Reworked random.py so that it no longer depends on, and offers all the
functionality of, whrandom.py. Also closes all the "XXX" todos in random.py. New frequently-requested functions/methods getstate() and setstate(). All exported functions are now bound methods of a hidden instance. Killed all unintended exports. Updated the docs. FRED: The more I fiddle the docs, the less I understand the exact intended use of the \var, \code, \method tags. Please review critically. GUIDO: See email. I updated NEWS as if whrandom were deprecated; I think it should be.
This commit is contained in:
Tim Peters
parent
83125775e0
commit
d7b5e88e8e
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@ -32,6 +32,18 @@ functions from multiple threads, you should explicitly serialize the calls.
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Else, because no critical sections are implemented internally, calls
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from different threads may see the same return values.
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The functions supplied by this module are actually bound methods of a
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hidden instance of the \var{random.Random} class. You can instantiate
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your own instances of \var{Random} to get generators that don't share state.
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This may be especially useful for multi-threaded programs, although there's
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no simple way to seed the distinct generators to ensure that the generated
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sequences won't overlap. Class \var{Random} can also be subclassed if you
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want to use a different basic generator of your own devising: in that
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case, override the \method{random()}, \method{seed()}, \method{getstate()}
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and \method{setstate()} methods.
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Bookkeeping functions:
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\begin{funcdesc}{seed}{\optional{x}}
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Initialize the basic random number generator.
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@ -45,15 +57,19 @@ from different threads may see the same return values.
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the module is first imported.
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\end{funcdesc}
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\begin{funcdesc}{choice}{seq}
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Return a random element from the non-empty sequence \var{seq}.
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\end{funcdesc}
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\begin{funcdesc}{getstate}{}
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Return an object capturing the current internal state of the generator.
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This object can be passed to \code{setstate()} to restore the state.
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\end{funcdesc}
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\begin{funcdesc}{randint}{a, b}
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\deprecated{2.0}{Use \function{randrange()} instead.}
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Return a random integer \var{N} such that
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\code{\var{a} <= \var{N} <= \var{b}}.
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\end{funcdesc}
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\begin{funcdesc}{setstate}{state}
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\var{state} should have been obtained from a previous call to
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\code{getstate()}, and \code{setstate()} restores the internal state
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of the generate to what it was at the time \code{setstate()} was called.
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\end{funcdesc}
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Functions for integers:
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\begin{funcdesc}{randrange}{\optional{start,} stop\optional{, step}}
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Return a randomly selected element from \code{range(\var{start},
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@ -63,6 +79,37 @@ from different threads may see the same return values.
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\versionadded{1.5.2}
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\end{funcdesc}
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\begin{funcdesc}{randint}{a, b}
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\deprecated{2.0}{Use \function{randrange()} instead.}
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Return a random integer \var{N} such that
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\code{\var{a} <= \var{N} <= \var{b}}.
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\end{funcdesc}
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Functions for sequences:
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\begin{funcdesc}{choice}{seq}
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Return a random element from the non-empty sequence \var{seq}.
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\end{funcdesc}
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\begin{funcdesc}{shuffle}{x\optional{, random}}
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Shuffle the sequence \var{x} in place.
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The optional argument \var{random} is a 0-argument function
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returning a random float in [0.0, 1.0); by default, this is the
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function \function{random()}.
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Note that for even rather small \code{len(\var{x})}, the total
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number of permutations of \var{x} is larger than the period of most
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random number generators; this implies that most permutations of a
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long sequence can never be generated.
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\end{funcdesc}
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The following functions generate specific real-valued distributions.
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Function parameters are named after the corresponding variables in the
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distribution's equation, as used in common mathematical practice; most of
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these equations can be found in any statistics text.
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\begin{funcdesc}{random}{}
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Return the next random floating point number in the range [0.0, 1.0).
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\end{funcdesc}
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@ -72,14 +119,6 @@ from different threads may see the same return values.
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\code{\var{a} <= \var{N} < \var{b}}.
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\end{funcdesc}
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The following functions are defined to support specific distributions,
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and all return real values. Function parameters are named after the
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corresponding variables in the distribution's equation, as used in
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common mathematical practice; most of these equations can be found in
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any statistics text.
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\begin{funcdesc}{betavariate}{alpha, beta}
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Beta distribution. Conditions on the parameters are
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\code{\var{alpha} > -1} and \code{\var{beta} > -1}.
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@ -143,21 +182,6 @@ any statistics text.
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\end{funcdesc}
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This function does not represent a specific distribution, but
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implements a standard useful algorithm:
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\begin{funcdesc}{shuffle}{x\optional{, random}}
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Shuffle the sequence \var{x} in place.
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The optional argument \var{random} is a 0-argument function
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returning a random float in [0.0, 1.0); by default, this is the
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function \function{random()}.
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Note that for even rather small \code{len(\var{x})}, the total
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number of permutations of \var{x} is larger than the period of most
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random number generators; this implies that most permutations of a
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long sequence can never be generated.
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\end{funcdesc}
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\begin{seealso}
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\seetext{Wichmann, B. A. \& Hill, I. D., ``Algorithm AS 183:
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An efficient and portable pseudo-random number generator'',
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710
Lib/random.py
710
Lib/random.py
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@ -1,7 +1,17 @@
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"""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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@ -17,328 +27,429 @@ 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. See whrandom.py for more info.
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value.
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"""
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# XXX The docstring sucks.
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import whrandom
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from whrandom import random, uniform, randint, choice, randrange # For export!
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from math import log, exp, pi, e, sqrt, acos, cos, sin
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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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# Interfaces to replace remaining needs for importing whrandom
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# XXX TO DO: make the distribution functions below into methods.
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def makeseed(a=None):
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"""Turn a hashable value into three seed values for whrandom.seed().
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None or no argument returns (0, 0, 0), to seed from current time.
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"""
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if a is None:
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return (0, 0, 0)
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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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return (x, y, z)
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def seed(a=None):
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"""Seed the default generator from any hashable value.
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None or no argument seeds from current time.
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"""
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x, y, z = makeseed(a)
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whrandom.seed(x, y, z)
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class generator(whrandom.whrandom):
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"""Random generator class."""
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def __init__(self, a=None):
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"""Constructor. Seed from current time or hashable value."""
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self.seed(a)
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def seed(self, a=None):
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"""Seed the generator from current time or hashable value."""
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x, y, z = makeseed(a)
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whrandom.whrandom.seed(self, x, y, z)
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def new_generator(a=None):
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"""Return a new random generator instance."""
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return generator(a)
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# Housekeeping function to verify that magic constants have been
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# computed correctly
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def verify(name, expected):
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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 (computed %g, expected %g)' % \
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(name, computed, expected)
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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 seed(), random(), getstate()
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# and setstate().
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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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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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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 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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|
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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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NV_MAGICCONST = 4*exp(-0.5)/sqrt(2.0)
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verify('NV_MAGICCONST', 1.71552776992141)
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def normalvariate(mu, sigma):
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# mu = mean, sigma = standard deviation
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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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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(mu, sigma):
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return exp(normalvariate(mu, sigma))
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# -------------------- circular uniform --------------------
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def cunifvariate(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 * (random() - 0.5)) % pi
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# -------------------- exponential distribution --------------------
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def expovariate(lambd):
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# lambd: rate lambd = 1/mean
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# ('lambda' is a Python reserved word)
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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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TWOPI = 2.0*pi
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verify('TWOPI', 6.28318530718)
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def vonmisesvariate(mu, kappa):
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# 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.
|
||||
|
||||
if kappa <= 1e-6:
|
||||
return TWOPI * random()
|
||||
|
||||
a = 1.0 + sqrt(1.0 + 4.0 * kappa * kappa)
|
||||
b = (a - sqrt(2.0 * a))/(2.0 * kappa)
|
||||
r = (1.0 + b * b)/(2.0 * b)
|
||||
|
||||
while 1:
|
||||
u1 = random()
|
||||
|
||||
z = cos(pi * u1)
|
||||
f = (1.0 + r * z)/(r + z)
|
||||
c = kappa * (r - f)
|
||||
|
||||
u2 = random()
|
||||
|
||||
if not (u2 >= c * (2.0 - c) and u2 > c * exp(1.0 - c)):
|
||||
break
|
||||
|
||||
u3 = random()
|
||||
if u3 > 0.5:
|
||||
theta = (mu % TWOPI) + acos(f)
|
||||
else:
|
||||
theta = (mu % TWOPI) - acos(f)
|
||||
|
||||
return theta
|
||||
|
||||
# -------------------- gamma distribution --------------------
|
||||
|
||||
LOG4 = log(4.0)
|
||||
verify('LOG4', 1.38629436111989)
|
||||
|
||||
def gammavariate(alpha, beta):
|
||||
# beta times standard gamma
|
||||
ainv = sqrt(2.0 * alpha - 1.0)
|
||||
return beta * stdgamma(alpha, ainv, alpha - LOG4, alpha + ainv)
|
||||
|
||||
SG_MAGICCONST = 1.0 + log(4.5)
|
||||
verify('SG_MAGICCONST', 2.50407739677627)
|
||||
|
||||
def stdgamma(alpha, ainv, bbb, ccc):
|
||||
# ainv = sqrt(2 * alpha - 1)
|
||||
# bbb = alpha - log(4)
|
||||
# ccc = alpha + ainv
|
||||
|
||||
if alpha <= 0.0:
|
||||
raise ValueError, 'stdgamma: alpha must be > 0.0'
|
||||
|
||||
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
|
||||
# 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 = 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
|
||||
z = NV_MAGICCONST*(u1-0.5)/u2
|
||||
zz = z*z/4.0
|
||||
if zz <= -_log(u2):
|
||||
break
|
||||
return mu + z*sigma
|
||||
|
||||
elif alpha == 1.0:
|
||||
# expovariate(1)
|
||||
# -------------------- lognormal distribution --------------------
|
||||
|
||||
def lognormvariate(self, mu, sigma):
|
||||
return _exp(self.normalvariate(mu, sigma))
|
||||
|
||||
# -------------------- circular uniform --------------------
|
||||
|
||||
def cunifvariate(self, mean, arc):
|
||||
# mean: mean angle (in radians between 0 and pi)
|
||||
# arc: range of distribution (in radians between 0 and pi)
|
||||
|
||||
return (mean + arc * (self.random() - 0.5)) % _pi
|
||||
|
||||
# -------------------- exponential distribution --------------------
|
||||
|
||||
def expovariate(self, lambd):
|
||||
# lambd: rate lambd = 1/mean
|
||||
# ('lambda' is a Python reserved word)
|
||||
|
||||
random = self.random
|
||||
u = random()
|
||||
while u <= 1e-7:
|
||||
u = random()
|
||||
return -log(u)
|
||||
return -_log(u)/lambd
|
||||
|
||||
else: # alpha is between 0 and 1 (exclusive)
|
||||
# -------------------- von Mises distribution --------------------
|
||||
|
||||
# Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
|
||||
def vonmisesvariate(self, mu, kappa):
|
||||
# mu: mean angle (in radians between 0 and 2*pi)
|
||||
# kappa: concentration parameter kappa (>= 0)
|
||||
# if kappa = 0 generate uniform random angle
|
||||
|
||||
# Based upon an algorithm published in: Fisher, N.I.,
|
||||
# "Statistical Analysis of Circular Data", Cambridge
|
||||
# University Press, 1993.
|
||||
|
||||
# Thanks to Magnus Kessler for a correction to the
|
||||
# implementation of step 4.
|
||||
|
||||
random = self.random
|
||||
if kappa <= 1e-6:
|
||||
return TWOPI * random()
|
||||
|
||||
a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa)
|
||||
b = (a - _sqrt(2.0 * a))/(2.0 * kappa)
|
||||
r = (1.0 + b * b)/(2.0 * b)
|
||||
|
||||
while 1:
|
||||
u = random()
|
||||
b = (e + alpha)/e
|
||||
p = b*u
|
||||
if p <= 1.0:
|
||||
x = pow(p, 1.0/alpha)
|
||||
else:
|
||||
# p > 1
|
||||
x = -log((b-p)/alpha)
|
||||
u1 = random()
|
||||
if not (((p <= 1.0) and (u1 > exp(-x))) or
|
||||
((p > 1) and (u1 > pow(x, alpha - 1.0)))):
|
||||
|
||||
z = _cos(_pi * u1)
|
||||
f = (1.0 + r * z)/(r + z)
|
||||
c = kappa * (r - f)
|
||||
|
||||
u2 = random()
|
||||
|
||||
if not (u2 >= c * (2.0 - c) and u2 > c * _exp(1.0 - c)):
|
||||
break
|
||||
return x
|
||||
|
||||
u3 = random()
|
||||
if u3 > 0.5:
|
||||
theta = (mu % TWOPI) + _acos(f)
|
||||
else:
|
||||
theta = (mu % TWOPI) - _acos(f)
|
||||
|
||||
return theta
|
||||
|
||||
# -------------------- gamma distribution --------------------
|
||||
|
||||
def gammavariate(self, alpha, beta):
|
||||
# beta times standard gamma
|
||||
ainv = _sqrt(2.0 * alpha - 1.0)
|
||||
return beta * self.stdgamma(alpha, ainv, alpha - LOG4, alpha + ainv)
|
||||
|
||||
def stdgamma(self, alpha, ainv, bbb, ccc):
|
||||
# ainv = sqrt(2 * alpha - 1)
|
||||
# bbb = alpha - log(4)
|
||||
# ccc = alpha + ainv
|
||||
|
||||
random = self.random
|
||||
if alpha <= 0.0:
|
||||
raise ValueError, 'stdgamma: alpha must be > 0.0'
|
||||
|
||||
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
|
||||
|
||||
while 1:
|
||||
u1 = random()
|
||||
u2 = 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
|
||||
|
||||
elif alpha == 1.0:
|
||||
# expovariate(1)
|
||||
u = random()
|
||||
while u <= 1e-7:
|
||||
u = random()
|
||||
return -_log(u)
|
||||
|
||||
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 = pow(p, 1.0/alpha)
|
||||
else:
|
||||
# p > 1
|
||||
x = -_log((b-p)/alpha)
|
||||
u1 = random()
|
||||
if not (((p <= 1.0) and (u1 > _exp(-x))) or
|
||||
((p > 1) and (u1 > pow(x, alpha - 1.0)))):
|
||||
break
|
||||
return x
|
||||
|
||||
|
||||
# -------------------- Gauss (faster alternative) --------------------
|
||||
|
||||
gauss_next = None
|
||||
def gauss(mu, sigma):
|
||||
def gauss(self, mu, sigma):
|
||||
|
||||
# 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)
|
||||
# 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.)
|
||||
# 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.)
|
||||
|
||||
global gauss_next
|
||||
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
|
||||
|
||||
z = gauss_next
|
||||
gauss_next = None
|
||||
if z is None:
|
||||
x2pi = random() * TWOPI
|
||||
g2rad = sqrt(-2.0 * log(1.0 - random()))
|
||||
z = cos(x2pi) * g2rad
|
||||
gauss_next = sin(x2pi) * g2rad
|
||||
|
||||
return mu + z*sigma
|
||||
return mu + z*sigma
|
||||
|
||||
# -------------------- beta --------------------
|
||||
|
||||
def betavariate(alpha, beta):
|
||||
def betavariate(self, alpha, beta):
|
||||
|
||||
# Discrete Event Simulation in C, pp 87-88.
|
||||
# Discrete Event Simulation in C, pp 87-88.
|
||||
|
||||
y = expovariate(alpha)
|
||||
z = expovariate(1.0/beta)
|
||||
return z/(y+z)
|
||||
y = self.expovariate(alpha)
|
||||
z = self.expovariate(1.0/beta)
|
||||
return z/(y+z)
|
||||
|
||||
# -------------------- Pareto --------------------
|
||||
|
||||
def paretovariate(alpha):
|
||||
# Jain, pg. 495
|
||||
def paretovariate(self, alpha):
|
||||
# Jain, pg. 495
|
||||
|
||||
u = random()
|
||||
return 1.0 / pow(u, 1.0/alpha)
|
||||
u = self.random()
|
||||
return 1.0 / pow(u, 1.0/alpha)
|
||||
|
||||
# -------------------- Weibull --------------------
|
||||
|
||||
def weibullvariate(alpha, beta):
|
||||
# Jain, pg. 499; bug fix courtesy Bill Arms
|
||||
def weibullvariate(self, alpha, beta):
|
||||
# Jain, pg. 499; bug fix courtesy Bill Arms
|
||||
|
||||
u = random()
|
||||
return alpha * pow(-log(u), 1.0/beta)
|
||||
|
||||
# -------------------- shuffle --------------------
|
||||
# Not quite a random distribution, but a standard algorithm.
|
||||
# This implementation due to Tim Peters.
|
||||
|
||||
def shuffle(x, random=random, int=int):
|
||||
"""x, random=random.random -> shuffle list x in place; return None.
|
||||
|
||||
Optional arg random is a 0-argument function returning a random
|
||||
float in [0.0, 1.0); by default, the standard random.random.
|
||||
|
||||
Note that for even rather small len(x), the total number of
|
||||
permutations of x is larger than the period of most random number
|
||||
generators; this implies that "most" permutations of a long
|
||||
sequence can never be generated.
|
||||
"""
|
||||
|
||||
for i in xrange(len(x)-1, 0, -1):
|
||||
# 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]
|
||||
u = self.random()
|
||||
return alpha * pow(-_log(u), 1.0/beta)
|
||||
|
||||
# -------------------- test program --------------------
|
||||
|
||||
def test(N = 200):
|
||||
print 'TWOPI =', TWOPI
|
||||
print 'LOG4 =', LOG4
|
||||
print 'NV_MAGICCONST =', NV_MAGICCONST
|
||||
print 'SG_MAGICCONST =', SG_MAGICCONST
|
||||
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, 'expovariate(1.0)')
|
||||
test_generator(N, 'vonmisesvariate(0.0, 1.0)')
|
||||
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, 'paretovariate(1.0)')
|
||||
test_generator(N, 'weibullvariate(1.0, 1.0)')
|
||||
|
||||
def test_generator(n, funccall):
|
||||
def _test_generator(n, funccall):
|
||||
import time
|
||||
print n, 'times', funccall
|
||||
code = compile(funccall, funccall, 'eval')
|
||||
|
|
@ -356,9 +467,54 @@ def test_generator(n, funccall):
|
|||
t1 = time.time()
|
||||
print round(t1-t0, 3), 'sec,',
|
||||
avg = sum/n
|
||||
stddev = sqrt(sqsum/n - avg*avg)
|
||||
stddev = _sqrt(sqsum/n - avg*avg)
|
||||
print 'avg %g, stddev %g, min %g, max %g' % \
|
||||
(avg, stddev, smallest, largest)
|
||||
|
||||
def _test(N=200):
|
||||
print 'TWOPI =', TWOPI
|
||||
print 'LOG4 =', LOG4
|
||||
print 'NV_MAGICCONST =', NV_MAGICCONST
|
||||
print 'SG_MAGICCONST =', SG_MAGICCONST
|
||||
_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, 'expovariate(1.0)')
|
||||
_test_generator(N, 'vonmisesvariate(0.0, 1.0)')
|
||||
_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, '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
|
||||
|
||||
if __name__ == '__main__':
|
||||
test()
|
||||
_test()
|
||||
|
|
|
|||
13
Misc/NEWS
13
Misc/NEWS
|
|
@ -1,3 +1,16 @@
|
|||
What's New in Python 2.1 alpha 2?
|
||||
=================================
|
||||
Core language, builtins, and interpreter
|
||||
|
||||
|
||||
Standard library
|
||||
|
||||
- random.py is now self-contained, and offers all the functionality of
|
||||
the now-deprecated whrandom.py. See the docs for details. random.py
|
||||
also supports new functions getstate() and setstate(), for saving
|
||||
and restoring the internal state of all the generators.
|
||||
|
||||
|
||||
What's New in Python 2.1 alpha 1?
|
||||
=================================
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue