises ValueError if n==0." |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 220 | |
Raymond Hettinger | c324697 | 2010-09-07 09:32:57 +0000 | [diff] [blame] | 221 | getrandbits = self.getrandbits |
| 222 | # Only call self.getrandbits if the original random() builtin method |
| 223 | # has not been overridden or if a new getrandbits() was supplied. |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 224 | if type(self.random) is BuiltinMethod or type(getrandbits) is Method: |
Raymond Hettinger | e4a3e99 | 2010-09-08 00:30:28 +0000 | [diff] [blame] | 225 | k = n.bit_length() # don't use (n-1) here because n can be 1 |
Raymond Hettinger | f015b3f | 2010-09-07 20:04:42 +0000 | [diff] [blame] | 226 | r = getrandbits(k) # 0 <= r < 2**k |
Raymond Hettinger | c324697 | 2010-09-07 09:32:57 +0000 | [diff] [blame] | 227 | while r >= n: |
| 228 | r = getrandbits(k) |
| 229 | return r |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 230 | # There's an overriden random() method but no new getrandbits() method, |
| 231 | # so we can only use random() from here. |
Raymond Hettinger | e4a3e99 | 2010-09-08 00:30:28 +0000 | [diff] [blame] | 232 | random = self.random |
| 233 | if n >= maxsize: |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 234 | _warn("Underlying random() generator does not supply \n" |
Raymond Hettinger | f015b3f | 2010-09-07 20:04:42 +0000 | [diff] [blame] | 235 | "enough bits to choose from a population range this large.\n" |
| 236 | "To remove the range limitation, add a getrandbits() method.") |
Raymond Hettinger | e4a3e99 | 2010-09-08 00:30:28 +0000 | [diff] [blame] | 237 | return int(random() * n) |
| 238 | rem = maxsize % n |
| 239 | limit = (maxsize - rem) / maxsize # int(limit * maxsize) % n == 0 |
| 240 | r = random() |
| 241 | while r >= limit: |
| 242 | r = random() |
| 243 | return int(r*maxsize) % n |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 244 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 245 | ## -------------------- sequence methods ------------------- |
| 246 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 247 | def choice(self, seq): |
| 248 | """Choose a random element from a non-empty sequence.""" |
Raymond Hettinger | dc4872e | 2010-09-07 10:06:56 +0000 | [diff] [blame] | 249 | try: |
| 250 | i = self._randbelow(len(seq)) |
| 251 | except ValueError: |
| 252 | raise IndexError('Cannot choose from an empty sequence') |
| 253 | return seq[i] |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 254 | |
| 255 | def shuffle(self, x, random=None, int=int): |
| 256 | """x, random=random.random -> shuffle list x in place; return None. |
| 257 | |
| 258 | Optional arg random is a 0-argument function returning a random |
| 259 | float in [0.0, 1.0); by default, the standard random.random. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 260 | """ |
| 261 | |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 262 | randbelow = self._randbelow |
| 263 | for i in reversed(range(1, len(x))): |
| 264 | # pick an element in x[:i+1] with which to exchange x[i] |
| 265 | j = randbelow(i+1) if random is None else int(random() * (i+1)) |
| 266 | x[i], x[j] = x[j], x[i] |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 267 | |
Raymond Hettinger | fdbe522 | 2003-06-13 07:01:51 +0000 | [diff] [blame] | 268 | def sample(self, population, k): |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 269 | """Chooses k unique random elements from a population sequence or set. |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 270 | |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 271 | Returns a new list containing elements from the population while |
| 272 | leaving the original population unchanged. The resulting list is |
| 273 | in selection order so that all sub-slices will also be valid random |
| 274 | samples. This allows raffle winners (the sample) to be partitioned |
| 275 | into grand prize and second place winners (the subslices). |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 276 | |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 277 | Members of the population need not be hashable or unique. If the |
| 278 | population contains repeats, then each occurrence is a possible |
| 279 | selection in the sample. |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 280 | |
Guido van Rossum | 805365e | 2007-05-07 22:24:25 +0000 | [diff] [blame] | 281 | To choose a sample in a range of integers, use range as an argument. |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 282 | This is especially fast and space efficient for sampling from a |
Guido van Rossum | 805365e | 2007-05-07 22:24:25 +0000 | [diff] [blame] | 283 | large population: sample(range(10000000), 60) |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 284 | """ |
| 285 | |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 286 | # Sampling without replacement entails tracking either potential |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 287 | # selections (the pool) in a list or previous selections in a set. |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 288 | |
Jeremy Hylton | 2b55d35 | 2004-02-23 17:27:57 +0000 | [diff] [blame] | 289 | # When the number of selections is small compared to the |
| 290 | # population, then tracking selections is efficient, requiring |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 291 | # only a small set and an occasional reselection. For |
Jeremy Hylton | 2b55d35 | 2004-02-23 17:27:57 +0000 | [diff] [blame] | 292 | # a larger number of selections, the pool tracking method is |
| 293 | # preferred since the list takes less space than the |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 294 | # set and it doesn't suffer from frequent reselections. |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 295 | |
Raymond Hettinger | 57d1a88 | 2011-02-23 00:46:28 +0000 | [diff] [blame] | 296 | if isinstance(population, _Set): |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 297 | population = tuple(population) |
Raymond Hettinger | 57d1a88 | 2011-02-23 00:46:28 +0000 | [diff] [blame] | 298 | if not isinstance(population, _Sequence): |
| 299 | raise TypeError("Population must be a sequence or set. For dicts, use list(d).") |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 300 | randbelow = self._randbelow |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 301 | n = len(population) |
| 302 | if not 0 <= k <= n: |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 303 | raise ValueError("Sample larger than population") |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 304 | result = [None] * k |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 305 | setsize = 21 # size of a small set minus size of an empty list |
| 306 | if k > 5: |
Tim Peters | 9e34c04 | 2005-08-26 15:20:46 +0000 | [diff] [blame] | 307 | setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 308 | if n <= setsize: |
| 309 | # An n-length list is smaller than a k-length set |
Raymond Hettinger | 311f419 | 2002-11-18 09:01:24 +0000 | [diff] [blame] | 310 | pool = list(population) |
Guido van Rossum | 805365e | 2007-05-07 22:24:25 +0000 | [diff] [blame] | 311 | for i in range(k): # invariant: non-selected at [0,n-i) |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 312 | j = randbelow(n-i) |
Raymond Hettinger | 311f419 | 2002-11-18 09:01:24 +0000 | [diff] [blame] | 313 | result[i] = pool[j] |
Raymond Hettinger | 8b9aa8d | 2003-01-04 05:20:33 +0000 | [diff] [blame] | 314 | pool[j] = pool[n-i-1] # move non-selected item into vacancy |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 315 | else: |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 316 | selected = set() |
| 317 | selected_add = selected.add |
| 318 | for i in range(k): |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 319 | j = randbelow(n) |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 320 | while j in selected: |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 321 | j = randbelow(n) |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 322 | selected_add(j) |
| 323 | result[i] = population[j] |
Raymond Hettinger | 311f419 | 2002-11-18 09:01:24 +0000 | [diff] [blame] | 324 | return result |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 325 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 326 | ## -------------------- real-valued distributions ------------------- |
| 327 | |
| 328 | ## -------------------- uniform distribution ------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 329 | |
| 330 | def uniform(self, a, b): |
Raymond Hettinger | be40db0 | 2009-06-11 23:12:14 +0000 | [diff] [blame] | 331 | "Get a random number in the range [a, b) or [a, b] depending on rounding." |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 332 | return a + (b-a) * self.random() |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 333 | |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 334 | ## -------------------- triangular -------------------- |
| 335 | |
| 336 | def triangular(self, low=0.0, high=1.0, mode=None): |
| 337 | """Triangular distribution. |
| 338 | |
| 339 | Continuous distribution bounded by given lower and upper limits, |
| 340 | and having a given mode value in-between. |
| 341 | |
| 342 | http://en.wikipedia.org/wiki/Triangular_distribution |
| 343 | |
| 344 | """ |
| 345 | u = self.random() |
| 346 | c = 0.5 if mode is None else (mode - low) / (high - low) |
| 347 | if u > c: |
| 348 | u = 1.0 - u |
| 349 | c = 1.0 - c |
| 350 | low, high = high, low |
| 351 | return low + (high - low) * (u * c) ** 0.5 |
| 352 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 353 | ## -------------------- normal distribution -------------------- |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 354 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 355 | def normalvariate(self, mu, sigma): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 356 | """Normal distribution. |
| 357 | |
| 358 | mu is the mean, and sigma is the standard deviation. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 359 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 360 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 361 | # mu = mean, sigma = standard deviation |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 362 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 363 | # Uses Kinderman and Monahan method. Reference: Kinderman, |
| 364 | # A.J. and Monahan, J.F., "Computer generation of random |
| 365 | # variables using the ratio of uniform deviates", ACM Trans |
| 366 | # Math Software, 3, (1977), pp257-260. |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 367 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 368 | random = self.random |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 369 | while 1: |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 370 | u1 = random() |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 371 | u2 = 1.0 - random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 372 | z = NV_MAGICCONST*(u1-0.5)/u2 |
| 373 | zz = z*z/4.0 |
| 374 | if zz <= -_log(u2): |
| 375 | break |
| 376 | return mu + z*sigma |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 377 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 378 | ## -------------------- lognormal distribution -------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 379 | |
| 380 | def lognormvariate(self, mu, sigma): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 381 | """Log normal distribution. |
| 382 | |
| 383 | If you take the natural logarithm of this distribution, you'll get a |
| 384 | normal distribution with mean mu and standard deviation sigma. |
| 385 | mu can have any value, and sigma must be greater than zero. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 386 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 387 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 388 | return _exp(self.normalvariate(mu, sigma)) |
| 389 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 390 | ## -------------------- exponential distribution -------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 391 | |
| 392 | def expovariate(self, lambd): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 393 | """Exponential distribution. |
| 394 | |
Mark Dickinson | 2f94736 | 2009-01-07 17:54:07 +0000 | [diff] [blame] | 395 | lambd is 1.0 divided by the desired mean. It should be |
| 396 | nonzero. (The parameter would be called "lambda", but that is |
| 397 | a reserved word in Python.) Returned values range from 0 to |
| 398 | positive infinity if lambd is positive, and from negative |
| 399 | infinity to 0 if lambd is negative. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 400 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 401 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 402 | # lambd: rate lambd = 1/mean |
| 403 | # ('lambda' is a Python reserved word) |
| 404 | |
| 405 | random = self.random |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 406 | u = random() |
| 407 | while u <= 1e-7: |
| 408 | u = random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 409 | return -_log(u)/lambd |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 410 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 411 | ## -------------------- von Mises distribution -------------------- |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 412 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 413 | def vonmisesvariate(self, mu, kappa): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 414 | """Circular data distribution. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 415 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 416 | mu is the mean angle, expressed in radians between 0 and 2*pi, and |
| 417 | kappa is the concentration parameter, which must be greater than or |
| 418 | equal to zero. If kappa is equal to zero, this distribution reduces |
| 419 | to a uniform random angle over the range 0 to 2*pi. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 420 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 421 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 422 | # mu: mean angle (in radians between 0 and 2*pi) |
| 423 | # kappa: concentration parameter kappa (>= 0) |
| 424 | # if kappa = 0 generate uniform random angle |
| 425 | |
| 426 | # Based upon an algorithm published in: Fisher, N.I., |
| 427 | # "Statistical Analysis of Circular Data", Cambridge |
| 428 | # University Press, 1993. |
| 429 | |
| 430 | # Thanks to Magnus Kessler for a correction to the |
| 431 | # implementation of step 4. |
| 432 | |
| 433 | random = self.random |
| 434 | if kappa <= 1e-6: |
| 435 | return TWOPI * random() |
| 436 | |
| 437 | a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa) |
| 438 | b = (a - _sqrt(2.0 * a))/(2.0 * kappa) |
| 439 | r = (1.0 + b * b)/(2.0 * b) |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 440 | |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 441 | while 1: |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 442 | u1 = random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 443 | |
| 444 | z = _cos(_pi * u1) |
| 445 | f = (1.0 + r * z)/(r + z) |
| 446 | c = kappa * (r - f) |
| 447 | |
| 448 | u2 = random() |
| 449 | |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 450 | if u2 < c * (2.0 - c) or u2 <= c * _exp(1.0 - c): |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 451 | break |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 452 | |
| 453 | u3 = random() |
| 454 | if u3 > 0.5: |
| 455 | theta = (mu % TWOPI) + _acos(f) |
| 456 | else: |
| 457 | theta = (mu % TWOPI) - _acos(f) |
| 458 | |
| 459 | return theta |
| 460 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 461 | ## -------------------- gamma distribution -------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 462 | |
| 463 | def gammavariate(self, alpha, beta): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 464 | """Gamma distribution. Not the gamma function! |
| 465 | |
| 466 | Conditions on the parameters are alpha > 0 and beta > 0. |
| 467 | |
Raymond Hettinger | a8e4d6e | 2011-03-22 15:55:51 -0700 | [diff] [blame] | 468 | The probability distribution function is: |
| 469 | |
| 470 | x ** (alpha - 1) * math.exp(-x / beta) |
| 471 | pdf(x) = -------------------------------------- |
| 472 | math.gamma(alpha) * beta ** alpha |
| 473 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 474 | """ |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 475 | |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 476 | # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 477 | |
Guido van Rossum | 570764d | 2002-05-14 14:08:12 +0000 | [diff] [blame] | 478 | # Warning: a few older sources define the gamma distribution in terms |
| 479 | # of alpha > -1.0 |
| 480 | if alpha <= 0.0 or beta <= 0.0: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 481 | raise ValueError('gammavariate: alpha and beta must be > 0.0') |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 482 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 483 | random = self.random |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 484 | if alpha > 1.0: |
| 485 | |
| 486 | # Uses R.C.H. Cheng, "The generation of Gamma |
| 487 | # variables with non-integral shape parameters", |
| 488 | # Applied Statistics, (1977), 26, No. 1, p71-74 |
| 489 | |
Raymond Hettinger | ca6cdc2 | 2002-05-13 23:40:14 +0000 | [diff] [blame] | 490 | ainv = _sqrt(2.0 * alpha - 1.0) |
| 491 | bbb = alpha - LOG4 |
| 492 | ccc = alpha + ainv |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 493 | |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 494 | while 1: |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 495 | u1 = random() |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 496 | if not 1e-7 < u1 < .9999999: |
| 497 | continue |
| 498 | u2 = 1.0 - random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 499 | v = _log(u1/(1.0-u1))/ainv |
| 500 | x = alpha*_exp(v) |
| 501 | z = u1*u1*u2 |
| 502 | r = bbb+ccc*v-x |
| 503 | if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 504 | return x * beta |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 505 | |
| 506 | elif alpha == 1.0: |
| 507 | # expovariate(1) |
| 508 | u = random() |
| 509 | while u <= 1e-7: |
| 510 | u = random() |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 511 | return -_log(u) * beta |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 512 | |
| 513 | else: # alpha is between 0 and 1 (exclusive) |
| 514 | |
| 515 | # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle |
| 516 | |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 517 | while 1: |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 518 | u = random() |
| 519 | b = (_e + alpha)/_e |
| 520 | p = b*u |
| 521 | if p <= 1.0: |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 522 | x = p ** (1.0/alpha) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 523 | else: |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 524 | x = -_log((b-p)/alpha) |
| 525 | u1 = random() |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 526 | if p > 1.0: |
| 527 | if u1 <= x ** (alpha - 1.0): |
| 528 | break |
| 529 | elif u1 <= _exp(-x): |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 530 | break |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 531 | return x * beta |
| 532 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 533 | ## -------------------- Gauss (faster alternative) -------------------- |
Guido van Rossum | 95bfcda | 1994-03-09 14:21:05 +0000 | [diff] [blame] | 534 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 535 | def gauss(self, mu, sigma): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 536 | """Gaussian distribution. |
| 537 | |
| 538 | mu is the mean, and sigma is the standard deviation. This is |
| 539 | slightly faster than the normalvariate() function. |
| 540 | |
| 541 | Not thread-safe without a lock around calls. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 542 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 543 | """ |
Guido van Rossum | cc32ac9 | 1994-03-15 16:10:24 +0000 | [diff] [blame] | 544 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 545 | # When x and y are two variables from [0, 1), uniformly |
| 546 | # distributed, then |
| 547 | # |
| 548 | # cos(2*pi*x)*sqrt(-2*log(1-y)) |
| 549 | # sin(2*pi*x)*sqrt(-2*log(1-y)) |
| 550 | # |
| 551 | # are two *independent* variables with normal distribution |
| 552 | # (mu = 0, sigma = 1). |
| 553 | # (Lambert Meertens) |
| 554 | # (corrected version; bug discovered by Mike Miller, fixed by LM) |
Guido van Rossum | cc32ac9 | 1994-03-15 16:10:24 +0000 | [diff] [blame] | 555 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 556 | # Multithreading note: When two threads call this function |
| 557 | # simultaneously, it is possible that they will receive the |
| 558 | # same return value. The window is very small though. To |
| 559 | # avoid this, you have to use a lock around all calls. (I |
| 560 | # didn't want to slow this down in the serial case by using a |
| 561 | # lock here.) |
Guido van Rossum | d03e119 | 1998-05-29 17:51:31 +0000 | [diff] [blame] | 562 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 563 | random = self.random |
| 564 | z = self.gauss_next |
| 565 | self.gauss_next = None |
| 566 | if z is None: |
| 567 | x2pi = random() * TWOPI |
| 568 | g2rad = _sqrt(-2.0 * _log(1.0 - random())) |
| 569 | z = _cos(x2pi) * g2rad |
| 570 | self.gauss_next = _sin(x2pi) * g2rad |
Guido van Rossum | cc32ac9 | 1994-03-15 16:10:24 +0000 | [diff] [blame] | 571 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 572 | return mu + z*sigma |
Guido van Rossum | 95bfcda | 1994-03-09 14:21:05 +0000 | [diff] [blame] | 573 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 574 | ## -------------------- beta -------------------- |
Tim Peters | 85e2e47 | 2001-01-26 06:49:56 +0000 | [diff] [blame] | 575 | ## See |
Ezio Melotti | 20f53f1 | 2011-04-15 08:25:16 +0300 | [diff] [blame] | 576 | ## http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html |
Tim Peters | 85e2e47 | 2001-01-26 06:49:56 +0000 | [diff] [blame] | 577 | ## for Ivan Frohne's insightful analysis of why the original implementation: |
| 578 | ## |
| 579 | ## def betavariate(self, alpha, beta): |
| 580 | ## # Discrete Event Simulation in C, pp 87-88. |
| 581 | ## |
| 582 | ## y = self.expovariate(alpha) |
| 583 | ## z = self.expovariate(1.0/beta) |
| 584 | ## return z/(y+z) |
| 585 | ## |
| 586 | ## was dead wrong, and how it probably got that way. |
Guido van Rossum | 95bfcda | 1994-03-09 14:21:05 +0000 | [diff] [blame] | 587 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 588 | def betavariate(self, alpha, beta): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 589 | """Beta distribution. |
| 590 | |
Thomas Wouters | b213704 | 2007-02-01 18:02:27 +0000 | [diff] [blame] | 591 | Conditions on the parameters are alpha > 0 and beta > 0. |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 592 | Returned values range between 0 and 1. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 593 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 594 | """ |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 595 | |
Tim Peters | 85e2e47 | 2001-01-26 06:49:56 +0000 | [diff] [blame] | 596 | # This version due to Janne Sinkkonen, and matches all the std |
| 597 | # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). |
| 598 | y = self.gammavariate(alpha, 1.) |
| 599 | if y == 0: |
| 600 | return 0.0 |
| 601 | else: |
| 602 | return y / (y + self.gammavariate(beta, 1.)) |
Guido van Rossum | 95bfcda | 1994-03-09 14:21:05 +0000 | [diff] [blame] | 603 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 604 | ## -------------------- Pareto -------------------- |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 605 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 606 | def paretovariate(self, alpha): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 607 | """Pareto distribution. alpha is the shape parameter.""" |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 608 | # Jain, pg. 495 |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 609 | |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 610 | u = 1.0 - self.random() |
Raymond Hettinger | 8ff1099 | 2010-09-08 18:58:33 +0000 | [diff] [blame] | 611 | return 1.0 / u ** (1.0/alpha) |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 612 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 613 | ## -------------------- Weibull -------------------- |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 614 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 615 | def weibullvariate(self, alpha, beta): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 616 | """Weibull distribution. |
| 617 | |
| 618 | alpha is the scale parameter and beta is the shape parameter. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 619 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 620 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 621 | # Jain, pg. 499; bug fix courtesy Bill Arms |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 622 | |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 623 | u = 1.0 - self.random() |
Raymond Hettinger | 183cd1f | 2010-09-08 18:48:21 +0000 | [diff] [blame] | 624 | return alpha * (-_log(u)) ** (1.0/beta) |
Guido van Rossum | 6c395ba | 1999-08-18 13:53:28 +0000 | [diff] [blame] | 625 | |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 626 | ## --------------- Operating System Random Source ------------------ |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 627 | |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 628 | class SystemRandom(Random): |
| 629 | """Alternate random number generator using sources provided |
| 630 | by the operating system (such as /dev/urandom on Unix or |
| 631 | CryptGenRandom on Windows). |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 632 | |
| 633 | Not available on all systems (see os.urandom() for details). |
| 634 | """ |
| 635 | |
| 636 | def random(self): |
| 637 | """Get the next random number in the range [0.0, 1.0).""" |
Raymond Hettinger | 183cd1f | 2010-09-08 18:48:21 +0000 | [diff] [blame] | 638 | return (int.from_bytes(_urandom(7), 'big') >> 3) * RECIP_BPF |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 639 | |
| 640 | def getrandbits(self, k): |
| 641 | """getrandbits(k) -> x. Generates a long int with k random bits.""" |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 642 | if k <= 0: |
| 643 | raise ValueError('number of bits must be greater than zero') |
| 644 | if k != int(k): |
| 645 | raise TypeError('number of bits should be an integer') |
Raymond Hettinger | 63b1767 | 2010-09-08 19:27:59 +0000 | [diff] [blame] | 646 | numbytes = (k + 7) // 8 # bits / 8 and rounded up |
| 647 | x = int.from_bytes(_urandom(numbytes), 'big') |
| 648 | return x >> (numbytes * 8 - k) # trim excess bits |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 649 | |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame] | 650 | def seed(self, *args, **kwds): |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 651 | "Stub method. Not used for a system random number generator." |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 652 | return None |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 653 | |
| 654 | def _notimplemented(self, *args, **kwds): |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 655 | "Method should not be called for a system random number generator." |
| 656 | raise NotImplementedError('System entropy source does not have state.') |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 657 | getstate = setstate = _notimplemented |
| 658 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 659 | ## -------------------- test program -------------------- |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 660 | |
Raymond Hettinger | 6229713 | 2003-08-30 01:24:19 +0000 | [diff] [blame] | 661 | def _test_generator(n, func, args): |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 662 | import time |
Guido van Rossum | be19ed7 | 2007-02-09 05:37:30 +0000 | [diff] [blame] | 663 | print(n, 'times', func.__name__) |
Raymond Hettinger | b98154e | 2003-05-24 17:26:02 +0000 | [diff] [blame] | 664 | total = 0.0 |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 665 | sqsum = 0.0 |
| 666 | smallest = 1e10 |
| 667 | largest = -1e10 |
| 668 | t0 = time.time() |
| 669 | for i in range(n): |
Raymond Hettinger | 6229713 | 2003-08-30 01:24:19 +0000 | [diff] [blame] | 670 | x = func(*args) |
Raymond Hettinger | b98154e | 2003-05-24 17:26:02 +0000 | [diff] [blame] | 671 | total += x |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 672 | sqsum = sqsum + x*x |
| 673 | smallest = min(x, smallest) |
| 674 | largest = max(x, largest) |
| 675 | t1 = time.time() |
Guido van Rossum | be19ed7 | 2007-02-09 05:37:30 +0000 | [diff] [blame] | 676 | print(round(t1-t0, 3), 'sec,', end=' ') |
Raymond Hettinger | b98154e | 2003-05-24 17:26:02 +0000 | [diff] [blame] | 677 | avg = total/n |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 678 | stddev = _sqrt(sqsum/n - avg*avg) |
Guido van Rossum | be19ed7 | 2007-02-09 05:37:30 +0000 | [diff] [blame] | 679 | print('avg %g, stddev %g, min %g, max %g' % \ |
| 680 | (avg, stddev, smallest, largest)) |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 681 | |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 682 | |
| 683 | def _test(N=2000): |
Raymond Hettinger | 6229713 | 2003-08-30 01:24:19 +0000 | [diff] [blame] | 684 | _test_generator(N, random, ()) |
| 685 | _test_generator(N, normalvariate, (0.0, 1.0)) |
| 686 | _test_generator(N, lognormvariate, (0.0, 1.0)) |
| 687 | _test_generator(N, vonmisesvariate, (0.0, 1.0)) |
| 688 | _test_generator(N, gammavariate, (0.01, 1.0)) |
| 689 | _test_generator(N, gammavariate, (0.1, 1.0)) |
| 690 | _test_generator(N, gammavariate, (0.1, 2.0)) |
| 691 | _test_generator(N, gammavariate, (0.5, 1.0)) |
| 692 | _test_generator(N, gammavariate, (0.9, 1.0)) |
| 693 | _test_generator(N, gammavariate, (1.0, 1.0)) |
| 694 | _test_generator(N, gammavariate, (2.0, 1.0)) |
| 695 | _test_generator(N, gammavariate, (20.0, 1.0)) |
| 696 | _test_generator(N, gammavariate, (200.0, 1.0)) |
| 697 | _test_generator(N, gauss, (0.0, 1.0)) |
| 698 | _test_generator(N, betavariate, (3.0, 3.0)) |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 699 | _test_generator(N, triangular, (0.0, 1.0, 1.0/3.0)) |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 700 | |
Tim Peters | 715c4c4 | 2001-01-26 22:56:56 +0000 | [diff] [blame] | 701 | # Create one instance, seeded from current time, and export its methods |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 702 | # as module-level functions. The functions share state across all uses |
| 703 | #(both in the user's code and in the Python libraries), but that's fine |
| 704 | # for most programs and is easier for the casual user than making them |
| 705 | # instantiate their own Random() instance. |
| 706 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 707 | _inst = Random() |
| 708 | seed = _inst.seed |
| 709 | random = _inst.random |
| 710 | uniform = _inst.uniform |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 711 | triangular = _inst.triangular |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 712 | randint = _inst.randint |
| 713 | choice = _inst.choice |
| 714 | randrange = _inst.randrange |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 715 | sample = _inst.sample |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 716 | shuffle = _inst.shuffle |
| 717 | normalvariate = _inst.normalvariate |
| 718 | lognormvariate = _inst.lognormvariate |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 719 | expovariate = _inst.expovariate |
| 720 | vonmisesvariate = _inst.vonmisesvariate |
| 721 | gammavariate = _inst.gammavariate |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 722 | gauss = _inst.gauss |
| 723 | betavariate = _inst.betavariate |
| 724 | paretovariate = _inst.paretovariate |
| 725 | weibullvariate = _inst.weibullvariate |
| 726 | getstate = _inst.getstate |
| 727 | setstate = _inst.setstate |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 728 | getrandbits = _inst.getrandbits |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 729 | |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 730 | if __name__ == '__main__': |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 731 | _test() |