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 |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 16 | normal (Gaussian) |
| 17 | lognormal |
| 18 | negative exponential |
| 19 | gamma |
| 20 | beta |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 21 | pareto |
| 22 | Weibull |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 23 | |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 24 | distributions on the circle (angles 0 to 2pi) |
| 25 | --------------------------------------------- |
| 26 | circular uniform |
| 27 | von Mises |
| 28 | |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 29 | General notes on the underlying Mersenne Twister core generator: |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 30 | |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 31 | * The period is 2**19937-1. |
Thomas Wouters | 0e3f591 | 2006-08-11 14:57:12 +0000 | [diff] [blame] | 32 | * It is one of the most extensively tested generators in existence. |
Thomas Wouters | 0e3f591 | 2006-08-11 14:57:12 +0000 | [diff] [blame] | 33 | * The random() method is implemented in C, executes in a single Python step, |
| 34 | and is, therefore, threadsafe. |
Tim Peters | e360d95 | 2001-01-26 10:00:39 +0000 | [diff] [blame] | 35 | |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 36 | """ |
Guido van Rossum | d03e119 | 1998-05-29 17:51:31 +0000 | [diff] [blame] | 37 | |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 38 | from warnings import warn as _warn |
| 39 | from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 40 | 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] | 41 | 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] | 42 | from os import urandom as _urandom |
| 43 | from binascii import hexlify as _hexlify |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 44 | |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 45 | __all__ = ["Random","seed","random","uniform","randint","choice","sample", |
Skip Montanaro | 0de6580 | 2001-02-15 22:15:14 +0000 | [diff] [blame] | 46 | "randrange","shuffle","normalvariate","lognormvariate", |
Raymond Hettinger | f8a52d3 | 2003-08-05 12:23:19 +0000 | [diff] [blame] | 47 | "expovariate","vonmisesvariate","gammavariate", |
| 48 | "gauss","betavariate","paretovariate","weibullvariate", |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame^] | 49 | "getstate","setstate", "getrandbits", |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 50 | "SystemRandom"] |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 51 | |
| 52 | NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 53 | TWOPI = 2.0*_pi |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 54 | LOG4 = _log(4.0) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 55 | SG_MAGICCONST = 1.0 + _log(4.5) |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 56 | BPF = 53 # Number of bits in a float |
Tim Peters | 7c2a85b | 2004-08-31 02:19:55 +0000 | [diff] [blame] | 57 | RECIP_BPF = 2**-BPF |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 58 | |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 59 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 60 | # Translated by Guido van Rossum from C source provided by |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 61 | # Adrian Baddeley. Adapted by Raymond Hettinger for use with |
Raymond Hettinger | 3fa19d7 | 2004-08-31 01:05:15 +0000 | [diff] [blame] | 62 | # the Mersenne Twister and os.urandom() core generators. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 63 | |
Raymond Hettinger | 145a4a0 | 2003-01-07 10:25:55 +0000 | [diff] [blame] | 64 | import _random |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 65 | |
Raymond Hettinger | 145a4a0 | 2003-01-07 10:25:55 +0000 | [diff] [blame] | 66 | class Random(_random.Random): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 67 | """Random number generator base class used by bound module functions. |
| 68 | |
| 69 | Used to instantiate instances of Random to get generators that don't |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame^] | 70 | share state. |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 71 | |
| 72 | Class Random can also be subclassed if you want to use a different basic |
| 73 | generator of your own devising: in that case, override the following |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame^] | 74 | methods: random(), seed(), getstate(), and setstate(). |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 75 | Optionally, implement a getrandombits() method so that randrange() |
| 76 | can cover arbitrarily large ranges. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 77 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 78 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 79 | |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 80 | VERSION = 3 # used by getstate/setstate |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 81 | |
| 82 | def __init__(self, x=None): |
| 83 | """Initialize an instance. |
| 84 | |
| 85 | Optional argument x controls seeding, as for Random.seed(). |
| 86 | """ |
| 87 | |
| 88 | self.seed(x) |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 89 | self.gauss_next = None |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 90 | |
Tim Peters | 0de88fc | 2001-02-01 04:59:18 +0000 | [diff] [blame] | 91 | def seed(self, a=None): |
| 92 | """Initialize internal state from hashable object. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 93 | |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 94 | None or no argument seeds from current time or from an operating |
| 95 | system specific randomness source if available. |
Tim Peters | 0de88fc | 2001-02-01 04:59:18 +0000 | [diff] [blame] | 96 | |
Tim Peters | bcd725f | 2001-02-01 10:06:53 +0000 | [diff] [blame] | 97 | If a is not None or an int or long, hash(a) is used instead. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 98 | """ |
| 99 | |
Raymond Hettinger | 3081d59 | 2003-08-09 18:30:57 +0000 | [diff] [blame] | 100 | if a is None: |
Raymond Hettinger | c1c43ca | 2004-09-05 00:00:42 +0000 | [diff] [blame] | 101 | try: |
Guido van Rossum | e2a383d | 2007-01-15 16:59:06 +0000 | [diff] [blame] | 102 | a = int(_hexlify(_urandom(16)), 16) |
Raymond Hettinger | c1c43ca | 2004-09-05 00:00:42 +0000 | [diff] [blame] | 103 | except NotImplementedError: |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 104 | import time |
Guido van Rossum | e2a383d | 2007-01-15 16:59:06 +0000 | [diff] [blame] | 105 | a = int(time.time() * 256) # use fractional seconds |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 106 | |
Guido van Rossum | cd16bf6 | 2007-06-13 18:07:49 +0000 | [diff] [blame] | 107 | super().seed(a) |
Tim Peters | 46c04e1 | 2002-05-05 20:40:00 +0000 | [diff] [blame] | 108 | self.gauss_next = None |
| 109 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 110 | def getstate(self): |
| 111 | """Return internal state; can be passed to setstate() later.""" |
Guido van Rossum | cd16bf6 | 2007-06-13 18:07:49 +0000 | [diff] [blame] | 112 | return self.VERSION, super().getstate(), self.gauss_next |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 113 | |
| 114 | def setstate(self, state): |
| 115 | """Restore internal state from object returned by getstate().""" |
| 116 | version = state[0] |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 117 | if version == 3: |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 118 | version, internalstate, self.gauss_next = state |
Guido van Rossum | cd16bf6 | 2007-06-13 18:07:49 +0000 | [diff] [blame] | 119 | super().setstate(internalstate) |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 120 | elif version == 2: |
| 121 | version, internalstate, self.gauss_next = state |
| 122 | # In version 2, the state was saved as signed ints, which causes |
| 123 | # inconsistencies between 32/64-bit systems. The state is |
| 124 | # really unsigned 32-bit ints, so we convert negative ints from |
| 125 | # version 2 to positive longs for version 3. |
| 126 | try: |
| 127 | internalstate = tuple( x % (2**32) for x in internalstate ) |
| 128 | except ValueError as e: |
| 129 | raise TypeError from e |
| 130 | super(Random, self).setstate(internalstate) |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 131 | else: |
| 132 | raise ValueError("state with version %s passed to " |
| 133 | "Random.setstate() of version %s" % |
| 134 | (version, self.VERSION)) |
| 135 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 136 | ## ---- Methods below this point do not need to be overridden when |
| 137 | ## ---- subclassing for the purpose of using a different core generator. |
| 138 | |
| 139 | ## -------------------- pickle support ------------------- |
| 140 | |
| 141 | def __getstate__(self): # for pickle |
| 142 | return self.getstate() |
| 143 | |
| 144 | def __setstate__(self, state): # for pickle |
| 145 | self.setstate(state) |
| 146 | |
Raymond Hettinger | 5f078ff | 2003-06-24 20:29:04 +0000 | [diff] [blame] | 147 | def __reduce__(self): |
| 148 | return self.__class__, (), self.getstate() |
| 149 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 150 | ## -------------------- integer methods ------------------- |
| 151 | |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 152 | def randrange(self, start, stop=None, step=1, int=int, default=None, |
Guido van Rossum | e2a383d | 2007-01-15 16:59:06 +0000 | [diff] [blame] | 153 | maxwidth=1<<BPF): |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 154 | """Choose a random item from range(start, stop[, step]). |
| 155 | |
| 156 | This fixes the problem with randint() which includes the |
| 157 | endpoint; in Python this is usually not what you want. |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 158 | Do not supply the 'int', 'default', and 'maxwidth' arguments. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 159 | """ |
| 160 | |
| 161 | # This code is a bit messy to make it fast for the |
Tim Peters | 9146f27 | 2002-08-16 03:41:39 +0000 | [diff] [blame] | 162 | # common case while still doing adequate error checking. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 163 | istart = int(start) |
| 164 | if istart != start: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 165 | raise ValueError("non-integer arg 1 for randrange()") |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 166 | if stop is default: |
| 167 | if istart > 0: |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 168 | if istart >= maxwidth: |
| 169 | return self._randbelow(istart) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 170 | return int(self.random() * istart) |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 171 | raise ValueError("empty range for randrange()") |
Tim Peters | 9146f27 | 2002-08-16 03:41:39 +0000 | [diff] [blame] | 172 | |
| 173 | # stop argument supplied. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 174 | istop = int(stop) |
| 175 | if istop != stop: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 176 | raise ValueError("non-integer stop for randrange()") |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 177 | width = istop - istart |
| 178 | if step == 1 and width > 0: |
Tim Peters | 76ca1d4 | 2003-06-19 03:46:46 +0000 | [diff] [blame] | 179 | # Note that |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 180 | # int(istart + self.random()*width) |
Tim Peters | 76ca1d4 | 2003-06-19 03:46:46 +0000 | [diff] [blame] | 181 | # instead would be incorrect. For example, consider istart |
| 182 | # = -2 and istop = 0. Then the guts would be in |
| 183 | # -2.0 to 0.0 exclusive on both ends (ignoring that random() |
| 184 | # might return 0.0), and because int() truncates toward 0, the |
| 185 | # final result would be -1 or 0 (instead of -2 or -1). |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 186 | # istart + int(self.random()*width) |
Tim Peters | 76ca1d4 | 2003-06-19 03:46:46 +0000 | [diff] [blame] | 187 | # would also be incorrect, for a subtler reason: the RHS |
| 188 | # can return a long, and then randrange() would also return |
| 189 | # a long, but we're supposed to return an int (for backward |
| 190 | # compatibility). |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 191 | |
| 192 | if width >= maxwidth: |
Tim Peters | 58eb11c | 2004-01-18 20:29:55 +0000 | [diff] [blame] | 193 | return int(istart + self._randbelow(width)) |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 194 | return int(istart + int(self.random()*width)) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 195 | if step == 1: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 196 | raise ValueError("empty range for randrange() (%d,%d, %d)" % (istart, istop, width)) |
Tim Peters | 9146f27 | 2002-08-16 03:41:39 +0000 | [diff] [blame] | 197 | |
| 198 | # Non-unit step argument supplied. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 199 | istep = int(step) |
| 200 | if istep != step: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 201 | raise ValueError("non-integer step for randrange()") |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 202 | if istep > 0: |
Raymond Hettinger | ffdb8bb | 2004-09-27 15:29:05 +0000 | [diff] [blame] | 203 | n = (width + istep - 1) // istep |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 204 | elif istep < 0: |
Raymond Hettinger | ffdb8bb | 2004-09-27 15:29:05 +0000 | [diff] [blame] | 205 | n = (width + istep + 1) // istep |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 206 | else: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 207 | raise ValueError("zero step for randrange()") |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 208 | |
| 209 | if n <= 0: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 210 | raise ValueError("empty range for randrange()") |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 211 | |
| 212 | if n >= maxwidth: |
Thomas Wouters | 902d6eb | 2007-01-09 23:18:33 +0000 | [diff] [blame] | 213 | return istart + istep*self._randbelow(n) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 214 | return istart + istep*int(self.random() * n) |
| 215 | |
| 216 | def randint(self, a, b): |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 217 | """Return random integer in range [a, b], including both end points. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 218 | """ |
| 219 | |
| 220 | return self.randrange(a, b+1) |
| 221 | |
Guido van Rossum | e2a383d | 2007-01-15 16:59:06 +0000 | [diff] [blame] | 222 | def _randbelow(self, n, _log=_log, int=int, _maxwidth=1<<BPF, |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 223 | _Method=_MethodType, _BuiltinMethod=_BuiltinMethodType): |
| 224 | """Return a random int in the range [0,n) |
| 225 | |
| 226 | Handles the case where n has more bits than returned |
| 227 | by a single call to the underlying generator. |
| 228 | """ |
| 229 | |
| 230 | try: |
| 231 | getrandbits = self.getrandbits |
| 232 | except AttributeError: |
| 233 | pass |
| 234 | else: |
| 235 | # Only call self.getrandbits if the original random() builtin method |
| 236 | # has not been overridden or if a new getrandbits() was supplied. |
| 237 | # This assures that the two methods correspond. |
| 238 | if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method: |
| 239 | k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2) |
| 240 | r = getrandbits(k) |
| 241 | while r >= n: |
| 242 | r = getrandbits(k) |
| 243 | return r |
| 244 | if n >= _maxwidth: |
| 245 | _warn("Underlying random() generator does not supply \n" |
| 246 | "enough bits to choose from a population range this large") |
| 247 | return int(self.random() * n) |
| 248 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 249 | ## -------------------- sequence methods ------------------- |
| 250 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 251 | def choice(self, seq): |
| 252 | """Choose a random element from a non-empty sequence.""" |
Raymond Hettinger | 5dae505 | 2004-06-07 02:07:15 +0000 | [diff] [blame] | 253 | return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty |
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 | |
| 262 | if random is None: |
| 263 | random = self.random |
Guido van Rossum | 805365e | 2007-05-07 22:24:25 +0000 | [diff] [blame] | 264 | for i in reversed(range(1, len(x))): |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 265 | # pick an element in x[:i+1] with which to exchange x[i] |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 266 | j = int(random() * (i+1)) |
| 267 | x[i], x[j] = x[j], x[i] |
| 268 | |
Raymond Hettinger | fdbe522 | 2003-06-13 07:01:51 +0000 | [diff] [blame] | 269 | def sample(self, population, k): |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 270 | """Chooses k unique random elements from a population sequence. |
| 271 | |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 272 | Returns a new list containing elements from the population while |
| 273 | leaving the original population unchanged. The resulting list is |
| 274 | in selection order so that all sub-slices will also be valid random |
| 275 | samples. This allows raffle winners (the sample) to be partitioned |
| 276 | into grand prize and second place winners (the subslices). |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 277 | |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 278 | Members of the population need not be hashable or unique. If the |
| 279 | population contains repeats, then each occurrence is a possible |
| 280 | selection in the sample. |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 281 | |
Guido van Rossum | 805365e | 2007-05-07 22:24:25 +0000 | [diff] [blame] | 282 | 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] | 283 | This is especially fast and space efficient for sampling from a |
Guido van Rossum | 805365e | 2007-05-07 22:24:25 +0000 | [diff] [blame] | 284 | large population: sample(range(10000000), 60) |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 285 | """ |
| 286 | |
Thomas Wouters | 49fd7fa | 2006-04-21 10:40:58 +0000 | [diff] [blame] | 287 | # XXX Although the documentation says `population` is "a sequence", |
| 288 | # XXX attempts are made to cater to any iterable with a __len__ |
| 289 | # XXX method. This has had mixed success. Examples from both |
| 290 | # XXX sides: sets work fine, and should become officially supported; |
| 291 | # XXX dicts are much harder, and have failed in various subtle |
| 292 | # XXX ways across attempts. Support for mapping types should probably |
| 293 | # XXX be dropped (and users should pass mapping.keys() or .values() |
| 294 | # XXX explicitly). |
| 295 | |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 296 | # Sampling without replacement entails tracking either potential |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 297 | # selections (the pool) in a list or previous selections in a set. |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 298 | |
Jeremy Hylton | 2b55d35 | 2004-02-23 17:27:57 +0000 | [diff] [blame] | 299 | # When the number of selections is small compared to the |
| 300 | # population, then tracking selections is efficient, requiring |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 301 | # only a small set and an occasional reselection. For |
Jeremy Hylton | 2b55d35 | 2004-02-23 17:27:57 +0000 | [diff] [blame] | 302 | # a larger number of selections, the pool tracking method is |
| 303 | # preferred since the list takes less space than the |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 304 | # set and it doesn't suffer from frequent reselections. |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 305 | |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 306 | n = len(population) |
| 307 | if not 0 <= k <= n: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 308 | raise ValueError("sample larger than population") |
Raymond Hettinger | 8b9aa8d | 2003-01-04 05:20:33 +0000 | [diff] [blame] | 309 | random = self.random |
Raymond Hettinger | fdbe522 | 2003-06-13 07:01:51 +0000 | [diff] [blame] | 310 | _int = int |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 311 | result = [None] * k |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 312 | setsize = 21 # size of a small set minus size of an empty list |
| 313 | if k > 5: |
Tim Peters | 9e34c04 | 2005-08-26 15:20:46 +0000 | [diff] [blame] | 314 | setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets |
Thomas Wouters | 49fd7fa | 2006-04-21 10:40:58 +0000 | [diff] [blame] | 315 | if n <= setsize or hasattr(population, "keys"): |
| 316 | # An n-length list is smaller than a k-length set, or this is a |
| 317 | # mapping type so the other algorithm wouldn't work. |
Raymond Hettinger | 311f419 | 2002-11-18 09:01:24 +0000 | [diff] [blame] | 318 | pool = list(population) |
Guido van Rossum | 805365e | 2007-05-07 22:24:25 +0000 | [diff] [blame] | 319 | for i in range(k): # invariant: non-selected at [0,n-i) |
Raymond Hettinger | fdbe522 | 2003-06-13 07:01:51 +0000 | [diff] [blame] | 320 | j = _int(random() * (n-i)) |
Raymond Hettinger | 311f419 | 2002-11-18 09:01:24 +0000 | [diff] [blame] | 321 | result[i] = pool[j] |
Raymond Hettinger | 8b9aa8d | 2003-01-04 05:20:33 +0000 | [diff] [blame] | 322 | pool[j] = pool[n-i-1] # move non-selected item into vacancy |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 323 | else: |
Raymond Hettinger | 66d09f1 | 2003-09-06 04:25:54 +0000 | [diff] [blame] | 324 | try: |
Thomas Wouters | 49fd7fa | 2006-04-21 10:40:58 +0000 | [diff] [blame] | 325 | selected = set() |
| 326 | selected_add = selected.add |
Guido van Rossum | 805365e | 2007-05-07 22:24:25 +0000 | [diff] [blame] | 327 | for i in range(k): |
Raymond Hettinger | fdbe522 | 2003-06-13 07:01:51 +0000 | [diff] [blame] | 328 | j = _int(random() * n) |
Thomas Wouters | 49fd7fa | 2006-04-21 10:40:58 +0000 | [diff] [blame] | 329 | while j in selected: |
| 330 | j = _int(random() * n) |
| 331 | selected_add(j) |
| 332 | result[i] = population[j] |
| 333 | except (TypeError, KeyError): # handle (at least) sets |
| 334 | if isinstance(population, list): |
| 335 | raise |
| 336 | return self.sample(tuple(population), k) |
Raymond Hettinger | 311f419 | 2002-11-18 09:01:24 +0000 | [diff] [blame] | 337 | return result |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 338 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 339 | ## -------------------- real-valued distributions ------------------- |
| 340 | |
| 341 | ## -------------------- uniform distribution ------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 342 | |
| 343 | def uniform(self, a, b): |
| 344 | """Get a random number in the range [a, b).""" |
| 345 | return a + (b-a) * self.random() |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 346 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 347 | ## -------------------- normal distribution -------------------- |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 348 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 349 | def normalvariate(self, mu, sigma): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 350 | """Normal distribution. |
| 351 | |
| 352 | mu is the mean, and sigma is the standard deviation. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 353 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 354 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 355 | # mu = mean, sigma = standard deviation |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 356 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 357 | # Uses Kinderman and Monahan method. Reference: Kinderman, |
| 358 | # A.J. and Monahan, J.F., "Computer generation of random |
| 359 | # variables using the ratio of uniform deviates", ACM Trans |
| 360 | # Math Software, 3, (1977), pp257-260. |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 361 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 362 | random = self.random |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 363 | while 1: |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 364 | u1 = random() |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 365 | u2 = 1.0 - random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 366 | z = NV_MAGICCONST*(u1-0.5)/u2 |
| 367 | zz = z*z/4.0 |
| 368 | if zz <= -_log(u2): |
| 369 | break |
| 370 | return mu + z*sigma |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 371 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 372 | ## -------------------- lognormal distribution -------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 373 | |
| 374 | def lognormvariate(self, mu, sigma): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 375 | """Log normal distribution. |
| 376 | |
| 377 | If you take the natural logarithm of this distribution, you'll get a |
| 378 | normal distribution with mean mu and standard deviation sigma. |
| 379 | mu can have any value, and sigma must be greater than zero. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 380 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 381 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 382 | return _exp(self.normalvariate(mu, sigma)) |
| 383 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 384 | ## -------------------- exponential distribution -------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 385 | |
| 386 | def expovariate(self, lambd): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 387 | """Exponential distribution. |
| 388 | |
| 389 | lambd is 1.0 divided by the desired mean. (The parameter would be |
| 390 | called "lambda", but that is a reserved word in Python.) Returned |
| 391 | values range from 0 to positive infinity. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 392 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 393 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 394 | # lambd: rate lambd = 1/mean |
| 395 | # ('lambda' is a Python reserved word) |
| 396 | |
| 397 | random = self.random |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 398 | u = random() |
| 399 | while u <= 1e-7: |
| 400 | u = random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 401 | return -_log(u)/lambd |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 402 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 403 | ## -------------------- von Mises distribution -------------------- |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 404 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 405 | def vonmisesvariate(self, mu, kappa): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 406 | """Circular data distribution. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 407 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 408 | mu is the mean angle, expressed in radians between 0 and 2*pi, and |
| 409 | kappa is the concentration parameter, which must be greater than or |
| 410 | equal to zero. If kappa is equal to zero, this distribution reduces |
| 411 | to a uniform random angle over the range 0 to 2*pi. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 412 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 413 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 414 | # mu: mean angle (in radians between 0 and 2*pi) |
| 415 | # kappa: concentration parameter kappa (>= 0) |
| 416 | # if kappa = 0 generate uniform random angle |
| 417 | |
| 418 | # Based upon an algorithm published in: Fisher, N.I., |
| 419 | # "Statistical Analysis of Circular Data", Cambridge |
| 420 | # University Press, 1993. |
| 421 | |
| 422 | # Thanks to Magnus Kessler for a correction to the |
| 423 | # implementation of step 4. |
| 424 | |
| 425 | random = self.random |
| 426 | if kappa <= 1e-6: |
| 427 | return TWOPI * random() |
| 428 | |
| 429 | a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa) |
| 430 | b = (a - _sqrt(2.0 * a))/(2.0 * kappa) |
| 431 | r = (1.0 + b * b)/(2.0 * b) |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 432 | |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 433 | while 1: |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 434 | u1 = random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 435 | |
| 436 | z = _cos(_pi * u1) |
| 437 | f = (1.0 + r * z)/(r + z) |
| 438 | c = kappa * (r - f) |
| 439 | |
| 440 | u2 = random() |
| 441 | |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 442 | 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] | 443 | break |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 444 | |
| 445 | u3 = random() |
| 446 | if u3 > 0.5: |
| 447 | theta = (mu % TWOPI) + _acos(f) |
| 448 | else: |
| 449 | theta = (mu % TWOPI) - _acos(f) |
| 450 | |
| 451 | return theta |
| 452 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 453 | ## -------------------- gamma distribution -------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 454 | |
| 455 | def gammavariate(self, alpha, beta): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 456 | """Gamma distribution. Not the gamma function! |
| 457 | |
| 458 | Conditions on the parameters are alpha > 0 and beta > 0. |
| 459 | |
| 460 | """ |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 461 | |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 462 | # 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] | 463 | |
Guido van Rossum | 570764d | 2002-05-14 14:08:12 +0000 | [diff] [blame] | 464 | # Warning: a few older sources define the gamma distribution in terms |
| 465 | # of alpha > -1.0 |
| 466 | if alpha <= 0.0 or beta <= 0.0: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 467 | raise ValueError('gammavariate: alpha and beta must be > 0.0') |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 468 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 469 | random = self.random |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 470 | if alpha > 1.0: |
| 471 | |
| 472 | # Uses R.C.H. Cheng, "The generation of Gamma |
| 473 | # variables with non-integral shape parameters", |
| 474 | # Applied Statistics, (1977), 26, No. 1, p71-74 |
| 475 | |
Raymond Hettinger | ca6cdc2 | 2002-05-13 23:40:14 +0000 | [diff] [blame] | 476 | ainv = _sqrt(2.0 * alpha - 1.0) |
| 477 | bbb = alpha - LOG4 |
| 478 | ccc = alpha + ainv |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 479 | |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 480 | while 1: |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 481 | u1 = random() |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 482 | if not 1e-7 < u1 < .9999999: |
| 483 | continue |
| 484 | u2 = 1.0 - random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 485 | v = _log(u1/(1.0-u1))/ainv |
| 486 | x = alpha*_exp(v) |
| 487 | z = u1*u1*u2 |
| 488 | r = bbb+ccc*v-x |
| 489 | 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] | 490 | return x * beta |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 491 | |
| 492 | elif alpha == 1.0: |
| 493 | # expovariate(1) |
| 494 | u = random() |
| 495 | while u <= 1e-7: |
| 496 | u = random() |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 497 | return -_log(u) * beta |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 498 | |
| 499 | else: # alpha is between 0 and 1 (exclusive) |
| 500 | |
| 501 | # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle |
| 502 | |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 503 | while 1: |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 504 | u = random() |
| 505 | b = (_e + alpha)/_e |
| 506 | p = b*u |
| 507 | if p <= 1.0: |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 508 | x = p ** (1.0/alpha) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 509 | else: |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 510 | x = -_log((b-p)/alpha) |
| 511 | u1 = random() |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 512 | if p > 1.0: |
| 513 | if u1 <= x ** (alpha - 1.0): |
| 514 | break |
| 515 | elif u1 <= _exp(-x): |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 516 | break |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 517 | return x * beta |
| 518 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 519 | ## -------------------- Gauss (faster alternative) -------------------- |
Guido van Rossum | 95bfcda | 1994-03-09 14:21:05 +0000 | [diff] [blame] | 520 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 521 | def gauss(self, mu, sigma): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 522 | """Gaussian distribution. |
| 523 | |
| 524 | mu is the mean, and sigma is the standard deviation. This is |
| 525 | slightly faster than the normalvariate() function. |
| 526 | |
| 527 | Not thread-safe without a lock around calls. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 528 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 529 | """ |
Guido van Rossum | cc32ac9 | 1994-03-15 16:10:24 +0000 | [diff] [blame] | 530 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 531 | # When x and y are two variables from [0, 1), uniformly |
| 532 | # distributed, then |
| 533 | # |
| 534 | # cos(2*pi*x)*sqrt(-2*log(1-y)) |
| 535 | # sin(2*pi*x)*sqrt(-2*log(1-y)) |
| 536 | # |
| 537 | # are two *independent* variables with normal distribution |
| 538 | # (mu = 0, sigma = 1). |
| 539 | # (Lambert Meertens) |
| 540 | # (corrected version; bug discovered by Mike Miller, fixed by LM) |
Guido van Rossum | cc32ac9 | 1994-03-15 16:10:24 +0000 | [diff] [blame] | 541 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 542 | # Multithreading note: When two threads call this function |
| 543 | # simultaneously, it is possible that they will receive the |
| 544 | # same return value. The window is very small though. To |
| 545 | # avoid this, you have to use a lock around all calls. (I |
| 546 | # didn't want to slow this down in the serial case by using a |
| 547 | # lock here.) |
Guido van Rossum | d03e119 | 1998-05-29 17:51:31 +0000 | [diff] [blame] | 548 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 549 | random = self.random |
| 550 | z = self.gauss_next |
| 551 | self.gauss_next = None |
| 552 | if z is None: |
| 553 | x2pi = random() * TWOPI |
| 554 | g2rad = _sqrt(-2.0 * _log(1.0 - random())) |
| 555 | z = _cos(x2pi) * g2rad |
| 556 | self.gauss_next = _sin(x2pi) * g2rad |
Guido van Rossum | cc32ac9 | 1994-03-15 16:10:24 +0000 | [diff] [blame] | 557 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 558 | return mu + z*sigma |
Guido van Rossum | 95bfcda | 1994-03-09 14:21:05 +0000 | [diff] [blame] | 559 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 560 | ## -------------------- beta -------------------- |
Tim Peters | 85e2e47 | 2001-01-26 06:49:56 +0000 | [diff] [blame] | 561 | ## See |
| 562 | ## http://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470 |
| 563 | ## for Ivan Frohne's insightful analysis of why the original implementation: |
| 564 | ## |
| 565 | ## def betavariate(self, alpha, beta): |
| 566 | ## # Discrete Event Simulation in C, pp 87-88. |
| 567 | ## |
| 568 | ## y = self.expovariate(alpha) |
| 569 | ## z = self.expovariate(1.0/beta) |
| 570 | ## return z/(y+z) |
| 571 | ## |
| 572 | ## was dead wrong, and how it probably got that way. |
Guido van Rossum | 95bfcda | 1994-03-09 14:21:05 +0000 | [diff] [blame] | 573 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 574 | def betavariate(self, alpha, beta): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 575 | """Beta distribution. |
| 576 | |
Thomas Wouters | b213704 | 2007-02-01 18:02:27 +0000 | [diff] [blame] | 577 | Conditions on the parameters are alpha > 0 and beta > 0. |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 578 | Returned values range between 0 and 1. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 579 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 580 | """ |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 581 | |
Tim Peters | 85e2e47 | 2001-01-26 06:49:56 +0000 | [diff] [blame] | 582 | # This version due to Janne Sinkkonen, and matches all the std |
| 583 | # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). |
| 584 | y = self.gammavariate(alpha, 1.) |
| 585 | if y == 0: |
| 586 | return 0.0 |
| 587 | else: |
| 588 | return y / (y + self.gammavariate(beta, 1.)) |
Guido van Rossum | 95bfcda | 1994-03-09 14:21:05 +0000 | [diff] [blame] | 589 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 590 | ## -------------------- Pareto -------------------- |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 591 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 592 | def paretovariate(self, alpha): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 593 | """Pareto distribution. alpha is the shape parameter.""" |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 594 | # Jain, pg. 495 |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 595 | |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 596 | u = 1.0 - self.random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 597 | return 1.0 / pow(u, 1.0/alpha) |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 598 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 599 | ## -------------------- Weibull -------------------- |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 600 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 601 | def weibullvariate(self, alpha, beta): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 602 | """Weibull distribution. |
| 603 | |
| 604 | alpha is the scale parameter and beta is the shape parameter. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 605 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 606 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 607 | # Jain, pg. 499; bug fix courtesy Bill Arms |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 608 | |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 609 | u = 1.0 - self.random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 610 | return alpha * pow(-_log(u), 1.0/beta) |
Guido van Rossum | 6c395ba | 1999-08-18 13:53:28 +0000 | [diff] [blame] | 611 | |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 612 | ## --------------- Operating System Random Source ------------------ |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 613 | |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 614 | class SystemRandom(Random): |
| 615 | """Alternate random number generator using sources provided |
| 616 | by the operating system (such as /dev/urandom on Unix or |
| 617 | CryptGenRandom on Windows). |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 618 | |
| 619 | Not available on all systems (see os.urandom() for details). |
| 620 | """ |
| 621 | |
| 622 | def random(self): |
| 623 | """Get the next random number in the range [0.0, 1.0).""" |
Guido van Rossum | e2a383d | 2007-01-15 16:59:06 +0000 | [diff] [blame] | 624 | return (int(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 625 | |
| 626 | def getrandbits(self, k): |
| 627 | """getrandbits(k) -> x. Generates a long int with k random bits.""" |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 628 | if k <= 0: |
| 629 | raise ValueError('number of bits must be greater than zero') |
| 630 | if k != int(k): |
| 631 | raise TypeError('number of bits should be an integer') |
| 632 | bytes = (k + 7) // 8 # bits / 8 and rounded up |
Guido van Rossum | e2a383d | 2007-01-15 16:59:06 +0000 | [diff] [blame] | 633 | x = int(_hexlify(_urandom(bytes)), 16) |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 634 | return x >> (bytes * 8 - k) # trim excess bits |
| 635 | |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame^] | 636 | def seed(self, *args, **kwds): |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 637 | "Stub method. Not used for a system random number generator." |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 638 | return None |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 639 | |
| 640 | def _notimplemented(self, *args, **kwds): |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 641 | "Method should not be called for a system random number generator." |
| 642 | raise NotImplementedError('System entropy source does not have state.') |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 643 | getstate = setstate = _notimplemented |
| 644 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 645 | ## -------------------- test program -------------------- |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 646 | |
Raymond Hettinger | 6229713 | 2003-08-30 01:24:19 +0000 | [diff] [blame] | 647 | def _test_generator(n, func, args): |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 648 | import time |
Guido van Rossum | be19ed7 | 2007-02-09 05:37:30 +0000 | [diff] [blame] | 649 | print(n, 'times', func.__name__) |
Raymond Hettinger | b98154e | 2003-05-24 17:26:02 +0000 | [diff] [blame] | 650 | total = 0.0 |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 651 | sqsum = 0.0 |
| 652 | smallest = 1e10 |
| 653 | largest = -1e10 |
| 654 | t0 = time.time() |
| 655 | for i in range(n): |
Raymond Hettinger | 6229713 | 2003-08-30 01:24:19 +0000 | [diff] [blame] | 656 | x = func(*args) |
Raymond Hettinger | b98154e | 2003-05-24 17:26:02 +0000 | [diff] [blame] | 657 | total += x |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 658 | sqsum = sqsum + x*x |
| 659 | smallest = min(x, smallest) |
| 660 | largest = max(x, largest) |
| 661 | t1 = time.time() |
Guido van Rossum | be19ed7 | 2007-02-09 05:37:30 +0000 | [diff] [blame] | 662 | print(round(t1-t0, 3), 'sec,', end=' ') |
Raymond Hettinger | b98154e | 2003-05-24 17:26:02 +0000 | [diff] [blame] | 663 | avg = total/n |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 664 | stddev = _sqrt(sqsum/n - avg*avg) |
Guido van Rossum | be19ed7 | 2007-02-09 05:37:30 +0000 | [diff] [blame] | 665 | print('avg %g, stddev %g, min %g, max %g' % \ |
| 666 | (avg, stddev, smallest, largest)) |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 667 | |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 668 | |
| 669 | def _test(N=2000): |
Raymond Hettinger | 6229713 | 2003-08-30 01:24:19 +0000 | [diff] [blame] | 670 | _test_generator(N, random, ()) |
| 671 | _test_generator(N, normalvariate, (0.0, 1.0)) |
| 672 | _test_generator(N, lognormvariate, (0.0, 1.0)) |
| 673 | _test_generator(N, vonmisesvariate, (0.0, 1.0)) |
| 674 | _test_generator(N, gammavariate, (0.01, 1.0)) |
| 675 | _test_generator(N, gammavariate, (0.1, 1.0)) |
| 676 | _test_generator(N, gammavariate, (0.1, 2.0)) |
| 677 | _test_generator(N, gammavariate, (0.5, 1.0)) |
| 678 | _test_generator(N, gammavariate, (0.9, 1.0)) |
| 679 | _test_generator(N, gammavariate, (1.0, 1.0)) |
| 680 | _test_generator(N, gammavariate, (2.0, 1.0)) |
| 681 | _test_generator(N, gammavariate, (20.0, 1.0)) |
| 682 | _test_generator(N, gammavariate, (200.0, 1.0)) |
| 683 | _test_generator(N, gauss, (0.0, 1.0)) |
| 684 | _test_generator(N, betavariate, (3.0, 3.0)) |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 685 | |
Tim Peters | 715c4c4 | 2001-01-26 22:56:56 +0000 | [diff] [blame] | 686 | # Create one instance, seeded from current time, and export its methods |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 687 | # as module-level functions. The functions share state across all uses |
| 688 | #(both in the user's code and in the Python libraries), but that's fine |
| 689 | # for most programs and is easier for the casual user than making them |
| 690 | # instantiate their own Random() instance. |
| 691 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 692 | _inst = Random() |
| 693 | seed = _inst.seed |
| 694 | random = _inst.random |
| 695 | uniform = _inst.uniform |
| 696 | randint = _inst.randint |
| 697 | choice = _inst.choice |
| 698 | randrange = _inst.randrange |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 699 | sample = _inst.sample |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 700 | shuffle = _inst.shuffle |
| 701 | normalvariate = _inst.normalvariate |
| 702 | lognormvariate = _inst.lognormvariate |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 703 | expovariate = _inst.expovariate |
| 704 | vonmisesvariate = _inst.vonmisesvariate |
| 705 | gammavariate = _inst.gammavariate |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 706 | gauss = _inst.gauss |
| 707 | betavariate = _inst.betavariate |
| 708 | paretovariate = _inst.paretovariate |
| 709 | weibullvariate = _inst.weibullvariate |
| 710 | getstate = _inst.getstate |
| 711 | setstate = _inst.setstate |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 712 | getrandbits = _inst.getrandbits |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 713 | |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 714 | if __name__ == '__main__': |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 715 | _test() |