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\section{\module{random} ---
Generate pseudo-random numbers}
\declaremodule{standard}{random}
\modulesynopsis{Generate pseudo-random numbers with various common
distributions.}
This module implements pseudo-random number generators for various
distributions.
For integers, uniform selection from a range.
For sequences, uniform selection of a random element, and a function to
generate a random permutation of a list in-place.
On the real line, there are functions to compute uniform, normal (Gaussian),
lognormal, negative exponential, gamma, and beta distributions.
For generating distribution of angles, the circular uniform and
von Mises distributions are available.
Almost all module functions depend on the basic function
\function{random()}, which generates a random float uniformly in
the semi-open range [0.0, 1.0). Python uses the standard Wichmann-Hill
generator, combining three pure multiplicative congruential
generators of modulus 30269, 30307 and 30323. Its period (how many
numbers it generates before repeating the sequence exactly) is
6,953,607,871,644. While of much higher quality than the \function{rand()}
function supplied by most C libraries, the theoretical properties
are much the same as for a single linear congruential generator of
large modulus.
The functions in this module are not threadsafe: if you want to call these
functions from multiple threads, you should explicitly serialize the calls.
Else, because no critical sections are implemented internally, calls
from different threads may see the same return values.
The functions supplied by this module are actually bound methods of a
hidden instance of the \var{random.Random} class. You can instantiate your
own instances of \var{Random} to get generators that don't share state.
This is especially useful for multi-threaded programs, creating a different
instance of \var{Random} for each thread, and using the \method{jumpahead()}
method to ensure that the generated sequences seen by each thread don't
overlap. Class \var{Random} can also be subclassed if you want to use a
different basic generator of your own devising: in that case, override the
\method{random()}, \method{seed()}, \method{getstate()},
\method{setstate()} and \method{jumpahead()} methods.
Bookkeeping functions:
\begin{funcdesc}{seed}{\optional{x}}
Initialize the basic random number generator.
Optional argument \var{x} can be any hashable object,
and the generator is seeded from its hash code.
It is not guaranteed that distinct hash codes will produce distinct
seeds.
If \var{x} is omitted or \code{None},
the seed is derived from the current system time.
The seed is also set from the current system time when
the module is first imported.
\end{funcdesc}
\begin{funcdesc}{getstate}{}
Return an object capturing the current internal state of the generator.
This object can be passed to \code{setstate()} to restore the state.
\end{funcdesc}
\begin{funcdesc}{setstate}{state}
\var{state} should have been obtained from a previous call to
\code{getstate()}, and \code{setstate()} restores the internal state
of the generate to what it was at the time \code{setstate()} was called.
\end{funcdesc}
\begin{funcdesc}{jumpahead}{n}
Change the internal state to what it would be if \code{random()} were
called n times, but do so quickly. \var{n} is a non-negative integer.
This is most useful in multi-threaded programs, in conjuction with
multiple instances of the \var{Random} class: \method{setstate()} or
\method{seed()} can be used to force all instances into the same
internal state, and then \method{jumpahead()} can be used to force the
instances' states as far apart as you like (up to the period of the
generator).
\end{funcdesc}
Functions for integers:
\begin{funcdesc}{randrange}{\optional{start,} stop\optional{, step}}
Return a randomly selected element from \code{range(\var{start},
\var{stop}, \var{step})}. This is equivalent to
\code{choice(range(\var{start}, \var{stop}, \var{step}))},
but doesn't actually build a range object.
\versionadded{1.5.2}
\end{funcdesc}
\begin{funcdesc}{randint}{a, b}
\deprecated{2.0}{Use \function{randrange()} instead.}
Return a random integer \var{N} such that
\code{\var{a} <= \var{N} <= \var{b}}.
\end{funcdesc}
Functions for sequences:
\begin{funcdesc}{choice}{seq}
Return a random element from the non-empty sequence \var{seq}.
\end{funcdesc}
\begin{funcdesc}{shuffle}{x\optional{, random}}
Shuffle the sequence \var{x} in place.
The optional argument \var{random} is a 0-argument function
returning a random float in [0.0, 1.0); by default, this is the
function \function{random()}.
Note that for even rather small \code{len(\var{x})}, the total
number of permutations of \var{x} is larger than the period of most
random number generators; this implies that most permutations of a
long sequence can never be generated.
\end{funcdesc}
The following functions generate specific real-valued distributions.
Function parameters are named after the corresponding variables in the
distribution's equation, as used in common mathematical practice; most of
these equations can be found in any statistics text.
\begin{funcdesc}{random}{}
Return the next random floating point number in the range [0.0, 1.0).
\end{funcdesc}
\begin{funcdesc}{uniform}{a, b}
Return a random real number \var{N} such that
\code{\var{a} <= \var{N} < \var{b}}.
\end{funcdesc}
\begin{funcdesc}{betavariate}{alpha, beta}
Beta distribution. Conditions on the parameters are
\code{\var{alpha} > -1} and \code{\var{beta} > -1}.
Returned values range between 0 and 1.
\end{funcdesc}
\begin{funcdesc}{cunifvariate}{mean, arc}
Circular uniform distribution. \var{mean} is the mean angle, and
\var{arc} is the range of the distribution, centered around the mean
angle. Both values must be expressed in radians, and can range
between 0 and \emph{pi}. Returned values range between
\code{\var{mean} - \var{arc}/2} and \code{\var{mean} +
\var{arc}/2}.
\end{funcdesc}
\begin{funcdesc}{expovariate}{lambd}
Exponential distribution. \var{lambd} is 1.0 divided by the desired
mean. (The parameter would be called ``lambda'', but that is a
reserved word in Python.) Returned values range from 0 to
positive infinity.
\end{funcdesc}
\begin{funcdesc}{gamma}{alpha, beta}
Gamma distribution. (\emph{Not} the gamma function!) Conditions on
the parameters are \code{\var{alpha} > -1} and \code{\var{beta} > 0}.
\end{funcdesc}
\begin{funcdesc}{gauss}{mu, sigma}
Gaussian distribution. \var{mu} is the mean, and \var{sigma} is the
standard deviation. This is slightly faster than the
\function{normalvariate()} function defined below.
\end{funcdesc}
\begin{funcdesc}{lognormvariate}{mu, sigma}
Log normal distribution. If you take the natural logarithm of this
distribution, you'll get a normal distribution with mean \var{mu}
and standard deviation \var{sigma}. \var{mu} can have any value,
and \var{sigma} must be greater than zero.
\end{funcdesc}
\begin{funcdesc}{normalvariate}{mu, sigma}
Normal distribution. \var{mu} is the mean, and \var{sigma} is the
standard deviation.
\end{funcdesc}
\begin{funcdesc}{vonmisesvariate}{mu, kappa}
\var{mu} is the mean angle, expressed in radians between 0 and
2*\emph{pi}, and \var{kappa} is the concentration parameter, which
must be greater than or equal to zero. If \var{kappa} is equal to
zero, this distribution reduces to a uniform random angle over the
range 0 to 2*\emph{pi}.
\end{funcdesc}
\begin{funcdesc}{paretovariate}{alpha}
Pareto distribution. \var{alpha} is the shape parameter.
\end{funcdesc}
\begin{funcdesc}{weibullvariate}{alpha, beta}
Weibull distribution. \var{alpha} is the scale parameter and
\var{beta} is the shape parameter.
\end{funcdesc}
\begin{seealso}
\seetext{Wichmann, B. A. \& Hill, I. D., ``Algorithm AS 183:
An efficient and portable pseudo-random number generator'',
\citetitle{Applied Statistics} 31 (1982) 188-190.}
\end{seealso}
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