ó
|
M\¬Qc @ s£ d Z d d l m 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# d d l$ Z% d
|
d d d d d d d d d d d d d d d d d d d d d d d! d" g Z& d# e d$ e d% Z' d% e Z( e d& Z) d' e d( Z* d) Z+ d* e+ Z, d d l- Z- d
|
e- j. f d+ YZ. d e. f d, YZ/ d" e. f d- YZ0 d. Z1 d/ d0 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 e3 jI ZI eJ d1 k re2 n d S(2 sP 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.
|
* Without a direct way to compute N steps forward, the semantics of
|
jumpahead(n) are weakened to simply jump to another distant state and rely
|
on the large period to avoid overlapping sequences.
|
* The random() method is implemented in C, executes in a single Python step,
|
and is, therefore, threadsafe.
|
|
iÿÿÿÿ( t division( t warn( t
|
MethodTypet BuiltinMethodType( t logt expt pit et ceil( t sqrtt acost cost sin( t urandom( t hexlifyNt Randomt seedt randomt uniformt randintt choicet samplet randranget shufflet normalvariatet lognormvariatet expovariatet vonmisesvariatet gammavariatet
|
triangulart gausst betavariatet paretovariatet weibullvariatet getstatet setstatet jumpaheadt WichmannHillt getrandbitst SystemRandomi g à¿g @g @g ð?g @i5 i c B s0 e Z d Z d Z d d Z d d Z d Z d Z d Z d Z
|
d Z d Z d d
|
e d d e >d Z d Z e e d e >e e d Z d Z d e d Z d Z d Z d d d d Z d Z d Z d Z d Z d Z d Z d Z d Z! d Z" RS( sÎ Random number generator base class used by bound module functions.
|
|
Used to instantiate instances of Random to get generators that don't
|
share state. 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 following
|
methods: random(), seed(), getstate(), setstate() and jumpahead().
|
Optionally, implement a getrandbits() method so that randrange() can cover
|
arbitrarily large ranges.
|
|
i c C s | j | d | _ d S( se Initialize an instance.
|
|
Optional argument x controls seeding, as for Random.seed().
|
N( R t Nonet
|
gauss_next( t selft x( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyt __init__[ s c C s | d k rd y t t t d d } Wqd t k
|
r` d d l } t | j d } qd Xn t t | j | d | _ d S( s Initialize internal state from hashable object.
|
|
None or no argument seeds from current time or from an operating
|
system specific randomness source if available.
|
|
If a is not None or an int or long, hash(a) is used instead.
|
i iÿÿÿÿNi (
|
R( t longt _hexlifyt _urandomt NotImplementedErrort timet superR R R) ( R* t aR1 ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR d s c C s" | j t t | j | j f S( s9 Return internal state; can be passed to setstate() later.( t VERSIONR2 R R" R) ( R* ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR" w s c C sÎ | d } | d k rA | \ } } | _ t t | j | n | d k r± | \ } } | _ y t d | D } Wn t k
|
r } t | n Xt t | j | n t d | | j f d S( s: Restore internal state from object returned by getstate().i i i c s s | ] } t | d Vq d S( i i NI ( R- ( t .0R+ ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pys <genexpr> s s? state with version %s passed to Random.setstate() of version %sN( R) R2 R R# t tuplet
|
ValueErrort TypeErrorR4 ( R* t statet versiont internalstateR ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR# { s
|
c C sW t | t | j } t t j d | j d } t t | j | d S( s® Change the internal state to one that is likely far away
|
from the current state. This method will not be in Py3.x,
|
so it is better to simply reseed.
|
t sha512i N( t reprR" t intt _hashlibt newt hexdigestR2 R R$ ( R* t nt s( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR$ s !c C s
|
| j S( N( R" ( R* ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyt __getstate__¢ s c C s | j | d S( N( R# ( R* R9 ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyt __setstate__¥ s c C s | j d | j f S( N( ( t __class__R" ( R* ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyt
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__reduce__¨ s i l c C så | | } | | k r$ t d n | | k ru | d k ri | | k rU | j | S| | j | St d n | | } | | k r t d n | | } | d k rü | d k rü | | k rÞ | | | j | S| | | | j | S| d k r!t d | | | f n | | }
|
|
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| k rEt d n |
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d k rf| |
|
d |
|
} n* |
|
d k r| |
|
d |
|
} n t d | d k r¨t d n | | k rÉ| |
|
| j | S| |
|
| | j | S( s 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.
|
Do not supply the 'int', 'default', and 'maxwidth' arguments.
|
s! non-integer arg 1 for randrange()i s empty range for randrange()s non-integer stop for randrange()i s' empty range for randrange() (%d,%d, %d)s non-integer step for randrange()s zero step for randrange()( R7 t
|
_randbelowR ( R* t startt stopt stepR> t defaultt maxwidtht istartt istopt widtht istepRB ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR s@
|
c C s | j | | d S( sJ Return random integer in range [a, b], including both end points.
|
i ( R ( R* R3 t b( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR í s c
|
C sÁ y | j } Wn t k
|
r nt Xt | j | k sH t | | k r | d | | d d } | | } x | | k r | | } qt W| S| | k r t d n | | j | S( s£ Return a random int in the range [0,n)
|
|
Handles the case where n has more bits than returned
|
by a single call to the underlying generator.
|
grÄZ|
|
ð?i g @sg Underlying random() generator does not supply
|
enough bits to choose from a population range this large( R& t AttributeErrort typeR t _warn(
|
R* RB t _logR> t _maxwidtht _Methodt _BuiltinMethodR& t kt r( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyRH ó s ' c C s | t | j t | S( s2 Choose a random element from a non-empty sequence.( R> R t len( R* t seq( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR s c C sv | d k r | j } n xW t t d t | D]: } | | | d } | | | | | | <| | <q4 Wd S( s× x, random=random.random -> 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( R( R t reversedt xrangeR\ ( R* R+ R R> t it j( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR s
|
"c C sÉ t | } d | k o# | k n s7 t d n | j } t } d g | } d } | d k r | d t t | d d 7} n | | k s¤ t | d rt | } xt | D]A } | | | | }
|
| |
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| | <| | | d | |
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<q½ WnÀ y~ t
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} | j } xe t | D]W } | | | }
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x# |
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|
qCW| |
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| | <q'WWn? t t f k
|
rÄt | t r® n | j t | | SX| S(
|
s8 Chooses k unique random elements from a population sequence.
|
|
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 in 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)
|
i s sample larger than populationi i i i t keysi N( R\ R7 R R> R( t _ceilRV t hasattrt listR_ t sett addR8 t KeyErrort
|
isinstanceR R6 ( R* t
|
populationRZ RB R t _intt resultt setsizet poolR` Ra t selectedt selected_add( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR " s: $
|
c C s | | | | j S( sH Get a random number in the range [a, b) or [a, b] depending on rounding.( R ( R* R3 RR ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR c s g g ð?c C sx | j } | d k r d n | | | | } | | k r` d | } d | } | | } } n | | | | | d S( sÜ 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 à?g ð?N( R R( ( R* t lowt hight modet ut c( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR i s $
|
|
c C sh | j } xP | } d | } t | d | } | | d } | t | k r Pq q | | | S( s\ Normal distribution.
|
|
mu is the mean, and sigma is the standard deviation.
|
|
g ð?g à?g @( R t NV_MAGICCONSTRV ( R* t mut sigmaR t u1t u2t zt zz( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR | s c C s t | j | | S( sû 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.
|
|
( t _expR ( R* Rw Rx ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR s c C s t d | j | S( s^ 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 ð?( RV R ( R* t lambd( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR ¡ s c C s | j } | d k r t | Sd | } | t d | | } xe | } t t | } | | | } | } | d | | k s£ | d | t | k rE PqE qE d | }
|
|
|
| d |
|
| } | } | d k rö | t | t } n | t | t } | S( sF 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.
|
|
gíµ ÷Æ°>g à?g ð?( R t TWOPIt _sqrtt _cost _piR} t _acos( R* Rw t kappaR RC R[ Ry R{ t dRz t qt ft u3t theta( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR ´ s&
|
.
|
c 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 qd n d | } t | d | | } | t | }
|
| | | } | | | |
|
} | t d | d k s| t | k rd |
|
| Sqd nè | d k r\| } x | d k rL| } q4Wt | | Sx | } t | t } | | } | d k r| d | }
|
n t | | | }
|
| } | d k râ| |
|
| d k rùPqùq_| t |
|
k r_Pq_q_|
|
| Sd S( sZ 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 s* gammavariate: alpha and beta must be > 0.0g ð?g @gH¯¼ò×z>gËPÊÿÿï?g @N( R7 R R t LOG4RV R} t SG_MAGICCONSTt _e( R* t alphat betaR t ainvt bbbt cccRy Rz t vR+ R{ R[ Rt RR t p( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR ä sJ
|
|
*
|
c C s | j } | j } d | _ | d k rw | t } t d t d | } t | | } t | | | _ n | | | S( sØ 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 Àg ð?N( R R) R( R R RV R t _sin( R* Rw Rx R R{ t x2pit g2rad( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR , s c C s> | j | d } | d k r" d S| | | j | d Sd S( s Beta distribution.
|
|
Conditions on the parameters are alpha > 0 and beta > 0.
|
Returned values range between 0 and 1.
|
|
g ð?i g N( R ( R* R R t y( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR a s
|
c C s% d | j } d t | d | S( s3 Pareto distribution. alpha is the shape parameter.g ð?( R t pow( R* R Rt ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR s s c C s, d | j } | t t | d | S( sf Weibull distribution.
|
|
alpha is the scale parameter and beta is the shape parameter.
|
|
g ð?( R R RV ( R* R R Rt ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR! | s N(# t __name__t
|
__module__t __doc__R4 R( R, R R" R# R$ RD RE RG R> t BPFR R RV t _MethodTypet _BuiltinMethodTypeRH R R R R R R R R R R R R R R! ( ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR H s: ? A 0 H 5 c B s\ e Z d Z d d Z d Z d Z d Z d Z d d d d Z d d Z
|
RS(
|
i c C s | d k rd y t t t d d } Wqd t k
|
r` d d l } t | j d } qd Xn t | t t f s t | } n t | d \ } } t | d \ } } t | d \ } } t | d t | d t | d f | _
|
d | _ d S( sü Initialize internal state from hashable object.
|
|
None or no argument seeds from current time or from an operating
|
system specific randomness source if available.
|
|
If a is not None or an int or long, hash(a) is used instead.
|
|
If a is an int or long, a is used directly. Distinct values between
|
0 and 27814431486575L inclusive are guaranteed to yield distinct
|
internal states (this guarantee is specific to the default
|
Wichmann-Hill generator).
|
i iÿÿÿÿNi i<v ibv irv i ( R( R- R. R/ R0 R1 Ri R> t hasht divmodt _seedR) ( R* R3 R1 R+ R R{ ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR s 0c C sj | j \ } } } d | d } d | d } d | d } | | | f | _ | d | d | d d
|
S( s3 Get the next random number in the range [0.0, 1.0).i« i=v i¬ icv iª isv g @Ý@g ÀÝ@g ÀÝ@g ð?( R¡ ( R* R+ R R{ ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR ¬ s c C s | j | j | j f S( s9 Return internal state; can be passed to setstate() later.( R4 R¡ R) ( R* ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR" Ë s c C sK | d } | d k r. | \ } | _ | _ n t d | | j f d S( s: Restore internal state from object returned by getstate().i i s? state with version %s passed to Random.setstate() of version %sN( R¡ R) R7 R4 ( R* R9 R: ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR# Ï s
|
|
c C s£ | d k s t d n | j \ } } } t | t d | d d } t | t d | d d } t | t d | d d } | | | f | _ d S(
|
sà Act as if n calls to random() were made, but quickly.
|
|
n is an int, greater than or equal to 0.
|
|
Example use: If you have 2 threads and know that each will
|
consume no more than a million random numbers, create two Random
|
objects r1 and r2, then do
|
r2.setstate(r1.getstate())
|
r2.jumpahead(1000000)
|
Then r1 and r2 will use guaranteed-disjoint segments of the full
|
period.
|
i s n must be >= 0i« i=v i¬ icv iª isv N( R7 R¡ R> R ( R* RB R+ R R{ ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR$ Ù s i c C s t | t | k o4 t | k o4 t k n sH t d n d | k o_ d k n o d | k o{ d k n o d | k o d k n s« t d n d | k oÍ | k oÍ | k n rNd d l } t | j d } t | d @| d ?A } t | d \ } } t | d \ } } t | d \ } } n | pWd | p`d | pid f | _ d | _ d S(
|
sj Set the Wichmann-Hill seed from (x, y, z).
|
|
These must be integers in the range [0, 256).
|
s seeds must be integersi i s seeds must be in range(0, 256)iÿÿÿÿNiÿÿÿ i i (
|
RT R> R8 R7 R1 R- R R¡ R( R) ( R* R+ R R{ R1 t t( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyt __whseedï s 9T' $c C s¸ | d k r | j d St | } t | d \ } } t | d \ } } t | d \ } } | | d pv d } | | d p d } | | d p d } | j | | | d S( sb Seed from hashable object's hash code.
|
|
None or no argument seeds from current time. It is not guaranteed
|
that objects with distinct hash codes lead to distinct internal
|
states.
|
|
This is obsolete, provided for compatibility with the seed routine
|
used prior to Python 2.1. Use the .seed() method instead.
|
Ni i ( R( t _WichmannHill__whseedR R ( R* R3 R+ R R{ ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyt whseed s
|
N( R R R4 R( R R R" R# R$ R¤ R¥ ( ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR% s
|
c B sF e Z d Z d Z d Z d Z e Z Z d Z e Z Z
|
RS( sÝ 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 t t d d d ?t S( s3 Get the next random number in the range [0.0, 1.0).i i i ( R- R. R/ t RECIP_BPF( R* ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR ' s c C su | d k r t d n | t | k r< t d n | d d } t t t | d } | | d | ?S( s> getrandbits(k) -> x. Generates a long int with k random bits.i s( number of bits must be greater than zeros# number of bits should be an integeri i i ( R7 R> R8 R- R. R/ ( R* RZ t bytesR+ ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR& + s c O s d S( s< Stub method. Not used for a system random number generator.N( R( ( R* t argst kwds( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyt _stub5 s c O s t d d S( sA Method should not be called for a system random number generator.s* System entropy source does not have state.N( R0 ( R* R¨ R© ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyt _notimplemented: s ( R R R R R& Rª R R$ R« R" R# ( ( ( sN /tmp/ndk-User/buildhost/install/prebuilt/darwin-x86_64/lib/python2.7/random.pyR' s
|
|
c C sõ d d l } | Gd G| j GHd } d } d } d } | j } xV t | D]H } | | }
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7} | |
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