e fe @ s d Z d d l m Z d d l m Z m Z d d l m
Z m Z
m Z m Z m Z d d l m Z m Z m Z m Z d d l m Z d d l m Z! m" Z# d d l$ m% Z& d d
d d d
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d! e d" Z( d" e Z) e d# Z* d$ e d% Z+ d& Z, d' e, Z- d d( l. Z. Gd) d d e. j/ Z/ Gd* d d e/ Z0 d+ d, Z1 d- d. d/ Z2 e/ Z3 e3 j4 Z4 e3 j5 Z5 e3 j6 Z6 e3 j7 Z7 e3 j8 Z8 e3 j9 Z9 e3 j: Z: e3 j; Z; e3 j< Z< e3 j= Z= e3 j> Z> e3 j? Z? e3 j@ Z@ e3 jA ZA e3 jB ZB e3 jC ZC e3 jD ZD e3 jE ZE e3 jF ZF e3 jG ZG e3 jH ZH eI d0 k r{e2 n d( S)1a Random variable generators.
integers
--------
uniform within range
sequences
---------
pick random element
pick 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)
MethodTypeBuiltinMethodType)logexppieceil)sqrtacoscossin)urandom)SetSequence)sha512Randomseedrandomuniformrandintchoicesample randrangeshuffle
normalvariatelognormvariate expovariatevonmisesvariate gammavariate
triangulargauss betavariate
paretovariateweibullvariategetstatesetstate getrandbits SystemRandom g ?g @g @g ?g @5 Nc s e Z d Z d Z d Z d d d Z d d f d d Z f d d
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d d Z e d e >e e e d d Z d d Z d d d Z d d Z d d! Z d" d# d d$ d% Z d& d' Z d( d) Z d* d+ Z d, d- Z d. d/ Z d0 d1 Z d2 d3 Z d4 d5 Z d6 d7 Z! S)8r 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 | j | d | _ d S)zeInitialize an instance.
Optional argument x controls seeding, as for Random.seed().
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r^ d d l } t | j d } Yqb Xn | d k r t | t t t f r t | t r | j } n | t
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| d | _ d S)a Initialize internal state from hashable object.
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system specific randomness source if available.
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bytes, or bytearray. For version 1, the hash() of *a* is used instead.
If *a* is an int, all bits are used.
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z Random.seedc s | j t j | j f S)z9Return internal state; can be passed to setstate() later.)VERSIONr@ r% r- )r. )rC r0 r1 r% } s zRandom.getstatec s | d } | d k r; | \ } } | _ t j | n | d k r | \ } } | _ y t d d | D } Wn. t k
r } z t | WYd d } ~ Xn Xt j | n t d | | j f d S)z:Restore internal state from object returned by getstate().r r, r+ c s s | ] } | d Vq d S)r+ Nl r0 ).0r/ r0 r0 r1 s z"Random.setstate..Nz?state with version %s passed to Random.setstate() of version %s)r- r@ r& tuple
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__reduce__ s zRandom.__reduce__ c
C s | | } | | k r' t d n | d k r[ | d k rL | j | St d n | | } | | k r t d n | | } | d k r | d k r | | j | S| d k r t d | | | f n | | } | | k rt d n | d k r%| | d | } n- | d k rF| | d | } n t d | d k rmt d n | | | j | S)
zChoose a random item from range(start, stop[, step]).
This fixes the problem with randint() which includes the
endpoint; in Python this is usually not what you want.
z!non-integer arg 1 for randrange()Nr zempty range for randrange()z non-integer stop for randrange()rO z'empty range for randrange() (%d,%d, %d)z non-integer step for randrange()zzero step for randrange())rI
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zRandom.randrangec C s | j | | d S)zJReturn random integer in range [a, b], including both end points.
rO )r )r. rA br0 r0 r1 r s zRandom.randintc
C s | j } | j } | | | k s6 | | | k rq | j } | | }
x |
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| | S)zCReturn a random int in the range [0,n). Raises ValueError if n==0.zUnderlying random() generator does not supply
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zRandom._randbelowc C sB y | j t | } Wn t k
r9 t d Yn X| | S)z2Choose a random element from a non-empty sequence.z$Cannot choose from an empty sequence)rP lenrI
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Random.choicec C s | d k rk | j } x t t d t | D]3 } | | d } | | | | | | <| | Population must be a sequence or set. For dicts, use list(d).r z Sample larger than populationN r) r, rO )r: _SetrH _SequencerJ rP r_ rI _ceil_loglistrd setadd) r. Z
populationr\ re rV resultZsetsizeZpoolrb rf ZselectedZ selected_addr0 r0 r1 r s6
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Random.samplec C s | | | | j S)zHGet a random number in the range [a, b) or [a, b] depending on rounding.)r )r. rA rW r0 r0 r1 r V s zRandom.uniformg g ?c C s | j } y( | d k r! d n | | | | } Wn t k
rL | SYn X| | k r} d | } d | } | | } } n | | | | | d S)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
Ng ?g ?)r ZeroDivisionError)r. ZlowZhighmodeucr0 r0 r1 r \ s (
zRandom.triangularc C si | j } xQ | } d | } t | d | } | | d } | t | k r Pq q W| | | S)z\Normal distribution.
mu is the mean, and sigma is the standard deviation.
g ?g ?g @)r
NV_MAGICCONSTrl )r. musigmar u1u2zZzzr0 r0 r1 r r s
zRandom.normalvariatec C s 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.
)_expr )r. rv rw r0 r0 r1 r s zRandom.lognormvariatec C s t d | j | 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.
g ?)rl r )r. Zlambdr0 r0 r1 r s zRandom.expovariatec C s | j } | d k r t | Sd | } | t d | | } xf | } t t | } | | | } | } | d | | k s | d | t | k rE PqE qE Wd | }
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S)aF Circular data distribution.
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.
gư>g ?g ?)r TWOPI_sqrt_cos_pir{ _acos)r. rv Zkappar sr] rx rz dry qfZu3Zthetar0 r0 r1 r s&
.
zRandom.vonmisesvariatec C s
| d k s | d k r' t d n | j } | d k r t d | d } | t } | | } x| } d | k o d k n s qg n d | } t | d | | } | t | }
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| Sd S) 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
g z*gammavariate: alpha and beta must be > 0.0g ?g @gHz>gP?g @N)rI r r} LOG4rl r{
SG_MAGICCONST_e)r. alphabetar ZainvZbbbZcccrx ry vr/ rz r] rs rW pr0 r0 r1 r sJ
*
zRandom.gammavariatec C s | j } | j } d | _ | d k rw | t } t d t d | } t | | } t | | | _ n | | | S)zGaussian distribution.
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 @g ?g )r r- r| r} rl r~ _sin)r. rv rw r rz Zx2piZg2radr0 r0 r1 r! " s
z Random.gaussc C s> | j | d } | d k r" d S| | | j | d Sd S)zBeta distribution.
Conditions on the parameters are alpha > 0 and beta > 0.
Returned values range between 0 and 1.
g ?r g N)r )r. r r yr0 r0 r1 r" W s
zRandom.betavariatec C s d | j } d | d | S)z3Pareto distribution. alpha is the shape parameter.g ?)r )r. r rs r0 r0 r1 r# i s zRandom.paretovariatec C s' d | j } | t | d | S)zfWeibull distribution.
alpha is the scale parameter and beta is the shape parameter.
g ?)r rl )r. r r rs r0 r0 r1 r$ r s zRandom.weibullvariate)"__name__
__module__ __qualname____doc__rD r2 r r% r& rL rM rN r5 r r BPFr[ _MethodType_BuiltinMethodTyperP r r r r r r r r r r r! r" r# r$ r0 r0 )rC r1 r D s6 ,
> 0 H 5 c @ sP e Z d Z d Z d d Z d d Z d d Z d d Z e Z Z d
S) r( zAlternate random number generator using sources provided
by the operating system (such as /dev/urandom on Unix or
CryptGenRandom on Windows).
Not available on all systems (see os.urandom() for details).
c C s t j t d d d ?t S)z3Get the next random number in the range [0.0, 1.0). r3 r, )r5 r6 r7 RECIP_BPF)r. r0 r0 r1 r s zSystemRandom.randomc C sr | d k r t d n | t | k r< t d n | d d } t j t | d } | | d | ?S)z:getrandbits(k) -> x. Generates an int with k random bits.r z(number of bits must be greater than zeroz#number of bits should be an integerr r3 )rI r5 rJ r6 r7 )r. r\ Znumbytesr/ r0 r0 r1 r' s zSystemRandom.getrandbitsc O s d S)z% sd ("
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