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797 lines
27 KiB
Python
797 lines
27 KiB
Python
"""Random variable generators.
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integers
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--------
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uniform within range
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sequences
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---------
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pick random element
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pick random sample
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generate random permutation
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distributions on the real line:
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------------------------------
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uniform
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normal (Gaussian)
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lognormal
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negative exponential
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gamma
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beta
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pareto
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Weibull
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distributions on the circle (angles 0 to 2pi)
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---------------------------------------------
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circular uniform
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von Mises
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General notes on the underlying Mersenne Twister core generator:
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* The period is 2**19937-1.
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* It is one of the most extensively tested generators in existence
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* Without a direct way to compute N steps forward, the
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semantics of jumpahead(n) are weakened to simply jump
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to another distant state and rely on the large period
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to avoid overlapping sequences.
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* The random() method is implemented in C, executes in
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a single Python step, and is, therefore, threadsafe.
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"""
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from math import log as _log, exp as _exp, pi as _pi, e as _e
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from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
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from math import floor as _floor
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__all__ = ["Random","seed","random","uniform","randint","choice","sample",
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"randrange","shuffle","normalvariate","lognormvariate",
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"cunifvariate","expovariate","vonmisesvariate","gammavariate",
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"stdgamma","gauss","betavariate","paretovariate","weibullvariate",
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"getstate","setstate","jumpahead"]
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NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
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TWOPI = 2.0*_pi
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LOG4 = _log(4.0)
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SG_MAGICCONST = 1.0 + _log(4.5)
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# Translated by Guido van Rossum from C source provided by
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# Adrian Baddeley. Adapted by Raymond Hettinger for use with
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# the Mersenne Twister core generator.
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import _random
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class Random(_random.Random):
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"""Random number generator base class used by bound module functions.
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Used to instantiate instances of Random to get generators that don't
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share state. Especially useful for multi-threaded programs, creating
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a different instance of Random for each thread, and using the jumpahead()
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method to ensure that the generated sequences seen by each thread don't
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overlap.
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Class Random can also be subclassed if you want to use a different basic
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generator of your own devising: in that case, override the following
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methods: random(), seed(), getstate(), setstate() and jumpahead().
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"""
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VERSION = 2 # used by getstate/setstate
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def __init__(self, x=None):
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"""Initialize an instance.
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Optional argument x controls seeding, as for Random.seed().
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"""
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self.seed(x)
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self.gauss_next = None
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def seed(self, a=None):
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"""Initialize internal state from hashable object.
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None or no argument seeds from current time.
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If a is not None or an int or long, hash(a) is used instead.
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"""
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super(Random, self).seed(a)
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self.gauss_next = None
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def getstate(self):
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"""Return internal state; can be passed to setstate() later."""
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return self.VERSION, super(Random, self).getstate(), self.gauss_next
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def setstate(self, state):
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"""Restore internal state from object returned by getstate()."""
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version = state[0]
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if version == 2:
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version, internalstate, self.gauss_next = state
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super(Random, self).setstate(internalstate)
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else:
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raise ValueError("state with version %s passed to "
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"Random.setstate() of version %s" %
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(version, self.VERSION))
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## ---- Methods below this point do not need to be overridden when
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## ---- subclassing for the purpose of using a different core generator.
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## -------------------- pickle support -------------------
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def __getstate__(self): # for pickle
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return self.getstate()
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def __setstate__(self, state): # for pickle
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self.setstate(state)
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## -------------------- integer methods -------------------
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def randrange(self, start, stop=None, step=1, int=int, default=None):
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"""Choose a random item from range(start, stop[, step]).
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This fixes the problem with randint() which includes the
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endpoint; in Python this is usually not what you want.
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Do not supply the 'int' and 'default' arguments.
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"""
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# This code is a bit messy to make it fast for the
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# common case while still doing adequate error checking.
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istart = int(start)
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if istart != start:
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raise ValueError, "non-integer arg 1 for randrange()"
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if stop is default:
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if istart > 0:
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return int(self.random() * istart)
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raise ValueError, "empty range for randrange()"
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# stop argument supplied.
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istop = int(stop)
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if istop != stop:
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raise ValueError, "non-integer stop for randrange()"
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if step == 1 and istart < istop:
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try:
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return istart + int(self.random()*(istop - istart))
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except OverflowError:
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# This can happen if istop-istart > sys.maxint + 1, and
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# multiplying by random() doesn't reduce it to something
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# <= sys.maxint. We know that the overall result fits
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# in an int, and can still do it correctly via math.floor().
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# But that adds another function call, so for speed we
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# avoided that whenever possible.
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return int(istart + _floor(self.random()*(istop - istart)))
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if step == 1:
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raise ValueError, "empty range for randrange()"
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# Non-unit step argument supplied.
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istep = int(step)
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if istep != step:
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raise ValueError, "non-integer step for randrange()"
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if istep > 0:
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n = (istop - istart + istep - 1) / istep
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elif istep < 0:
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n = (istop - istart + istep + 1) / istep
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else:
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raise ValueError, "zero step for randrange()"
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if n <= 0:
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raise ValueError, "empty range for randrange()"
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return istart + istep*int(self.random() * n)
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def randint(self, a, b):
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"""Return random integer in range [a, b], including both end points.
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"""
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return self.randrange(a, b+1)
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## -------------------- sequence methods -------------------
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def choice(self, seq):
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"""Choose a random element from a non-empty sequence."""
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return seq[int(self.random() * len(seq))]
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def shuffle(self, x, random=None, int=int):
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"""x, random=random.random -> shuffle list x in place; return None.
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Optional arg random is a 0-argument function returning a random
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float in [0.0, 1.0); by default, the standard random.random.
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Note that for even rather small len(x), the total number of
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permutations of x is larger than the period of most random number
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generators; this implies that "most" permutations of a long
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sequence can never be generated.
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"""
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if random is None:
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random = self.random
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for i in xrange(len(x)-1, 0, -1):
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# pick an element in x[:i+1] with which to exchange x[i]
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j = int(random() * (i+1))
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x[i], x[j] = x[j], x[i]
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def sample(self, population, k, int=int):
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"""Chooses k unique random elements from a population sequence.
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Returns a new list containing elements from the population while
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leaving the original population unchanged. The resulting list is
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in selection order so that all sub-slices will also be valid random
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samples. This allows raffle winners (the sample) to be partitioned
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into grand prize and second place winners (the subslices).
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Members of the population need not be hashable or unique. If the
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population contains repeats, then each occurrence is a possible
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selection in the sample.
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To choose a sample in a range of integers, use xrange as an argument.
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This is especially fast and space efficient for sampling from a
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large population: sample(xrange(10000000), 60)
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"""
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# Sampling without replacement entails tracking either potential
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# selections (the pool) in a list or previous selections in a
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# dictionary.
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# When the number of selections is small compared to the population,
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# then tracking selections is efficient, requiring only a small
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# dictionary and an occasional reselection. For a larger number of
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# selections, the pool tracking method is preferred since the list takes
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# less space than the dictionary and it doesn't suffer from frequent
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# reselections.
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n = len(population)
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if not 0 <= k <= n:
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raise ValueError, "sample larger than population"
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random = self.random
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result = [None] * k
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if n < 6 * k: # if n len list takes less space than a k len dict
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pool = list(population)
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for i in xrange(k): # invariant: non-selected at [0,n-i)
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j = int(random() * (n-i))
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result[i] = pool[j]
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pool[j] = pool[n-i-1] # move non-selected item into vacancy
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else:
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selected = {}
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for i in xrange(k):
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j = int(random() * n)
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while j in selected:
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j = int(random() * n)
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result[i] = selected[j] = population[j]
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return result
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## -------------------- real-valued distributions -------------------
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## -------------------- uniform distribution -------------------
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def uniform(self, a, b):
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"""Get a random number in the range [a, b)."""
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return a + (b-a) * self.random()
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## -------------------- normal distribution --------------------
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def normalvariate(self, mu, sigma):
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"""Normal distribution.
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mu is the mean, and sigma is the standard deviation.
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"""
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# mu = mean, sigma = standard deviation
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# Uses Kinderman and Monahan method. Reference: Kinderman,
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# A.J. and Monahan, J.F., "Computer generation of random
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# variables using the ratio of uniform deviates", ACM Trans
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# Math Software, 3, (1977), pp257-260.
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random = self.random
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while True:
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u1 = random()
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u2 = 1.0 - random()
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z = NV_MAGICCONST*(u1-0.5)/u2
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zz = z*z/4.0
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if zz <= -_log(u2):
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break
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return mu + z*sigma
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## -------------------- lognormal distribution --------------------
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def lognormvariate(self, mu, sigma):
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"""Log normal distribution.
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If you take the natural logarithm of this distribution, you'll get a
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normal distribution with mean mu and standard deviation sigma.
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mu can have any value, and sigma must be greater than zero.
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"""
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return _exp(self.normalvariate(mu, sigma))
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## -------------------- circular uniform --------------------
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def cunifvariate(self, mean, arc):
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"""Circular uniform distribution.
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mean is the mean angle, and arc is the range of the distribution,
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centered around the mean angle. Both values must be expressed in
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radians. Returned values range between mean - arc/2 and
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mean + arc/2 and are normalized to between 0 and pi.
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Deprecated in version 2.3. Use:
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(mean + arc * (Random.random() - 0.5)) % Math.pi
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"""
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# mean: mean angle (in radians between 0 and pi)
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# arc: range of distribution (in radians between 0 and pi)
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import warnings
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warnings.warn("The cunifvariate function is deprecated; Use (mean "
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"+ arc * (Random.random() - 0.5)) % Math.pi instead",
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DeprecationWarning)
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return (mean + arc * (self.random() - 0.5)) % _pi
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## -------------------- exponential distribution --------------------
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def expovariate(self, lambd):
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"""Exponential distribution.
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lambd is 1.0 divided by the desired mean. (The parameter would be
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called "lambda", but that is a reserved word in Python.) Returned
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values range from 0 to positive infinity.
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"""
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# lambd: rate lambd = 1/mean
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# ('lambda' is a Python reserved word)
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random = self.random
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u = random()
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while u <= 1e-7:
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u = random()
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return -_log(u)/lambd
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## -------------------- von Mises distribution --------------------
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def vonmisesvariate(self, mu, kappa):
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"""Circular data distribution.
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mu is the mean angle, expressed in radians between 0 and 2*pi, and
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kappa is the concentration parameter, which must be greater than or
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equal to zero. If kappa is equal to zero, this distribution reduces
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to a uniform random angle over the range 0 to 2*pi.
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"""
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# mu: mean angle (in radians between 0 and 2*pi)
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# kappa: concentration parameter kappa (>= 0)
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# if kappa = 0 generate uniform random angle
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# Based upon an algorithm published in: Fisher, N.I.,
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# "Statistical Analysis of Circular Data", Cambridge
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# University Press, 1993.
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# Thanks to Magnus Kessler for a correction to the
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# implementation of step 4.
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random = self.random
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if kappa <= 1e-6:
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return TWOPI * random()
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a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa)
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b = (a - _sqrt(2.0 * a))/(2.0 * kappa)
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r = (1.0 + b * b)/(2.0 * b)
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while True:
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u1 = random()
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z = _cos(_pi * u1)
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f = (1.0 + r * z)/(r + z)
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c = kappa * (r - f)
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u2 = random()
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if not (u2 >= c * (2.0 - c) and u2 > c * _exp(1.0 - c)):
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break
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u3 = random()
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if u3 > 0.5:
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theta = (mu % TWOPI) + _acos(f)
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else:
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theta = (mu % TWOPI) - _acos(f)
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return theta
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## -------------------- gamma distribution --------------------
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def gammavariate(self, alpha, beta):
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"""Gamma distribution. Not the gamma function!
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Conditions on the parameters are alpha > 0 and beta > 0.
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"""
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# alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2
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# Warning: a few older sources define the gamma distribution in terms
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# of alpha > -1.0
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if alpha <= 0.0 or beta <= 0.0:
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raise ValueError, 'gammavariate: alpha and beta must be > 0.0'
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random = self.random
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if alpha > 1.0:
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# Uses R.C.H. Cheng, "The generation of Gamma
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# variables with non-integral shape parameters",
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# Applied Statistics, (1977), 26, No. 1, p71-74
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ainv = _sqrt(2.0 * alpha - 1.0)
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bbb = alpha - LOG4
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ccc = alpha + ainv
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while True:
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u1 = random()
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if not 1e-7 < u1 < .9999999:
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continue
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u2 = 1.0 - random()
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v = _log(u1/(1.0-u1))/ainv
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x = alpha*_exp(v)
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z = u1*u1*u2
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r = bbb+ccc*v-x
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if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z):
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return x * beta
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elif alpha == 1.0:
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# expovariate(1)
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u = random()
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while u <= 1e-7:
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u = random()
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return -_log(u) * beta
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else: # alpha is between 0 and 1 (exclusive)
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# Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
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while True:
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u = random()
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b = (_e + alpha)/_e
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p = b*u
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if p <= 1.0:
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x = pow(p, 1.0/alpha)
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else:
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# p > 1
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x = -_log((b-p)/alpha)
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u1 = random()
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if not (((p <= 1.0) and (u1 > _exp(-x))) or
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((p > 1) and (u1 > pow(x, alpha - 1.0)))):
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break
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return x * beta
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def stdgamma(self, alpha, ainv, bbb, ccc):
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# This method was (and shall remain) undocumented.
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# This method is deprecated
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# for the following reasons:
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# 1. Returns same as .gammavariate(alpha, 1.0)
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# 2. Requires caller to provide 3 extra arguments
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# that are functions of alpha anyway
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# 3. Can't be used for alpha < 0.5
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# ainv = sqrt(2 * alpha - 1)
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# bbb = alpha - log(4)
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# ccc = alpha + ainv
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import warnings
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warnings.warn("The stdgamma function is deprecated; "
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"use gammavariate() instead",
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DeprecationWarning)
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return self.gammavariate(alpha, 1.0)
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## -------------------- Gauss (faster alternative) --------------------
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def gauss(self, mu, sigma):
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"""Gaussian distribution.
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mu is the mean, and sigma is the standard deviation. This is
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slightly faster than the normalvariate() function.
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Not thread-safe without a lock around calls.
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"""
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# When x and y are two variables from [0, 1), uniformly
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# distributed, then
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#
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# cos(2*pi*x)*sqrt(-2*log(1-y))
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# sin(2*pi*x)*sqrt(-2*log(1-y))
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#
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# are two *independent* variables with normal distribution
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# (mu = 0, sigma = 1).
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# (Lambert Meertens)
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# (corrected version; bug discovered by Mike Miller, fixed by LM)
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# Multithreading note: When two threads call this function
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# simultaneously, it is possible that they will receive the
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# same return value. The window is very small though. To
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# avoid this, you have to use a lock around all calls. (I
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# didn't want to slow this down in the serial case by using a
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# lock here.)
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random = self.random
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z = self.gauss_next
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self.gauss_next = None
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if z is None:
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x2pi = random() * TWOPI
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g2rad = _sqrt(-2.0 * _log(1.0 - random()))
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z = _cos(x2pi) * g2rad
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self.gauss_next = _sin(x2pi) * g2rad
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return mu + z*sigma
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## -------------------- beta --------------------
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## See
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## http://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470
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## for Ivan Frohne's insightful analysis of why the original implementation:
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##
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## def betavariate(self, alpha, beta):
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## # Discrete Event Simulation in C, pp 87-88.
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##
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## y = self.expovariate(alpha)
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## z = self.expovariate(1.0/beta)
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## 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 > -1 and beta} > -1.
|
|
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)
|
|
|
|
## -------------------- Wichmann-Hill -------------------
|
|
|
|
class WichmannHill(Random):
|
|
|
|
VERSION = 1 # used by getstate/setstate
|
|
|
|
def seed(self, a=None):
|
|
"""Initialize internal state from hashable object.
|
|
|
|
None or no argument seeds from current time.
|
|
|
|
If a is not None or an int or long, hash(a) is used instead.
|
|
|
|
If a is an int or long, a is used directly. Distinct values between
|
|
0 and 27814431486575L inclusive are guaranteed to yield distinct
|
|
internal states (this guarantee is specific to the default
|
|
Wichmann-Hill generator).
|
|
"""
|
|
|
|
if a is None:
|
|
# Initialize from current time
|
|
import time
|
|
a = long(time.time() * 256)
|
|
|
|
if not isinstance(a, (int, long)):
|
|
a = hash(a)
|
|
|
|
a, x = divmod(a, 30268)
|
|
a, y = divmod(a, 30306)
|
|
a, z = divmod(a, 30322)
|
|
self._seed = int(x)+1, int(y)+1, int(z)+1
|
|
|
|
self.gauss_next = None
|
|
|
|
def random(self):
|
|
"""Get the next random number in the range [0.0, 1.0)."""
|
|
|
|
# Wichman-Hill random number generator.
|
|
#
|
|
# Wichmann, B. A. & Hill, I. D. (1982)
|
|
# Algorithm AS 183:
|
|
# An efficient and portable pseudo-random number generator
|
|
# Applied Statistics 31 (1982) 188-190
|
|
#
|
|
# see also:
|
|
# Correction to Algorithm AS 183
|
|
# Applied Statistics 33 (1984) 123
|
|
#
|
|
# McLeod, A. I. (1985)
|
|
# A remark on Algorithm AS 183
|
|
# Applied Statistics 34 (1985),198-200
|
|
|
|
# This part is thread-unsafe:
|
|
# BEGIN CRITICAL SECTION
|
|
x, y, z = self._seed
|
|
x = (171 * x) % 30269
|
|
y = (172 * y) % 30307
|
|
z = (170 * z) % 30323
|
|
self._seed = x, y, z
|
|
# END CRITICAL SECTION
|
|
|
|
# Note: on a platform using IEEE-754 double arithmetic, this can
|
|
# never return 0.0 (asserted by Tim; proof too long for a comment).
|
|
return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0
|
|
|
|
def getstate(self):
|
|
"""Return internal state; can be passed to setstate() later."""
|
|
return self.VERSION, self._seed, self.gauss_next
|
|
|
|
def setstate(self, state):
|
|
"""Restore internal state from object returned by getstate()."""
|
|
version = state[0]
|
|
if version == 1:
|
|
version, self._seed, self.gauss_next = state
|
|
else:
|
|
raise ValueError("state with version %s passed to "
|
|
"Random.setstate() of version %s" %
|
|
(version, self.VERSION))
|
|
|
|
def jumpahead(self, n):
|
|
"""Act as if n calls to random() were made, but quickly.
|
|
|
|
n is an int, greater than or equal to 0.
|
|
|
|
Example use: If you have 2 threads and know that each will
|
|
consume no more than a million random numbers, create two Random
|
|
objects r1 and r2, then do
|
|
r2.setstate(r1.getstate())
|
|
r2.jumpahead(1000000)
|
|
Then r1 and r2 will use guaranteed-disjoint segments of the full
|
|
period.
|
|
"""
|
|
|
|
if not n >= 0:
|
|
raise ValueError("n must be >= 0")
|
|
x, y, z = self._seed
|
|
x = int(x * pow(171, n, 30269)) % 30269
|
|
y = int(y * pow(172, n, 30307)) % 30307
|
|
z = int(z * pow(170, n, 30323)) % 30323
|
|
self._seed = x, y, z
|
|
|
|
def __whseed(self, x=0, y=0, z=0):
|
|
"""Set the Wichmann-Hill seed from (x, y, z).
|
|
|
|
These must be integers in the range [0, 256).
|
|
"""
|
|
|
|
if not type(x) == type(y) == type(z) == int:
|
|
raise TypeError('seeds must be integers')
|
|
if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256):
|
|
raise ValueError('seeds must be in range(0, 256)')
|
|
if 0 == x == y == z:
|
|
# Initialize from current time
|
|
import time
|
|
t = long(time.time() * 256)
|
|
t = int((t&0xffffff) ^ (t>>24))
|
|
t, x = divmod(t, 256)
|
|
t, y = divmod(t, 256)
|
|
t, z = divmod(t, 256)
|
|
# Zero is a poor seed, so substitute 1
|
|
self._seed = (x or 1, y or 1, z or 1)
|
|
|
|
self.gauss_next = None
|
|
|
|
def whseed(self, a=None):
|
|
"""Seed from hashable object's hash code.
|
|
|
|
None or no argument seeds from current time. It is not guaranteed
|
|
that objects with distinct hash codes lead to distinct internal
|
|
states.
|
|
|
|
This is obsolete, provided for compatibility with the seed routine
|
|
used prior to Python 2.1. Use the .seed() method instead.
|
|
"""
|
|
|
|
if a is None:
|
|
self.__whseed()
|
|
return
|
|
a = hash(a)
|
|
a, x = divmod(a, 256)
|
|
a, y = divmod(a, 256)
|
|
a, z = divmod(a, 256)
|
|
x = (x + a) % 256 or 1
|
|
y = (y + a) % 256 or 1
|
|
z = (z + a) % 256 or 1
|
|
self.__whseed(x, y, z)
|
|
|
|
## -------------------- test program --------------------
|
|
|
|
def _test_generator(n, funccall):
|
|
import time
|
|
print n, 'times', funccall
|
|
code = compile(funccall, funccall, 'eval')
|
|
sum = 0.0
|
|
sqsum = 0.0
|
|
smallest = 1e10
|
|
largest = -1e10
|
|
t0 = time.time()
|
|
for i in range(n):
|
|
x = eval(code)
|
|
sum = sum + x
|
|
sqsum = sqsum + x*x
|
|
smallest = min(x, smallest)
|
|
largest = max(x, largest)
|
|
t1 = time.time()
|
|
print round(t1-t0, 3), 'sec,',
|
|
avg = sum/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, 'cunifvariate(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)')
|
|
|
|
# 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
|
|
randint = _inst.randint
|
|
choice = _inst.choice
|
|
randrange = _inst.randrange
|
|
sample = _inst.sample
|
|
shuffle = _inst.shuffle
|
|
normalvariate = _inst.normalvariate
|
|
lognormvariate = _inst.lognormvariate
|
|
cunifvariate = _inst.cunifvariate
|
|
expovariate = _inst.expovariate
|
|
vonmisesvariate = _inst.vonmisesvariate
|
|
gammavariate = _inst.gammavariate
|
|
stdgamma = _inst.stdgamma
|
|
gauss = _inst.gauss
|
|
betavariate = _inst.betavariate
|
|
paretovariate = _inst.paretovariate
|
|
weibullvariate = _inst.weibullvariate
|
|
getstate = _inst.getstate
|
|
setstate = _inst.setstate
|
|
jumpahead = _inst.jumpahead
|
|
|
|
if __name__ == '__main__':
|
|
_test()
|