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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, a function to generate a random permutation of a list in-place, and a function for
random sampling without replacement.
On the real line, there are functions to compute uniform, normal (Gaussian), lognormal,
negative exponential, gamma, and beta distributions. For generating distributions of angles,
the von Mises distribution is available.
Almost all module functions depend on the basic function random(),
which generates a random float uniformly in the semi-open range [0.0, 1.0). Python uses the
Mersenne Twister as the core generator. It produces 53-bit precision floats and has a period
of 2**19937-1. The underlying implementation in C is both fast and threadsafe. The Mersenne
Twister is one of the most extensively tested random number generators in existence. However,
being completely deterministic, it is not suitable for all purposes, and is completely
unsuitable for cryptographic purposes.
The functions supplied by this module are actually bound methods of a hidden instance of
the random.Random class. You can instantiate your own instances of Random to get generators that don't share state. This is especially useful
for multi-threaded programs, creating a different instance of Random
for each thread, and using the jumpahead() method to ensure that the
generated sequences seen by each thread don't overlap.
Class Random can also be subclassed if you want to use a different
basic generator of your own devising: in that case, override the random(),
seed(), getstate(), setstate()
and jumpahead() methods.
As an example of subclassing, the random module provides the WichmannHill class which implements an alternative generator in pure
Python. The class provides a backward compatible way to reproduce results from earlier
versions of Python which used the Wichmann-Hill algorithm as the core generator. Changed in version 2.3: Substituted MersenneTwister for Wichmann-Hill.
Bookkeeping functions:
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- Initialize the basic random number generator. Optional argument x can be any
hashable object. If x is omitted or
None, current system time is
used; current system time is also used to initialize the generator when the module is
first imported. If x is not None or an int or long, hash(x)
is used instead. If x is an int or long, x is used directly.
-
- Return an object capturing the current internal state of the generator. This object can
be passed to setstate() to restore the state. New in version 2.1.
-
- state should have been obtained from a previous call to getstate(),
and setstate() restores the internal state of the generator to
what it was at the time setstate() was called. New in version 2.1.
-
- Change the internal state to one different from and likely far away from the current
state. n is a non-negative integer which is used to scramble the current state
vector. This is most useful in multi-threaded programs, in conjuction with multiple
instances of the Random class: setstate()
or seed() can be used to force all instances into the same
internal state, and then jumpahead() can be used to force the
instances' states far apart. New in version 2.1. Changed in version 2.3: Instead of jumping to a specific state, n
steps ahead, jumpahead(n) jumps to another state likely
to be separated by many steps..
Functions for integers:
-
| randrange( |
[start,] stop[, step]) |
- Return a randomly selected element from
range(start, stop, step).
This is equivalent to choice(range(start, stop, step)),
but doesn't actually build a range object. New in version 1.5.2.
-
- Return a random integer N such that
a <= N
<= b.
Functions for sequences:
-
- Return a random element from the non-empty sequence seq.
-
- Shuffle the sequence x in place. The optional argument random is a
0-argument function returning a random float in [0.0, 1.0); by default, this is the
function 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.
-
- Return a k length list of unique elements chosen from the population
sequence. Used for random sampling without replacement. New in
version 2.3.
Returns a new list containing elements from the population while leaving the original
population unchanged. The resulting list is in selection order so that all sub-slices will
also be valid random samples. This allows raffle winners (the sample) to be partitioned
into grand prize and second place winners (the subslices).
Members of the population need not be hashable or unique. If the population contains
repeats, then each occurrence is a possible selection in the sample.
To choose a sample from a range of integers, use xrange as an
argument. This is especially fast and space efficient for sampling from a large
population: sample(xrange(10000000), 60).
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.
-
- Return the next random floating point number in the range [0.0, 1.0).
-
- Return a random real number N such that
a <= N
< b.
-
| betavariate( |
alpha, beta) |
- Beta distribution. Conditions on the parameters are
alpha > -1
and beta > -1. Returned values range between 0 and 1.
-
- Circular uniform distribution. mean is the mean angle, and 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 pi. Returned values range between
mean - arc/2 and mean + arc/2
and are normalized to between 0 and pi.
Deprecated since release 2.3. Instead, use (mean + arc
* (random.random() - 0.5)) % math.pi.
-
- Exponential distribution. 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.
-
| gammavariate( |
alpha, beta) |
- Gamma distribution. (Not the gamma function!) Conditions on the parameters are
alpha
> 0 and beta > 0.
-
- Gaussian distribution. mu is the mean, and sigma is the standard
deviation. This is slightly faster than the normalvariate()
function defined below.
-
| lognormvariate( |
mu, sigma) |
- Log normal distribution. If you take the natural logarithm of this distribution, you'll
get a normal distribution with mean mu and standard deviation sigma.
mu can have any value, and sigma must be greater than zero.
-
| normalvariate( |
mu, sigma) |
- Normal distribution. mu is the mean, and sigma is the standard
deviation.
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| vonmisesvariate( |
mu, kappa) |
- mu is the mean angle, expressed in radians between 0 and 2*pi, and kappa
is the concentration parameter, which must be greater than or equal to zero. If kappa
is equal to zero, this distribution reduces to a uniform random angle over the range 0 to
2*pi.
-
- Pareto distribution. alpha is the shape parameter.
-
| weibullvariate( |
alpha, beta) |
- Weibull distribution. alpha is the scale parameter and beta is the
shape parameter.
Alternative Generator
-
| class WichmannHill( |
[seed]) |
- Class that implements the Wichmann-Hill algorithm as the core generator. Has all of the
same methods as Random plus the whseed
method described below. Because this class is implemented in pure Python, it is not
threadsafe and may require locks between calls. The period of the generator is
6,953,607,871,644 which is small enough to require care that two independent random
sequences do not overlap.
-
- This is obsolete, supplied for bit-level compatibility with versions of Python prior to
2.1. See seed for details. whseed does
not guarantee that distinct integer arguments yield distinct internal states, and can
yield no more than about 2**24 distinct internal states in all.
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