d52269bfd0
got broken). Also added new method .jumpahead(N). This finally gives us a semi-decent answer to how Python's RNGs can be used safely and efficiently in multithreaded programs (although it requires the user to use the new machinery!).
555 lines
17 KiB
Python
555 lines
17 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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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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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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Translated from anonymously contributed C/C++ source.
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Multi-threading note: the random number generator used here is not
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thread-safe; it is possible that two calls return the same random
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value.
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"""
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# XXX The docstring sucks.
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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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def _verify(name, expected):
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computed = eval(name)
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if abs(computed - expected) > 1e-7:
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raise ValueError(
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"computed value for %s deviates too much "
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"(computed %g, expected %g)" % (name, computed, expected))
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NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
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_verify('NV_MAGICCONST', 1.71552776992141)
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TWOPI = 2.0*_pi
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_verify('TWOPI', 6.28318530718)
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LOG4 = _log(4.0)
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_verify('LOG4', 1.38629436111989)
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SG_MAGICCONST = 1.0 + _log(4.5)
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_verify('SG_MAGICCONST', 2.50407739677627)
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del _verify
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# Translated by Guido van Rossum from C source provided by
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# Adrian Baddeley.
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class Random:
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VERSION = 1 # 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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# Specific to Wichmann-Hill generator. Subclasses wishing to use a
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# different core generator should override the seed(), random(),
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# getstate(), setstate(), and jumpahead() methods.
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def __whseed(self, x=0, y=0, z=0):
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"""Set the Wichmann-Hill seed from (x, y, z).
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These must be integers in the range [0, 256).
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"""
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if not type(x) == type(y) == type(z) == type(0):
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raise TypeError('seeds must be integers')
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if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256):
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raise ValueError('seeds must be in range(0, 256)')
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if 0 == x == y == z:
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# Initialize from current time
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import time
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t = long(time.time()) * 256
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t = int((t&0xffffff) ^ (t>>24))
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t, x = divmod(t, 256)
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t, y = divmod(t, 256)
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t, z = divmod(t, 256)
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# Zero is a poor seed, so substitute 1
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self._seed = (x or 1, y or 1, z or 1)
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def seed(self, a=None):
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"""Seed from hashable value
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None or no argument seeds from current time.
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"""
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if a is None:
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self.__whseed()
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return
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a = hash(a)
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a, x = divmod(a, 256)
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a, y = divmod(a, 256)
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a, z = divmod(a, 256)
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x = (x + a) % 256 or 1
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y = (y + a) % 256 or 1
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z = (z + a) % 256 or 1
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self.__whseed(x, y, z)
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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, self._seed, self.gauss_next
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def __getstate__(self): # for pickle
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return self.getstate()
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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 == 1:
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version, self._seed, self.gauss_next = state
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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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def __setstate__(self, state): # for pickle
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self.setstate(state)
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def jumpahead(self, n):
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"""Act as if n calls to random() were made, but quickly.
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n is an int, greater than or equal to 0.
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Example use: If you have 2 threads and know that each will
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consume no more than a million random numbers, create two Random
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objects r1 and r2, then do
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r2.setstate(r1.getstate())
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r2.jumpahead(1000000)
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Then r1 and r2 will use guaranteed-disjoint segments of the full
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period.
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"""
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if not n >= 0:
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raise ValueError("n must be >= 0")
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x, y, z = self._seed
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x = int(x * pow(171, n, 30269)) % 30269
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y = int(y * pow(172, n, 30307)) % 30307
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z = int(z * pow(170, n, 30323)) % 30323
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self._seed = x, y, z
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def random(self):
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"""Get the next random number in the range [0.0, 1.0)."""
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# Wichman-Hill random number generator.
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#
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# Wichmann, B. A. & Hill, I. D. (1982)
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# Algorithm AS 183:
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# An efficient and portable pseudo-random number generator
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# Applied Statistics 31 (1982) 188-190
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#
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# see also:
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# Correction to Algorithm AS 183
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# Applied Statistics 33 (1984) 123
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#
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# McLeod, A. I. (1985)
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# A remark on Algorithm AS 183
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# Applied Statistics 34 (1985),198-200
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# This part is thread-unsafe:
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# BEGIN CRITICAL SECTION
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x, y, z = self._seed
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x = (171 * x) % 30269
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y = (172 * y) % 30307
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z = (170 * z) % 30323
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self._seed = x, y, z
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# END CRITICAL SECTION
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# Note: on a platform using IEEE-754 double arithmetic, this can
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# never return 0.0 (asserted by Tim; proof too long for a comment).
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return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0
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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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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:
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if istart < istop:
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return istart + int(self.random() *
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(istop - istart))
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raise ValueError, "empty range for randrange()"
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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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"""Get a random integer in the range [a, b] including
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both end points.
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(Deprecated; use randrange below.)
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"""
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return self.randrange(a, b+1)
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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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# -------------------- 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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# 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 1:
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u1 = random()
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u2 = 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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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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# 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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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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# 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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# 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 1:
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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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# beta times standard gamma
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ainv = _sqrt(2.0 * alpha - 1.0)
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return beta * self.stdgamma(alpha, ainv, alpha - LOG4, alpha + ainv)
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def stdgamma(self, alpha, ainv, bbb, ccc):
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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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random = self.random
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if alpha <= 0.0:
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raise ValueError, 'stdgamma: alpha must be > 0.0'
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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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while 1:
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u1 = random()
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u2 = 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
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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)
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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 1:
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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
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# -------------------- Gauss (faster alternative) --------------------
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def gauss(self, mu, sigma):
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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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def betavariate(self, alpha, beta):
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# Discrete Event Simulation in C, pp 87-88.
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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)
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# -------------------- Pareto --------------------
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def paretovariate(self, alpha):
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# Jain, pg. 495
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u = self.random()
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return 1.0 / pow(u, 1.0/alpha)
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# -------------------- Weibull --------------------
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def weibullvariate(self, alpha, beta):
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# Jain, pg. 499; bug fix courtesy Bill Arms
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u = self.random()
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return alpha * pow(-_log(u), 1.0/beta)
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# -------------------- test program --------------------
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def _test_generator(n, funccall):
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import time
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print n, 'times', funccall
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code = compile(funccall, funccall, 'eval')
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sum = 0.0
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sqsum = 0.0
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smallest = 1e10
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largest = -1e10
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t0 = time.time()
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for i in range(n):
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x = eval(code)
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sum = sum + x
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sqsum = sqsum + x*x
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smallest = min(x, smallest)
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largest = max(x, largest)
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t1 = time.time()
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print round(t1-t0, 3), 'sec,',
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avg = sum/n
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stddev = _sqrt(sqsum/n - avg*avg)
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print 'avg %g, stddev %g, min %g, max %g' % \
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(avg, stddev, smallest, largest)
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s = getstate()
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N = 1019
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jumpahead(N)
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r1 = random()
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setstate(s)
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for i in range(N): # now do it the slow way
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random()
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r2 = random()
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if r1 != r2:
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raise ValueError("jumpahead test failed " + `(N, r1, r2)`)
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def _test(N=200):
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print 'TWOPI =', TWOPI
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print 'LOG4 =', LOG4
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print 'NV_MAGICCONST =', NV_MAGICCONST
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print 'SG_MAGICCONST =', SG_MAGICCONST
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_test_generator(N, 'random()')
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_test_generator(N, 'normalvariate(0.0, 1.0)')
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_test_generator(N, 'lognormvariate(0.0, 1.0)')
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_test_generator(N, 'cunifvariate(0.0, 1.0)')
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_test_generator(N, 'expovariate(1.0)')
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_test_generator(N, 'vonmisesvariate(0.0, 1.0)')
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_test_generator(N, 'gammavariate(0.5, 1.0)')
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_test_generator(N, 'gammavariate(0.9, 1.0)')
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_test_generator(N, 'gammavariate(1.0, 1.0)')
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_test_generator(N, 'gammavariate(2.0, 1.0)')
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_test_generator(N, 'gammavariate(20.0, 1.0)')
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_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, 'paretovariate(1.0)')
|
|
_test_generator(N, 'weibullvariate(1.0, 1.0)')
|
|
|
|
# Initialize from current time.
|
|
_inst = Random()
|
|
seed = _inst.seed
|
|
random = _inst.random
|
|
uniform = _inst.uniform
|
|
randint = _inst.randint
|
|
choice = _inst.choice
|
|
randrange = _inst.randrange
|
|
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()
|