mirror of
https://github.com/python/cpython.git
synced 2024-11-24 18:34:43 +08:00
812 lines
28 KiB
Python
812 lines
28 KiB
Python
"""Random variable generators.
|
|
|
|
integers
|
|
--------
|
|
uniform within range
|
|
|
|
sequences
|
|
---------
|
|
pick random element
|
|
pick random sample
|
|
pick weighted 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 warnings import warn as _warn
|
|
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 _collections_abc import Set as _Set, Sequence as _Sequence
|
|
from hashlib import sha512 as _sha512
|
|
import itertools as _itertools
|
|
import bisect as _bisect
|
|
import os as _os
|
|
|
|
__all__ = ["Random","seed","random","uniform","randint","choice","sample",
|
|
"randrange","shuffle","normalvariate","lognormvariate",
|
|
"expovariate","vonmisesvariate","gammavariate","triangular",
|
|
"gauss","betavariate","paretovariate","weibullvariate",
|
|
"getstate","setstate", "getrandbits", "choices",
|
|
"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 getrandbits() 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 __init_subclass__(cls, **kwargs):
|
|
"""Control how subclasses generate random integers.
|
|
|
|
The algorithm a subclass can use depends on the random() and/or
|
|
getrandbits() implementation available to it and determines
|
|
whether it can generate random integers from arbitrarily large
|
|
ranges.
|
|
"""
|
|
|
|
for c in cls.__mro__:
|
|
if '_randbelow' in c.__dict__:
|
|
# just inherit it
|
|
break
|
|
if 'getrandbits' in c.__dict__:
|
|
cls._randbelow = cls._randbelow_with_getrandbits
|
|
break
|
|
if 'random' in c.__dict__:
|
|
cls._randbelow = cls._randbelow_without_getrandbits
|
|
break
|
|
|
|
def seed(self, a=None, version=2):
|
|
"""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 an int, all bits are used.
|
|
|
|
For version 2 (the default), all of the bits are used if *a* is a str,
|
|
bytes, or bytearray. For version 1 (provided for reproducing random
|
|
sequences from older versions of Python), the algorithm for str and
|
|
bytes generates a narrower range of seeds.
|
|
|
|
"""
|
|
|
|
if version == 1 and isinstance(a, (str, bytes)):
|
|
a = a.decode('latin-1') if isinstance(a, bytes) else a
|
|
x = ord(a[0]) << 7 if a else 0
|
|
for c in map(ord, a):
|
|
x = ((1000003 * x) ^ c) & 0xFFFFFFFFFFFFFFFF
|
|
x ^= len(a)
|
|
a = -2 if x == -1 else x
|
|
|
|
if version == 2 and isinstance(a, (str, bytes, bytearray)):
|
|
if isinstance(a, str):
|
|
a = a.encode()
|
|
a += _sha512(a).digest()
|
|
a = int.from_bytes(a, 'big')
|
|
|
|
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().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 -------------------
|
|
|
|
# Issue 17489: Since __reduce__ was defined to fix #759889 this is no
|
|
# longer called; we leave it here because it has been here since random was
|
|
# rewritten back in 2001 and why risk breaking something.
|
|
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):
|
|
"""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.
|
|
|
|
"""
|
|
|
|
# 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 None:
|
|
if istart > 0:
|
|
return self._randbelow(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:
|
|
return istart + self._randbelow(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()")
|
|
|
|
return istart + istep*self._randbelow(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_with_getrandbits(self, n):
|
|
"Return a random int in the range [0,n). Raises ValueError if n==0."
|
|
|
|
getrandbits = self.getrandbits
|
|
k = n.bit_length() # don't use (n-1) here because n can be 1
|
|
r = getrandbits(k) # 0 <= r < 2**k
|
|
while r >= n:
|
|
r = getrandbits(k)
|
|
return r
|
|
|
|
def _randbelow_without_getrandbits(self, n, int=int, maxsize=1<<BPF):
|
|
"""Return a random int in the range [0,n). Raises ValueError if n==0.
|
|
|
|
The implementation does not use getrandbits, but only random.
|
|
"""
|
|
|
|
random = self.random
|
|
if n >= maxsize:
|
|
_warn("Underlying random() generator does not supply \n"
|
|
"enough bits to choose from a population range this large.\n"
|
|
"To remove the range limitation, add a getrandbits() method.")
|
|
return int(random() * n)
|
|
if n == 0:
|
|
raise ValueError("Boundary cannot be zero")
|
|
rem = maxsize % n
|
|
limit = (maxsize - rem) / maxsize # int(limit * maxsize) % n == 0
|
|
r = random()
|
|
while r >= limit:
|
|
r = random()
|
|
return int(r*maxsize) % n
|
|
|
|
_randbelow = _randbelow_with_getrandbits
|
|
|
|
## -------------------- sequence methods -------------------
|
|
|
|
def choice(self, seq):
|
|
"""Choose a random element from a non-empty sequence."""
|
|
try:
|
|
i = self._randbelow(len(seq))
|
|
except ValueError:
|
|
raise IndexError('Cannot choose from an empty sequence') from None
|
|
return seq[i]
|
|
|
|
def shuffle(self, x, random=None):
|
|
"""Shuffle list x in place, and return None.
|
|
|
|
Optional argument random is a 0-argument function returning a
|
|
random float in [0.0, 1.0); if it is the default None, the
|
|
standard random.random will be used.
|
|
|
|
"""
|
|
|
|
if random is None:
|
|
randbelow = self._randbelow
|
|
for i in reversed(range(1, len(x))):
|
|
# pick an element in x[:i+1] with which to exchange x[i]
|
|
j = randbelow(i+1)
|
|
x[i], x[j] = x[j], x[i]
|
|
else:
|
|
_int = int
|
|
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.
|
|
|
|
# The number of calls to _randbelow() is kept at or near k, the
|
|
# theoretical minimum. This is important because running time
|
|
# is dominated by _randbelow() and because it extracts the
|
|
# least entropy from the underlying random number generators.
|
|
|
|
# Memory requirements are kept to the smaller of a k-length
|
|
# set or an n-length list.
|
|
|
|
# There are other sampling algorithms that do not require
|
|
# auxiliary memory, but they were rejected because they made
|
|
# too many calls to _randbelow(), making them slower and
|
|
# causing them to eat more entropy than necessary.
|
|
|
|
if isinstance(population, _Set):
|
|
population = tuple(population)
|
|
if not isinstance(population, _Sequence):
|
|
raise TypeError("Population must be a sequence or set. For dicts, use list(d).")
|
|
randbelow = self._randbelow
|
|
n = len(population)
|
|
if not 0 <= k <= n:
|
|
raise ValueError("Sample larger than population or is negative")
|
|
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 = randbelow(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 = randbelow(n)
|
|
while j in selected:
|
|
j = randbelow(n)
|
|
selected_add(j)
|
|
result[i] = population[j]
|
|
return result
|
|
|
|
def choices(self, population, weights=None, *, cum_weights=None, k=1):
|
|
"""Return a k sized list of population elements chosen with replacement.
|
|
|
|
If the relative weights or cumulative weights are not specified,
|
|
the selections are made with equal probability.
|
|
|
|
"""
|
|
random = self.random
|
|
n = len(population)
|
|
if cum_weights is None:
|
|
if weights is None:
|
|
_int = int
|
|
n += 0.0 # convert to float for a small speed improvement
|
|
return [population[_int(random() * n)] for i in range(k)]
|
|
cum_weights = list(_itertools.accumulate(weights))
|
|
elif weights is not None:
|
|
raise TypeError('Cannot specify both weights and cumulative weights')
|
|
if len(cum_weights) != n:
|
|
raise ValueError('The number of weights does not match the population')
|
|
bisect = _bisect.bisect
|
|
total = cum_weights[-1] + 0.0 # convert to float
|
|
hi = n - 1
|
|
return [population[bisect(cum_weights, random() * total, 0, hi)]
|
|
for i in range(k)]
|
|
|
|
## -------------------- real-valued distributions -------------------
|
|
|
|
## -------------------- uniform distribution -------------------
|
|
|
|
def uniform(self, a, b):
|
|
"Get a random number in the range [a, b) or [a, b] depending on rounding."
|
|
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()
|
|
try:
|
|
c = 0.5 if mode is None else (mode - low) / (high - low)
|
|
except ZeroDivisionError:
|
|
return low
|
|
if u > c:
|
|
u = 1.0 - u
|
|
c = 1.0 - c
|
|
low, high = high, low
|
|
return low + (high - low) * _sqrt(u * c)
|
|
|
|
## -------------------- 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. It should be
|
|
nonzero. (The parameter would be called "lambda", but that is
|
|
a reserved word in Python.) Returned values range from 0 to
|
|
positive infinity if lambd is positive, and from negative
|
|
infinity to 0 if lambd is negative.
|
|
|
|
"""
|
|
# lambd: rate lambd = 1/mean
|
|
# ('lambda' is a Python reserved word)
|
|
|
|
# we use 1-random() instead of random() to preclude the
|
|
# possibility of taking the log of zero.
|
|
return -_log(1.0 - self.random())/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()
|
|
|
|
s = 0.5 / kappa
|
|
r = s + _sqrt(1.0 + s * s)
|
|
|
|
while 1:
|
|
u1 = random()
|
|
z = _cos(_pi * u1)
|
|
|
|
d = z / (r + z)
|
|
u2 = random()
|
|
if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d):
|
|
break
|
|
|
|
q = 1.0 / r
|
|
f = (q + z) / (1.0 + q * z)
|
|
u3 = random()
|
|
if u3 > 0.5:
|
|
theta = (mu + _acos(f)) % TWOPI
|
|
else:
|
|
theta = (mu - _acos(f)) % TWOPI
|
|
|
|
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.
|
|
|
|
The probability distribution function is:
|
|
|
|
x ** (alpha - 1) * math.exp(-x / beta)
|
|
pdf(x) = --------------------------------------
|
|
math.gamma(alpha) * beta ** alpha
|
|
|
|
"""
|
|
|
|
# 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/beta)
|
|
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://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html
|
|
## 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, 1.0)
|
|
if y == 0:
|
|
return 0.0
|
|
else:
|
|
return y / (y + self.gammavariate(beta, 1.0))
|
|
|
|
## -------------------- Pareto --------------------
|
|
|
|
def paretovariate(self, alpha):
|
|
"""Pareto distribution. alpha is the shape parameter."""
|
|
# Jain, pg. 495
|
|
|
|
u = 1.0 - self.random()
|
|
return 1.0 / 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 * (-_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.from_bytes(_urandom(7), 'big') >> 3) * RECIP_BPF
|
|
|
|
def getrandbits(self, k):
|
|
"""getrandbits(k) -> x. Generates an int with k random bits."""
|
|
if k <= 0:
|
|
raise ValueError('number of bits must be greater than zero')
|
|
numbytes = (k + 7) // 8 # bits / 8 and rounded up
|
|
x = int.from_bytes(_urandom(numbytes), 'big')
|
|
return x >> (numbytes * 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\n' % \
|
|
(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
|
|
choices = _inst.choices
|
|
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 hasattr(_os, "fork"):
|
|
_os.register_at_fork(after_in_child=_inst.seed)
|
|
|
|
|
|
if __name__ == '__main__':
|
|
_test()
|