mirror of
https://github.com/python/cpython
synced 2024-09-04 15:56:13 +00:00
![Christian Heimes](/assets/img/avatar_default.png)
svn+ssh://pythondev@svn.python.org/python/trunk ................ r61724 | martin.v.loewis | 2008-03-22 01:01:12 +0100 (Sat, 22 Mar 2008) | 49 lines Merged revisions 61602-61723 via svnmerge from svn+ssh://pythondev@svn.python.org/sandbox/trunk/2to3/lib2to3 ........ r61626 | david.wolever | 2008-03-19 17:19:16 +0100 (Mi, 19 M?\195?\164r 2008) | 1 line Added fixer for implicit local imports. See #2414. ........ r61628 | david.wolever | 2008-03-19 17:57:43 +0100 (Mi, 19 M?\195?\164r 2008) | 1 line Added a class for tests which should not run if a particular import is found. ........ r61629 | collin.winter | 2008-03-19 17:58:19 +0100 (Mi, 19 M?\195?\164r 2008) | 1 line Two more relative import fixes in pgen2. ........ r61635 | david.wolever | 2008-03-19 20:16:03 +0100 (Mi, 19 M?\195?\164r 2008) | 1 line Fixed print fixer so it will do the Right Thing when it encounters __future__.print_function. 2to3 gets upset, though, so the tests have been commented out. ........ r61637 | david.wolever | 2008-03-19 21:37:17 +0100 (Mi, 19 M?\195?\164r 2008) | 3 lines Added a fixer for itertools imports (from itertools import imap, ifilterfalse --> from itertools import filterfalse) ........ r61645 | david.wolever | 2008-03-19 23:22:35 +0100 (Mi, 19 M?\195?\164r 2008) | 1 line SVN is happier when you add the files you create... -_-' ........ r61654 | david.wolever | 2008-03-20 01:09:56 +0100 (Do, 20 M?\195?\164r 2008) | 1 line Added an explicit sort order to fixers -- fixes problems like #2427 ........ r61664 | david.wolever | 2008-03-20 04:32:40 +0100 (Do, 20 M?\195?\164r 2008) | 3 lines Fixes #2428 -- comments are no longer eatten by __future__ fixer. ........ r61673 | david.wolever | 2008-03-20 17:22:40 +0100 (Do, 20 M?\195?\164r 2008) | 1 line Added 2to3 node pretty-printer ........ r61679 | david.wolever | 2008-03-20 20:50:42 +0100 (Do, 20 M?\195?\164r 2008) | 1 line Made node printing a little bit prettier ........ r61723 | martin.v.loewis | 2008-03-22 00:59:27 +0100 (Sa, 22 M?\195?\164r 2008) | 2 lines Fix whitespace. ........ ................ r61725 | martin.v.loewis | 2008-03-22 01:02:41 +0100 (Sat, 22 Mar 2008) | 2 lines Install lib2to3. ................ r61731 | facundo.batista | 2008-03-22 03:45:37 +0100 (Sat, 22 Mar 2008) | 4 lines Small fix that complicated the test actually when that test failed. ................ r61732 | alexandre.vassalotti | 2008-03-22 05:08:44 +0100 (Sat, 22 Mar 2008) | 2 lines Added warning for the removal of 'hotshot' in Py3k. ................ r61733 | georg.brandl | 2008-03-22 11:07:29 +0100 (Sat, 22 Mar 2008) | 4 lines #1918: document that weak references *to* an object are cleared before the object's __del__ is called, to ensure that the weak reference callback (if any) finds the object healthy. ................ r61734 | georg.brandl | 2008-03-22 11:56:23 +0100 (Sat, 22 Mar 2008) | 2 lines Activate the Sphinx doctest extension and convert howto/functional to use it. ................ r61735 | georg.brandl | 2008-03-22 11:58:38 +0100 (Sat, 22 Mar 2008) | 2 lines Allow giving source names on the cmdline. ................ r61737 | georg.brandl | 2008-03-22 12:00:48 +0100 (Sat, 22 Mar 2008) | 2 lines Fixup this HOWTO's doctest blocks so that they can be run with sphinx' doctest builder. ................ r61739 | georg.brandl | 2008-03-22 12:47:10 +0100 (Sat, 22 Mar 2008) | 2 lines Test decimal.rst doctests as far as possible with sphinx doctest. ................ r61741 | georg.brandl | 2008-03-22 13:04:26 +0100 (Sat, 22 Mar 2008) | 2 lines Make doctests in re docs usable with sphinx' doctest. ................ r61743 | georg.brandl | 2008-03-22 13:59:37 +0100 (Sat, 22 Mar 2008) | 2 lines Make more doctests in pprint docs testable. ................ r61744 | georg.brandl | 2008-03-22 14:07:06 +0100 (Sat, 22 Mar 2008) | 2 lines No need to specify explicit "doctest_block" anymore. ................ r61753 | georg.brandl | 2008-03-22 21:08:43 +0100 (Sat, 22 Mar 2008) | 2 lines Fix-up syntax problems. ................ r61761 | georg.brandl | 2008-03-22 22:06:20 +0100 (Sat, 22 Mar 2008) | 4 lines Make collections' doctests executable. (The <BLANKLINE>s will be stripped from presentation output.) ................ r61765 | georg.brandl | 2008-03-22 22:21:57 +0100 (Sat, 22 Mar 2008) | 2 lines Test doctests in datetime docs. ................ r61766 | georg.brandl | 2008-03-22 22:26:44 +0100 (Sat, 22 Mar 2008) | 2 lines Test doctests in operator docs. ................ r61767 | georg.brandl | 2008-03-22 22:38:33 +0100 (Sat, 22 Mar 2008) | 2 lines Enable doctests in functions.rst. Already found two errors :) ................ r61769 | georg.brandl | 2008-03-22 23:04:10 +0100 (Sat, 22 Mar 2008) | 3 lines Enable doctest running for several other documents. We have now over 640 doctests that are run with "make doctest". ................ r61773 | raymond.hettinger | 2008-03-23 01:55:46 +0100 (Sun, 23 Mar 2008) | 1 line Simplify demo code. ................ r61776 | neal.norwitz | 2008-03-23 04:43:33 +0100 (Sun, 23 Mar 2008) | 7 lines Try to make this test a little more robust and not fail with: timeout (10.0025) is more than 2 seconds more than expected (0.001) I'm assuming this problem is caused by DNS lookup. This change does a DNS lookup of the hostname before trying to connect, so the time is not included. ................ r61777 | neal.norwitz | 2008-03-23 05:08:30 +0100 (Sun, 23 Mar 2008) | 1 line Speed up the test by avoiding socket timeouts. ................ r61778 | neal.norwitz | 2008-03-23 05:43:09 +0100 (Sun, 23 Mar 2008) | 1 line Skip the epoll test if epoll() does not work ................ r61780 | neal.norwitz | 2008-03-23 06:47:20 +0100 (Sun, 23 Mar 2008) | 1 line Suppress failure (to avoid a flaky test) if we cannot connect to svn.python.org ................ r61781 | neal.norwitz | 2008-03-23 07:13:25 +0100 (Sun, 23 Mar 2008) | 4 lines Move itertools before future_builtins since the latter depends on the former. From a clean build importing future_builtins would fail since itertools wasn't built yet. ................ r61782 | neal.norwitz | 2008-03-23 07:16:04 +0100 (Sun, 23 Mar 2008) | 1 line Try to prevent the alarm going off early in tearDown ................ r61783 | neal.norwitz | 2008-03-23 07:19:57 +0100 (Sun, 23 Mar 2008) | 4 lines Remove compiler warnings (on Alpha at least) about using chars as array subscripts. Using chars are dangerous b/c they are signed on some platforms and unsigned on others. ................ r61788 | georg.brandl | 2008-03-23 09:05:30 +0100 (Sun, 23 Mar 2008) | 2 lines Make the doctests presentation-friendlier. ................ r61793 | amaury.forgeotdarc | 2008-03-23 10:55:29 +0100 (Sun, 23 Mar 2008) | 4 lines #1477: ur'\U0010FFFF' raised in narrow unicode builds. Corrected the raw-unicode-escape codec to use UTF-16 surrogates in this case, just like the unicode-escape codec. ................ r61796 | raymond.hettinger | 2008-03-23 14:32:32 +0100 (Sun, 23 Mar 2008) | 1 line Issue 1681432: Add triangular distribution the random module. ................ r61807 | raymond.hettinger | 2008-03-23 20:37:53 +0100 (Sun, 23 Mar 2008) | 4 lines Adopt Nick's suggestion for useful default arguments. Clean-up floating point issues by adding true division and float constants. ................ r61813 | gregory.p.smith | 2008-03-23 22:04:43 +0100 (Sun, 23 Mar 2008) | 6 lines Fix gzip to deal with CRC's being signed values in Python 2.x properly and to read 32bit values as unsigned to start with rather than applying signedness fixups allover the place afterwards. This hopefully fixes the test_tarfile failure on the alpha/tru64 buildbot. ................
728 lines
25 KiB
Python
728 lines
25 KiB
Python
"""Random variable generators.
|
|
|
|
integers
|
|
--------
|
|
uniform within range
|
|
|
|
sequences
|
|
---------
|
|
pick random element
|
|
pick random sample
|
|
generate random permutation
|
|
|
|
distributions on the real line:
|
|
------------------------------
|
|
uniform
|
|
triangular
|
|
normal (Gaussian)
|
|
lognormal
|
|
negative exponential
|
|
gamma
|
|
beta
|
|
pareto
|
|
Weibull
|
|
|
|
distributions on the circle (angles 0 to 2pi)
|
|
---------------------------------------------
|
|
circular uniform
|
|
von Mises
|
|
|
|
General notes on the underlying Mersenne Twister core generator:
|
|
|
|
* The period is 2**19937-1.
|
|
* It is one of the most extensively tested generators in existence.
|
|
* The random() method is implemented in C, executes in a single Python step,
|
|
and is, therefore, threadsafe.
|
|
|
|
"""
|
|
|
|
from __future__ import division
|
|
from warnings import warn as _warn
|
|
from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType
|
|
from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil
|
|
from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
|
|
from os import urandom as _urandom
|
|
from binascii import hexlify as _hexlify
|
|
|
|
__all__ = ["Random","seed","random","uniform","randint","choice","sample",
|
|
"randrange","shuffle","normalvariate","lognormvariate",
|
|
"expovariate","vonmisesvariate","gammavariate","triangular",
|
|
"gauss","betavariate","paretovariate","weibullvariate",
|
|
"getstate","setstate", "getrandbits",
|
|
"SystemRandom"]
|
|
|
|
NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
|
|
TWOPI = 2.0*_pi
|
|
LOG4 = _log(4.0)
|
|
SG_MAGICCONST = 1.0 + _log(4.5)
|
|
BPF = 53 # Number of bits in a float
|
|
RECIP_BPF = 2**-BPF
|
|
|
|
|
|
# Translated by Guido van Rossum from C source provided by
|
|
# Adrian Baddeley. Adapted by Raymond Hettinger for use with
|
|
# the Mersenne Twister and os.urandom() core generators.
|
|
|
|
import _random
|
|
|
|
class Random(_random.Random):
|
|
"""Random number generator base class used by bound module functions.
|
|
|
|
Used to instantiate instances of Random to get generators that don't
|
|
share state.
|
|
|
|
Class Random can also be subclassed if you want to use a different basic
|
|
generator of your own devising: in that case, override the following
|
|
methods: random(), seed(), getstate(), and setstate().
|
|
Optionally, implement a getrandombits() method so that randrange()
|
|
can cover arbitrarily large ranges.
|
|
|
|
"""
|
|
|
|
VERSION = 3 # used by getstate/setstate
|
|
|
|
def __init__(self, x=None):
|
|
"""Initialize an instance.
|
|
|
|
Optional argument x controls seeding, as for Random.seed().
|
|
"""
|
|
|
|
self.seed(x)
|
|
self.gauss_next = None
|
|
|
|
def seed(self, a=None):
|
|
"""Initialize internal state from hashable object.
|
|
|
|
None or no argument seeds from current time or from an operating
|
|
system specific randomness source if available.
|
|
|
|
If a is not None or an int or long, hash(a) is used instead.
|
|
"""
|
|
|
|
if a is None:
|
|
try:
|
|
a = int(_hexlify(_urandom(16)), 16)
|
|
except NotImplementedError:
|
|
import time
|
|
a = int(time.time() * 256) # use fractional seconds
|
|
|
|
super().seed(a)
|
|
self.gauss_next = None
|
|
|
|
def getstate(self):
|
|
"""Return internal state; can be passed to setstate() later."""
|
|
return self.VERSION, super().getstate(), self.gauss_next
|
|
|
|
def setstate(self, state):
|
|
"""Restore internal state from object returned by getstate()."""
|
|
version = state[0]
|
|
if version == 3:
|
|
version, internalstate, self.gauss_next = state
|
|
super().setstate(internalstate)
|
|
elif version == 2:
|
|
version, internalstate, self.gauss_next = state
|
|
# In version 2, the state was saved as signed ints, which causes
|
|
# inconsistencies between 32/64-bit systems. The state is
|
|
# really unsigned 32-bit ints, so we convert negative ints from
|
|
# version 2 to positive longs for version 3.
|
|
try:
|
|
internalstate = tuple( x % (2**32) for x in internalstate )
|
|
except ValueError as e:
|
|
raise TypeError from e
|
|
super(Random, self).setstate(internalstate)
|
|
else:
|
|
raise ValueError("state with version %s passed to "
|
|
"Random.setstate() of version %s" %
|
|
(version, self.VERSION))
|
|
|
|
## ---- Methods below this point do not need to be overridden when
|
|
## ---- subclassing for the purpose of using a different core generator.
|
|
|
|
## -------------------- pickle support -------------------
|
|
|
|
def __getstate__(self): # for pickle
|
|
return self.getstate()
|
|
|
|
def __setstate__(self, state): # for pickle
|
|
self.setstate(state)
|
|
|
|
def __reduce__(self):
|
|
return self.__class__, (), self.getstate()
|
|
|
|
## -------------------- integer methods -------------------
|
|
|
|
def randrange(self, start, stop=None, step=1, int=int, default=None,
|
|
maxwidth=1<<BPF):
|
|
"""Choose a random item from range(start, stop[, step]).
|
|
|
|
This fixes the problem with randint() which includes the
|
|
endpoint; in Python this is usually not what you want.
|
|
Do not supply the 'int', 'default', and 'maxwidth' arguments.
|
|
"""
|
|
|
|
# This code is a bit messy to make it fast for the
|
|
# common case while still doing adequate error checking.
|
|
istart = int(start)
|
|
if istart != start:
|
|
raise ValueError("non-integer arg 1 for randrange()")
|
|
if stop is default:
|
|
if istart > 0:
|
|
if istart >= maxwidth:
|
|
return self._randbelow(istart)
|
|
return int(self.random() * istart)
|
|
raise ValueError("empty range for randrange()")
|
|
|
|
# stop argument supplied.
|
|
istop = int(stop)
|
|
if istop != stop:
|
|
raise ValueError("non-integer stop for randrange()")
|
|
width = istop - istart
|
|
if step == 1 and width > 0:
|
|
# Note that
|
|
# int(istart + self.random()*width)
|
|
# instead would be incorrect. For example, consider istart
|
|
# = -2 and istop = 0. Then the guts would be in
|
|
# -2.0 to 0.0 exclusive on both ends (ignoring that random()
|
|
# might return 0.0), and because int() truncates toward 0, the
|
|
# final result would be -1 or 0 (instead of -2 or -1).
|
|
# istart + int(self.random()*width)
|
|
# would also be incorrect, for a subtler reason: the RHS
|
|
# can return a long, and then randrange() would also return
|
|
# a long, but we're supposed to return an int (for backward
|
|
# compatibility).
|
|
|
|
if width >= maxwidth:
|
|
return int(istart + self._randbelow(width))
|
|
return int(istart + int(self.random()*width))
|
|
if step == 1:
|
|
raise ValueError("empty range for randrange() (%d,%d, %d)" % (istart, istop, width))
|
|
|
|
# Non-unit step argument supplied.
|
|
istep = int(step)
|
|
if istep != step:
|
|
raise ValueError("non-integer step for randrange()")
|
|
if istep > 0:
|
|
n = (width + istep - 1) // istep
|
|
elif istep < 0:
|
|
n = (width + istep + 1) // istep
|
|
else:
|
|
raise ValueError("zero step for randrange()")
|
|
|
|
if n <= 0:
|
|
raise ValueError("empty range for randrange()")
|
|
|
|
if n >= maxwidth:
|
|
return istart + istep*self._randbelow(n)
|
|
return istart + istep*int(self.random() * n)
|
|
|
|
def randint(self, a, b):
|
|
"""Return random integer in range [a, b], including both end points.
|
|
"""
|
|
|
|
return self.randrange(a, b+1)
|
|
|
|
def _randbelow(self, n, _log=_log, int=int, _maxwidth=1<<BPF,
|
|
_Method=_MethodType, _BuiltinMethod=_BuiltinMethodType):
|
|
"""Return a random int in the range [0,n)
|
|
|
|
Handles the case where n has more bits than returned
|
|
by a single call to the underlying generator.
|
|
"""
|
|
|
|
try:
|
|
getrandbits = self.getrandbits
|
|
except AttributeError:
|
|
pass
|
|
else:
|
|
# Only call self.getrandbits if the original random() builtin method
|
|
# has not been overridden or if a new getrandbits() was supplied.
|
|
# This assures that the two methods correspond.
|
|
if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method:
|
|
k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2)
|
|
r = getrandbits(k)
|
|
while r >= n:
|
|
r = getrandbits(k)
|
|
return r
|
|
if n >= _maxwidth:
|
|
_warn("Underlying random() generator does not supply \n"
|
|
"enough bits to choose from a population range this large")
|
|
return int(self.random() * n)
|
|
|
|
## -------------------- sequence methods -------------------
|
|
|
|
def choice(self, seq):
|
|
"""Choose a random element from a non-empty sequence."""
|
|
return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty
|
|
|
|
def shuffle(self, x, random=None, int=int):
|
|
"""x, random=random.random -> shuffle list x in place; return None.
|
|
|
|
Optional arg random is a 0-argument function returning a random
|
|
float in [0.0, 1.0); by default, the standard random.random.
|
|
"""
|
|
|
|
if random is None:
|
|
random = self.random
|
|
for i in reversed(range(1, len(x))):
|
|
# pick an element in x[:i+1] with which to exchange x[i]
|
|
j = int(random() * (i+1))
|
|
x[i], x[j] = x[j], x[i]
|
|
|
|
def sample(self, population, k):
|
|
"""Chooses k unique random elements from a population sequence or set.
|
|
|
|
Returns a new list containing elements from the population while
|
|
leaving the original population unchanged. The resulting list is
|
|
in selection order so that all sub-slices will also be valid random
|
|
samples. This allows raffle winners (the sample) to be partitioned
|
|
into grand prize and second place winners (the subslices).
|
|
|
|
Members of the population need not be hashable or unique. If the
|
|
population contains repeats, then each occurrence is a possible
|
|
selection in the sample.
|
|
|
|
To choose a sample in a range of integers, use range as an argument.
|
|
This is especially fast and space efficient for sampling from a
|
|
large population: sample(range(10000000), 60)
|
|
"""
|
|
|
|
# Sampling without replacement entails tracking either potential
|
|
# selections (the pool) in a list or previous selections in a set.
|
|
|
|
# When the number of selections is small compared to the
|
|
# population, then tracking selections is efficient, requiring
|
|
# only a small set and an occasional reselection. For
|
|
# a larger number of selections, the pool tracking method is
|
|
# preferred since the list takes less space than the
|
|
# set and it doesn't suffer from frequent reselections.
|
|
|
|
if isinstance(population, (set, frozenset)):
|
|
population = tuple(population)
|
|
if not hasattr(population, '__getitem__') or hasattr(population, 'keys'):
|
|
raise TypeError("Population must be a sequence or set. For dicts, use dict.keys().")
|
|
random = self.random
|
|
n = len(population)
|
|
if not 0 <= k <= n:
|
|
raise ValueError("Sample larger than population")
|
|
_int = int
|
|
result = [None] * k
|
|
setsize = 21 # size of a small set minus size of an empty list
|
|
if k > 5:
|
|
setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets
|
|
if n <= setsize:
|
|
# An n-length list is smaller than a k-length set
|
|
pool = list(population)
|
|
for i in range(k): # invariant: non-selected at [0,n-i)
|
|
j = _int(random() * (n-i))
|
|
result[i] = pool[j]
|
|
pool[j] = pool[n-i-1] # move non-selected item into vacancy
|
|
else:
|
|
selected = set()
|
|
selected_add = selected.add
|
|
for i in range(k):
|
|
j = _int(random() * n)
|
|
while j in selected:
|
|
j = _int(random() * n)
|
|
selected_add(j)
|
|
result[i] = population[j]
|
|
return result
|
|
|
|
## -------------------- real-valued distributions -------------------
|
|
|
|
## -------------------- uniform distribution -------------------
|
|
|
|
def uniform(self, a, b):
|
|
"""Get a random number in the range [a, b)."""
|
|
return a + (b-a) * self.random()
|
|
|
|
## -------------------- triangular --------------------
|
|
|
|
def triangular(self, low=0.0, high=1.0, mode=None):
|
|
"""Triangular distribution.
|
|
|
|
Continuous distribution bounded by given lower and upper limits,
|
|
and having a given mode value in-between.
|
|
|
|
http://en.wikipedia.org/wiki/Triangular_distribution
|
|
|
|
"""
|
|
u = self.random()
|
|
c = 0.5 if mode is None else (mode - low) / (high - low)
|
|
if u > c:
|
|
u = 1.0 - u
|
|
c = 1.0 - c
|
|
low, high = high, low
|
|
return low + (high - low) * (u * c) ** 0.5
|
|
|
|
## -------------------- normal distribution --------------------
|
|
|
|
def normalvariate(self, mu, sigma):
|
|
"""Normal distribution.
|
|
|
|
mu is the mean, and sigma is the standard deviation.
|
|
|
|
"""
|
|
# mu = mean, sigma = standard deviation
|
|
|
|
# Uses Kinderman and Monahan method. Reference: Kinderman,
|
|
# A.J. and Monahan, J.F., "Computer generation of random
|
|
# variables using the ratio of uniform deviates", ACM Trans
|
|
# Math Software, 3, (1977), pp257-260.
|
|
|
|
random = self.random
|
|
while 1:
|
|
u1 = random()
|
|
u2 = 1.0 - random()
|
|
z = NV_MAGICCONST*(u1-0.5)/u2
|
|
zz = z*z/4.0
|
|
if zz <= -_log(u2):
|
|
break
|
|
return mu + z*sigma
|
|
|
|
## -------------------- lognormal distribution --------------------
|
|
|
|
def lognormvariate(self, mu, sigma):
|
|
"""Log normal distribution.
|
|
|
|
If you take the natural logarithm of this distribution, you'll get a
|
|
normal distribution with mean mu and standard deviation sigma.
|
|
mu can have any value, and sigma must be greater than zero.
|
|
|
|
"""
|
|
return _exp(self.normalvariate(mu, sigma))
|
|
|
|
## -------------------- exponential distribution --------------------
|
|
|
|
def expovariate(self, lambd):
|
|
"""Exponential distribution.
|
|
|
|
lambd is 1.0 divided by the desired mean. (The parameter would be
|
|
called "lambda", but that is a reserved word in Python.) Returned
|
|
values range from 0 to positive infinity.
|
|
|
|
"""
|
|
# lambd: rate lambd = 1/mean
|
|
# ('lambda' is a Python reserved word)
|
|
|
|
random = self.random
|
|
u = random()
|
|
while u <= 1e-7:
|
|
u = random()
|
|
return -_log(u)/lambd
|
|
|
|
## -------------------- von Mises distribution --------------------
|
|
|
|
def vonmisesvariate(self, mu, kappa):
|
|
"""Circular data distribution.
|
|
|
|
mu is the mean angle, expressed in radians between 0 and 2*pi, and
|
|
kappa is the concentration parameter, which must be greater than or
|
|
equal to zero. If kappa is equal to zero, this distribution reduces
|
|
to a uniform random angle over the range 0 to 2*pi.
|
|
|
|
"""
|
|
# mu: mean angle (in radians between 0 and 2*pi)
|
|
# kappa: concentration parameter kappa (>= 0)
|
|
# if kappa = 0 generate uniform random angle
|
|
|
|
# Based upon an algorithm published in: Fisher, N.I.,
|
|
# "Statistical Analysis of Circular Data", Cambridge
|
|
# University Press, 1993.
|
|
|
|
# Thanks to Magnus Kessler for a correction to the
|
|
# implementation of step 4.
|
|
|
|
random = self.random
|
|
if kappa <= 1e-6:
|
|
return TWOPI * random()
|
|
|
|
a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa)
|
|
b = (a - _sqrt(2.0 * a))/(2.0 * kappa)
|
|
r = (1.0 + b * b)/(2.0 * b)
|
|
|
|
while 1:
|
|
u1 = random()
|
|
|
|
z = _cos(_pi * u1)
|
|
f = (1.0 + r * z)/(r + z)
|
|
c = kappa * (r - f)
|
|
|
|
u2 = random()
|
|
|
|
if u2 < c * (2.0 - c) or u2 <= c * _exp(1.0 - c):
|
|
break
|
|
|
|
u3 = random()
|
|
if u3 > 0.5:
|
|
theta = (mu % TWOPI) + _acos(f)
|
|
else:
|
|
theta = (mu % TWOPI) - _acos(f)
|
|
|
|
return theta
|
|
|
|
## -------------------- gamma distribution --------------------
|
|
|
|
def gammavariate(self, alpha, beta):
|
|
"""Gamma distribution. Not the gamma function!
|
|
|
|
Conditions on the parameters are alpha > 0 and beta > 0.
|
|
|
|
"""
|
|
|
|
# alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2
|
|
|
|
# Warning: a few older sources define the gamma distribution in terms
|
|
# of alpha > -1.0
|
|
if alpha <= 0.0 or beta <= 0.0:
|
|
raise ValueError('gammavariate: alpha and beta must be > 0.0')
|
|
|
|
random = self.random
|
|
if alpha > 1.0:
|
|
|
|
# Uses R.C.H. Cheng, "The generation of Gamma
|
|
# variables with non-integral shape parameters",
|
|
# Applied Statistics, (1977), 26, No. 1, p71-74
|
|
|
|
ainv = _sqrt(2.0 * alpha - 1.0)
|
|
bbb = alpha - LOG4
|
|
ccc = alpha + ainv
|
|
|
|
while 1:
|
|
u1 = random()
|
|
if not 1e-7 < u1 < .9999999:
|
|
continue
|
|
u2 = 1.0 - random()
|
|
v = _log(u1/(1.0-u1))/ainv
|
|
x = alpha*_exp(v)
|
|
z = u1*u1*u2
|
|
r = bbb+ccc*v-x
|
|
if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z):
|
|
return x * beta
|
|
|
|
elif alpha == 1.0:
|
|
# expovariate(1)
|
|
u = random()
|
|
while u <= 1e-7:
|
|
u = random()
|
|
return -_log(u) * beta
|
|
|
|
else: # alpha is between 0 and 1 (exclusive)
|
|
|
|
# Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
|
|
|
|
while 1:
|
|
u = random()
|
|
b = (_e + alpha)/_e
|
|
p = b*u
|
|
if p <= 1.0:
|
|
x = p ** (1.0/alpha)
|
|
else:
|
|
x = -_log((b-p)/alpha)
|
|
u1 = random()
|
|
if p > 1.0:
|
|
if u1 <= x ** (alpha - 1.0):
|
|
break
|
|
elif u1 <= _exp(-x):
|
|
break
|
|
return x * beta
|
|
|
|
## -------------------- Gauss (faster alternative) --------------------
|
|
|
|
def gauss(self, mu, sigma):
|
|
"""Gaussian distribution.
|
|
|
|
mu is the mean, and sigma is the standard deviation. This is
|
|
slightly faster than the normalvariate() function.
|
|
|
|
Not thread-safe without a lock around calls.
|
|
|
|
"""
|
|
|
|
# When x and y are two variables from [0, 1), uniformly
|
|
# distributed, then
|
|
#
|
|
# cos(2*pi*x)*sqrt(-2*log(1-y))
|
|
# sin(2*pi*x)*sqrt(-2*log(1-y))
|
|
#
|
|
# are two *independent* variables with normal distribution
|
|
# (mu = 0, sigma = 1).
|
|
# (Lambert Meertens)
|
|
# (corrected version; bug discovered by Mike Miller, fixed by LM)
|
|
|
|
# Multithreading note: When two threads call this function
|
|
# simultaneously, it is possible that they will receive the
|
|
# same return value. The window is very small though. To
|
|
# avoid this, you have to use a lock around all calls. (I
|
|
# didn't want to slow this down in the serial case by using a
|
|
# lock here.)
|
|
|
|
random = self.random
|
|
z = self.gauss_next
|
|
self.gauss_next = None
|
|
if z is None:
|
|
x2pi = random() * TWOPI
|
|
g2rad = _sqrt(-2.0 * _log(1.0 - random()))
|
|
z = _cos(x2pi) * g2rad
|
|
self.gauss_next = _sin(x2pi) * g2rad
|
|
|
|
return mu + z*sigma
|
|
|
|
## -------------------- beta --------------------
|
|
## See
|
|
## http://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470
|
|
## for Ivan Frohne's insightful analysis of why the original implementation:
|
|
##
|
|
## def betavariate(self, alpha, beta):
|
|
## # Discrete Event Simulation in C, pp 87-88.
|
|
##
|
|
## y = self.expovariate(alpha)
|
|
## z = self.expovariate(1.0/beta)
|
|
## return z/(y+z)
|
|
##
|
|
## was dead wrong, and how it probably got that way.
|
|
|
|
def betavariate(self, alpha, beta):
|
|
"""Beta distribution.
|
|
|
|
Conditions on the parameters are alpha > 0 and beta > 0.
|
|
Returned values range between 0 and 1.
|
|
|
|
"""
|
|
|
|
# This version due to Janne Sinkkonen, and matches all the std
|
|
# texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution").
|
|
y = self.gammavariate(alpha, 1.)
|
|
if y == 0:
|
|
return 0.0
|
|
else:
|
|
return y / (y + self.gammavariate(beta, 1.))
|
|
|
|
## -------------------- Pareto --------------------
|
|
|
|
def paretovariate(self, alpha):
|
|
"""Pareto distribution. alpha is the shape parameter."""
|
|
# Jain, pg. 495
|
|
|
|
u = 1.0 - self.random()
|
|
return 1.0 / pow(u, 1.0/alpha)
|
|
|
|
## -------------------- Weibull --------------------
|
|
|
|
def weibullvariate(self, alpha, beta):
|
|
"""Weibull distribution.
|
|
|
|
alpha is the scale parameter and beta is the shape parameter.
|
|
|
|
"""
|
|
# Jain, pg. 499; bug fix courtesy Bill Arms
|
|
|
|
u = 1.0 - self.random()
|
|
return alpha * pow(-_log(u), 1.0/beta)
|
|
|
|
## --------------- Operating System Random Source ------------------
|
|
|
|
class SystemRandom(Random):
|
|
"""Alternate random number generator using sources provided
|
|
by the operating system (such as /dev/urandom on Unix or
|
|
CryptGenRandom on Windows).
|
|
|
|
Not available on all systems (see os.urandom() for details).
|
|
"""
|
|
|
|
def random(self):
|
|
"""Get the next random number in the range [0.0, 1.0)."""
|
|
return (int(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF
|
|
|
|
def getrandbits(self, k):
|
|
"""getrandbits(k) -> x. Generates a long int with k random bits."""
|
|
if k <= 0:
|
|
raise ValueError('number of bits must be greater than zero')
|
|
if k != int(k):
|
|
raise TypeError('number of bits should be an integer')
|
|
bytes = (k + 7) // 8 # bits / 8 and rounded up
|
|
x = int(_hexlify(_urandom(bytes)), 16)
|
|
return x >> (bytes * 8 - k) # trim excess bits
|
|
|
|
def seed(self, *args, **kwds):
|
|
"Stub method. Not used for a system random number generator."
|
|
return None
|
|
|
|
def _notimplemented(self, *args, **kwds):
|
|
"Method should not be called for a system random number generator."
|
|
raise NotImplementedError('System entropy source does not have state.')
|
|
getstate = setstate = _notimplemented
|
|
|
|
## -------------------- test program --------------------
|
|
|
|
def _test_generator(n, func, args):
|
|
import time
|
|
print(n, 'times', func.__name__)
|
|
total = 0.0
|
|
sqsum = 0.0
|
|
smallest = 1e10
|
|
largest = -1e10
|
|
t0 = time.time()
|
|
for i in range(n):
|
|
x = func(*args)
|
|
total += x
|
|
sqsum = sqsum + x*x
|
|
smallest = min(x, smallest)
|
|
largest = max(x, largest)
|
|
t1 = time.time()
|
|
print(round(t1-t0, 3), 'sec,', end=' ')
|
|
avg = total/n
|
|
stddev = _sqrt(sqsum/n - avg*avg)
|
|
print('avg %g, stddev %g, min %g, max %g' % \
|
|
(avg, stddev, smallest, largest))
|
|
|
|
|
|
def _test(N=2000):
|
|
_test_generator(N, random, ())
|
|
_test_generator(N, normalvariate, (0.0, 1.0))
|
|
_test_generator(N, lognormvariate, (0.0, 1.0))
|
|
_test_generator(N, vonmisesvariate, (0.0, 1.0))
|
|
_test_generator(N, gammavariate, (0.01, 1.0))
|
|
_test_generator(N, gammavariate, (0.1, 1.0))
|
|
_test_generator(N, gammavariate, (0.1, 2.0))
|
|
_test_generator(N, gammavariate, (0.5, 1.0))
|
|
_test_generator(N, gammavariate, (0.9, 1.0))
|
|
_test_generator(N, gammavariate, (1.0, 1.0))
|
|
_test_generator(N, gammavariate, (2.0, 1.0))
|
|
_test_generator(N, gammavariate, (20.0, 1.0))
|
|
_test_generator(N, gammavariate, (200.0, 1.0))
|
|
_test_generator(N, gauss, (0.0, 1.0))
|
|
_test_generator(N, betavariate, (3.0, 3.0))
|
|
_test_generator(N, triangular, (0.0, 1.0, 1.0/3.0))
|
|
|
|
# Create one instance, seeded from current time, and export its methods
|
|
# as module-level functions. The functions share state across all uses
|
|
#(both in the user's code and in the Python libraries), but that's fine
|
|
# for most programs and is easier for the casual user than making them
|
|
# instantiate their own Random() instance.
|
|
|
|
_inst = Random()
|
|
seed = _inst.seed
|
|
random = _inst.random
|
|
uniform = _inst.uniform
|
|
triangular = _inst.triangular
|
|
randint = _inst.randint
|
|
choice = _inst.choice
|
|
randrange = _inst.randrange
|
|
sample = _inst.sample
|
|
shuffle = _inst.shuffle
|
|
normalvariate = _inst.normalvariate
|
|
lognormvariate = _inst.lognormvariate
|
|
expovariate = _inst.expovariate
|
|
vonmisesvariate = _inst.vonmisesvariate
|
|
gammavariate = _inst.gammavariate
|
|
gauss = _inst.gauss
|
|
betavariate = _inst.betavariate
|
|
paretovariate = _inst.paretovariate
|
|
weibullvariate = _inst.weibullvariate
|
|
getstate = _inst.getstate
|
|
setstate = _inst.setstate
|
|
getrandbits = _inst.getrandbits
|
|
|
|
if __name__ == '__main__':
|
|
_test()
|