f 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(1 u 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.
i ( u warn( u
MethodTypeu BuiltinMethodType( u logu expu piu eu ceil( u sqrtu acosu cosu sin( u urandom( u Setu Sequence( u sha512u Randomu seedu randomu uniformu randintu choiceu sampleu randrangeu shuffleu
normalvariateu lognormvariateu expovariateu vonmisesvariateu gammavariateu
triangularu gaussu betavariateu
paretovariateu weibullvariateu getstateu setstateu getrandbitsu SystemRandomi g ?g @g @g ?g @i5 i Nc s | Ee Z d Z d Z d Z d7 d d Z d7 d f d d Z f d d Z f d
d Z d d
Z
d d Z d d Z d7 d e
d d Z d d Z e
d e >e e e d d Z d d Z d7 d d Z d d Z d d Z d! d" d7 d# d$ Z d% d& Z d' d( Z d) d* Z d+ d, Z d- d. Z d/ d0 Z d1 d2 Z d3 d4 Z! d5 d6 Z" S(8 u Randomu 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.
i c C s | j | d | _ d S( ue Initialize an instance.
Optional argument x controls seeding, as for Random.seed().
N( u seedu Noneu
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u Random.__init__i c
s | d k rb y t j t d d } Wqb t k
r^ d d l } t | j d } Yqb Xn | d k r t | t t t f r t | t r | j
} n | t | j 7} t j | d } q n t
j | d | _ d S( u Initialize internal state from hashable object.
None or no argument seeds from current time or from an operating
system specific randomness source if available.
For version 2 (the default), all of the bits are used if *a* is a str,
bytes, or bytearray. For version 1, the hash() of *a* is used instead.
If *a* is an int, all bits are used.
i u bigi Ni i ( u Noneu intu
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u Random.seedc s | j t j | j f S( u9 Return internal state; can be passed to setstate() later.( u VERSIONu superu getstateu
gauss_next( u self( u __class__( u+ /opt/alt/python33/lib64/python3.3/random.pyu getstate{ s u Random.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( u: Restore internal state from object returned by getstate().i i i c s s | ] } | d Vq d S( i i Nl ( ( u .0u x( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu s u" Random.setstate..Nu? state with version %s passed to Random.setstate() of version %s( u
gauss_nextu superu setstateu tupleu
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u Random.setstatec C s
| j S( N( u getstate( u self( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu __getstate__ s u Random.__getstate__c C s | j | d S( N( u setstate( u selfu state( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu __setstate__ s u Random.__setstate__c C s | j f | j f S( N( u __class__u getstate( u self( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu
__reduce__ s u Random.__reduce__i 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(
u Choose 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.
u! non-integer arg 1 for randrange()i u empty range for randrange()u non-integer stop for randrange()i u' empty range for randrange() (%d,%d, %d)u non-integer step for randrange()u zero step for randrange()N( u
ValueErroru Noneu
_randbelow(
u selfu startu stopu stepu _intu istartu istopu widthu istepu n( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu randrange s4
u Random.randrangec C s | j | | d S( uJ Return random integer in range [a, b], including both end points.
i ( u randrange( u selfu au b( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu randint s u Random.randintc
C s | j } | | j | k s0 | | | k rk | j } | | } x | | k rf | | } qK W| S| j }
| | k r t d | |
| S| | } | | | } |
} x | | k r |
} q W| | | | S( uC Return a random int in the range [0,n). Raises ValueError if n==0.u Underlying random() generator does not supply
enough bits to choose from a population range this large.
To remove the range limitation, add a getrandbits() method.( u getrandbitsu randomu
bit_lengthu _warn(
u selfu nu intu maxsizeu typeu Methodu
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u Random._randbelowc C sB y | j t | } Wn t k
r9 t d Yn X| | S( u2 Choose a random element from a non-empty sequence.u$ Cannot choose from an empty sequence( u
_randbelowu lenu
ValueErroru
IndexError( u selfu sequ i( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu choice s
u
Random.choicec C s | d k rk | j } x t t d t | D]3 } | | d } | | | | | | <| | shuffle list x in place; return None.
Optional arg random is a 0-argument function returning a random
float in [0.0, 1.0); by default, the standard random.random.
i N( u Noneu
_randbelowu reversedu rangeu lenu int( u selfu xu randomu randbelowu iu ju _int( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu shuffle s "$"u Random.shufflec C s t | t r t | } n t | t s< t d n | j } t | } d | k oh | k n s| t d n d g | } d } | d k r | d t t
| d d 7} n | | k r%t | } x t | D]: } | | | } | | | | <| | | d | | Population must be a sequence or set. For dicts, use list(d).i u Sample larger than populationi i i i i N( u
isinstanceu _Setu tupleu _Sequenceu TypeErroru
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$
u
Random.samplec C s | | | | j S( uH Get a random number in the range [a, b) or [a, b] depending on rounding.( u random( u selfu au b( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu uniformP s u Random.uniformg g ?c C sx | j } | d k r d n | | | | } | | k r` d | } d | } | | } } n | | | | | d S( u Triangular 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
g ?g ?N( u randomu None( u selfu lowu highu modeu uu c( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu
triangularV s $
u Random.triangularc C sh | j } xP | } d | } t | d | } | | d } | t | k r Pq q | | | S( u\ Normal distribution.
mu is the mean, and sigma is the standard deviation.
g ?g ?g @( u randomu
NV_MAGICCONSTu _log( u selfu muu sigmau randomu u1u u2u zu zz( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu
normalvariatei s
u Random.normalvariatec C s t | j | | S( u 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.
( u _expu
normalvariate( u selfu muu sigma( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu lognormvariate s u Random.lognormvariatec C s t d | j | S( u^ 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 ?( u _logu random( u selfu lambd( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu expovariate s u Random.expovariatec C s | j } | d k r t | Sd | } | t d | | } xe | } t t | } | | | } | } | d | | k s | d | t | k rE PqE qE d | }
|
| d |
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n | t | t }
|
S( uF 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 ?( u randomu TWOPIu _sqrtu _cosu _piu _expu _acos( u selfu muu kappau randomu su ru u1u zu du u2u qu fu u3u theta( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu vonmisesvariate s&
.
u Random.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( uZ 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 u* gammavariate: alpha and beta must be > 0.0g ?g @gHz>gP?g @N( u
ValueErroru randomu _sqrtu LOG4u _logu _expu
SG_MAGICCONSTu _e( u selfu alphau betau randomu ainvu bbbu cccu u1u u2u vu xu zu ru uu bu p( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu gammavariate sJ
*
u Random.gammavariatec C s | j } | j } d | _ | d k rw | t } t d t d | } t | | } t | | | _ n | | | S( u Gaussian 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.
g @g ?Ng ( u randomu
gauss_nextu Noneu TWOPIu _sqrtu _logu _cosu _sin( u selfu muu sigmau randomu zu x2piu g2rad( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu gauss s
u Random.gaussc C s> | j | d } | d k r" d S| | | j | d Sd S( u Beta distribution.
Conditions on the parameters are alpha > 0 and beta > 0.
Returned values range between 0 and 1.
g ?i g N( u gammavariate( u selfu alphau betau y( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu betavariateN s
u Random.betavariatec C s d | j } d | d | S( u3 Pareto distribution. alpha is the shape parameter.g ?( u random( u selfu alphau u( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu
paretovariate` s u Random.paretovariatec C s' d | j } | t | d | S( uf Weibull distribution.
alpha is the scale parameter and beta is the shape parameter.
g ?( u randomu _log( u selfu alphau betau u( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu weibullvariatei s u Random.weibullvariateN(# u __name__u
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__reduce__u intu randrangeu randintu BPFu typeu _MethodTypeu _BuiltinMethodTypeu
_randbelowu choiceu shuffleu sampleu uniformu
triangularu
normalvariateu lognormvariateu expovariateu vonmisesvariateu gammavariateu gaussu betavariateu
paretovariateu weibullvariate( u
__locals__( ( u __class__u+ /opt/alt/python33/lib64/python3.3/random.pyu RandomD s6 ,
> 0 H 5 c B sT | Ee Z d Z d Z d d Z d d Z d d Z d d Z e Z Z d
S( u SystemRandomu Alternate 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( u3 Get the next random number in the range [0.0, 1.0).i u bigi ( u intu
from_bytesu _urandomu RECIP_BPF( u self( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu random~ s u SystemRandom.randomc C sr | d k r t d n | t | k r< t d n | d d } t j t | d } | | d | ?S( u: getrandbits(k) -> x. Generates an int with k random bits.i u( number of bits must be greater than zerou# number of bits should be an integeri i u big( u
ValueErroru intu TypeErroru
from_bytesu _urandom( u selfu ku numbytesu x( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu getrandbits s u SystemRandom.getrandbitsc O s d S( u< Stub method. Not used for a system random number generator.N( u None( u selfu argsu kwds( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu seed s u SystemRandom.seedc O s t d d S( uA Method should not be called for a system random number generator.u* System entropy source does not have state.N( u NotImplementedError( u selfu argsu kwds( ( u+ /opt/alt/python33/lib64/python3.3/random.pyu _notimplemented s u SystemRandom._notimplementedN(
u __name__u
__module__u __qualname__u __doc__u randomu getrandbitsu seedu _notimplementedu getstateu setstate( u
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u _test_generatori c C s t | t f t | t d t | t d t | t d
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normalvariateu lognormvariateu vonmisesvariateu gammavariateu gaussu betavariateu
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