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S )"a 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
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.
)warn)logexppieceil)sqrtacoscossin)taufloor)urandom)SetSequence)
accumulaterepeat)bisectN)sha512)Random SystemRandom betavariatechoicechoices expovariate gammavariategauss getrandbitsgetstatelognormvariate
normalvariate
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triangularuniformvonmisesvariateweibullvariate g @ @ ? @5 c s* e Zd ZdZdZdBddZdC fdd Z fd d
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Zdd ZdDd d Zd d Zd d! ZdEd"d#Zdd$d%d&ZdFddd'd(d)Zd*d+ ZdGd.d/Zd0d1 Zd2d3 Zd4d5 Z d6d7 Z d8d9 Z d:d; Z dd? Z!d@dA Z" Z#S )Hr a Random number generator base class used by bound module functions.
Used to instantiate instances of Random to get generators that don't
share state.
Class Random can also be subclassed if you want to use a different basic
generator of your own devising: in that case, override the following
methods: random(), seed(), getstate(), and setstate().
Optionally, implement a getrandbits() method so that randrange()
can cover arbitrarily large ranges.
Nc C s | | d| _dS )zeInitialize an instance.
Optional argument x controls seeding, as for Random.seed().
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zRandom.__init__r4 c s |dkrt |ttfrt |tr*|dn|}|rBt|d d> nd}tt|D ]}d| |A d@ }qP|t|N }|dkr~dn|}nj|d krt |tttfrt |tr| }t
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a\ Initialize internal state from a seed.
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system specific randomness source if available.
If *a* is an int, all bits are used.
For version 2 (the default), all of the bits are used if *a* is a str,
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zlatin-1r iCB l r4 bigNzSeeding based on hashing is deprecated
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__reduce__ s zRandom.__reduce__c K sJ | j D ]>}d|jv r qFd|jv r.| j| _ qFd|jv r| j| _ qFqdS )a Control how subclasses generate random integers.
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getrandbits() implementation available to it and determines
whether it can generate random integers from arbitrarily large
ranges.
_randbelowr r$ N)__mro____dict___randbelow_with_getrandbitsrd _randbelow_without_getrandbits)clskwargsrT r9 r9 r: __init_subclass__ s
zRandom.__init_subclass__c C s4 |sdS | j }| }||}||kr0||}q |S )z;Return a random int in the range [0,n). Returns 0 if n==0.r )r
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z"Random._randbelow_with_getrandbitsr< c C sj | j }||kr$td t| | S |dkr0dS || }|| | }| }||krZ| }qJt|| | S )zReturn a random int in the range [0,n). Returns 0 if n==0.
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zChoose a random item from range(start, stop[, step]).
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z!non-integer arg 1 for randrange()Nr zempty range for randrange()z non-integer stop for randrange()r< z(empty range for randrange() (%d, %d, %d)z non-integer step for randrange()zzero step for randrange())rJ r] rd ) r7 startstopstepZistartZistopwidthZisteprm r9 r9 r: r% " s4
zRandom.randrangec C s | ||d S )zJReturn random integer in range [a, b], including both end points.
r< )r% r7 rR br9 r9 r: r# N s zRandom.randintc C s || t| S )z2Choose a random element from a non-empty sequence.)rd rG )r7 seqr9 r9 r: r W s z
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v r||} q||| | || < qp|S )am Chooses k unique random elements from a population sequence or set.
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in selection order so that all sub-slices will also be valid random
samples. This allows raffle winners (the sample) to be partitioned
into grand prize and second place winners (the subslices).
Members of the population need not be hashable or unique. If the
population contains repeats, then each occurrence is a possible
selection in the sample.
Repeated elements can be specified one at a time or with the optional
counts parameter. For example:
sample(['red', 'blue'], counts=[4, 2], k=5)
is equivalent to:
sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5)
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population argument. This is especially fast and space efficient
for sampling from a large population:
sample(range(10000000), 60)
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zRandom.choicesc C s ||| | S )zHGet a random number in the range [a, b) or [a, b] depending on rounding.r$ r| r9 r9 r: r+ s zRandom.uniformr r1 c C sz | }z |du rdn|| || }W n ty> | Y S 0 ||krbd| }d| }|| }}||| t|| S )zTriangular distribution.
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http://en.wikipedia.org/wiki/Triangular_distribution
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zRandom.triangularc C sP | j }| }d| }t|d | }|| d }|t| krqDq||| S )z\Normal distribution.
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positive infinity if lambd is positive, and from negative
infinity to 0 if lambd is negative.
r1 )r r$ )r7 Zlambdr9 r9 r: r \ s zRandom.expovariatec C s | j }|dkrt| S d| }|td|| }| }tt| }||| }| } | d|| k s| d| t| kr4qq4d| }
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equal to zero. If kappa is equal to zero, this distribution reduces
to a uniform random angle over the range 0 to 2*pi.
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$zRandom.vonmisesvariatec C s~ |dks|dkrt d| j}|dkrtd| d }|t }|| }| }d| k r`dk sdqF qFd| }t|d| | } |t| }
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pdf(x) = --------------------------------------
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zRandom.gammavariatec C s( | |d}|r$||| |d S dS )zBeta distribution.
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r1 r )r )r7 r r yr9 r9 r: r s zRandom.betavariatec C s d| }d|d| S )z3Pareto distribution. alpha is the shape parameter.r1 r )r7 r r r9 r9 r: r! s zRandom.paretovariatec C s" d| }|t| d| S )zfWeibull distribution.
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