python (3.12.0)
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l8m6Z5 Y w xY w)"aE Random variable generators.
bytes
-----
uniform bytes (values between 0 and 255)
integers
--------
uniform within range
sequences
---------
pick random element
pick random sample
pick weighted random sample
generate random permutation
distributions on the real line:
------------------------------
uniform
triangular
normal (Gaussian)
lognormal
negative exponential
gamma
beta
pareto
Weibull
distributions on the circle (angles 0 to 2pi)
---------------------------------------------
circular uniform
von Mises
discrete distributions
----------------------
binomial
General notes on the underlying Mersenne Twister core generator:
* The period is 2**19937-1.
* It is one of the most extensively tested generators in existence.
* The random() method is implemented in C, executes in a single Python step,
and is, therefore, threadsafe.
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accumulaterepeat)bisectN)sha512)Random SystemRandom betavariatebinomialvariatechoicechoices expovariate gammavariategauss getrandbitsgetstatelognormvariate
normalvariate
paretovariate randbytesrandintrandom randrangesampleseedsetstateshuffle
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ddZd Zd&dZd'dZd'dZ d Z d(d Z d Z d Z d Z!d! Z"d" Z#d)d#Z$ xZ%S )*r a Random number generator base class used by bound module functions.
Used to instantiate instances of Random to get generators that don't
share state.
Class Random can also be subclassed if you want to use a different basic
generator of your own devising: in that case, override the following
methods: random(), seed(), getstate(), and setstate().
Optionally, implement a getrandbits() method so that randrange()
can cover arbitrarily large ranges.
Nc 4 | j | d| _ y)zeInitialize an instance.
Optional argument x controls seeding, as for Random.seed().
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) a\ Initialize internal state from a seed.
The only supported seed types are None, int, float,
str, bytes, and bytearray.
None or no argument seeds from current time or from an operating
system specific randomness source if available.
If *a* is an int, all bits are used.
For version 2 (the default), all of the bits are used if *a* is a str,
bytes, or bytearray. For version 1 (provided for reproducing random
sequences from older versions of Python), the algorithm for str and
bytes generates a narrower range of seeds.
r; zlatin-1r iCB l r: NzOThe only supported seed types are: None,
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|d}~ww xY w)z:Restore internal state from object returned by getstate().r r= r: c 3 & K | ] }|d z yw)l N ).0rA s rB <genexpr>z"Random.setstate.<locals>.<genexpr> s %Ka7m%Ks Nzstate with version z( passed to Random.setstate() of version )r? rY r. tuple
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__reduce__zRandom.__reduce__ s ~~r4==?22rD c | j D ]T }d|j v r yd|j v r| j | _ yd|j v sC| j | _ y y)a Control how subclasses generate random integers.
The algorithm a subclass can use depends on the random() and/or
getrandbits() implementation available to it and determines
whether it can generate random integers from arbitrarily large
ranges.
_randbelowr# r* N)__mro____dict___randbelow_with_getrandbitsrr _randbelow_without_getrandbits)clskwargsr\ s rB __init_subclass__zRandom.__init_subclass__ s^ Aqzz)
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|z }n |dk r ||z dz |z }n t d |dk rt d| d| d| d ||| j | z z S ) zChoose a random item from range(stop) or range(start, stop[, step]).
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z Missing a non-None stop argumentr zempty range for randrange()r; zempty range in randrange(z, )zzero step for randrange())_index_ONErX rr rf ) r@ startstopstepistartistopwidthistepr| s rB r+ zRandom.randrange# s' < 4 BCCzv.. :; ; t t A:qy 666 8r$q IJ J 19 "u,A
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leaving the original population unchanged. The resulting list is
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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.
Repeated elements can be specified one at a time or with the optional
counts parameter. For example:
sample(['red', 'blue'], counts=[4, 2], k=5)
is equivalent to:
sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5)
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population argument. This is especially fast and space efficient
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t ||z z z S # t $ r |cY S w xY w)zTriangular distribution.
Continuous distribution bounded by given lower and upper limits,
and having a given mode value in-between.
http://en.wikipedia.org/wiki/Triangular_distribution
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z |z }||z dz }|t | k rn9|||z z S )z\Normal distribution.
mu is the mean, and sigma is the standard deviation.
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mu is the mean, and sigma is the standard deviation. This is
slightly faster than the normalvariate() function.
Not thread-safe without a lock around calls.
Ng r7 )r* r? TWOPIr r _cos_sin)r@ r r r* r x2pig2rads rB r" z Random.gauss st 6 OO 98e#D$cFHn!556ET
U"A "4j5 0DOAI~ rD c 8 t | j || S )zLog 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.
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|z S )a^ Exponential distribution.
lambd is 1.0 divided by the desired mean. It should be
nonzero. (The parameter would be called "lambda", but that is
a reserved word in Python.) Returned values range from 0 to
positive infinity if lambd is positive, and from negative
infinity to 0 if lambd is negative.
r7 )r r* )r@ lambds rB r zRandom.expovariateK s" S4;;=())E11rD c | j }|dk rt | z S d|z }|t d||z z z } | }t t |z }|||z z } | } | d||z z
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to a uniform random angle over the range 0 to 2*pi.
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|z S o)aZ Gamma distribution. Not the gamma function!
Conditions on the parameters are alpha > 0 and beta > 0.
The probability distribution function is:
x ** (alpha - 1) * math.exp(-x / beta)
pdf(x) = --------------------------------------
math.gamma(alpha) * beta ** alpha
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H%Z2%E8cEk*A q1uo..AXs7Q53; // t8O 48^t8O rD c \ | j |d }|r||| j |d z z S y)zBeta distribution.
Conditions on the parameters are alpha > 0 and beta > 0.
Returned values range between 0 and 1.
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r7 )r* r )r@ r r r s rB r3 zRandom.weibullvariate s.
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