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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.
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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 �g @g @g �?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
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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( s� 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( ( s /usr/lib64/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.
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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* ( ( s /usr/lib64/python2.7/random.pyR" w s c C s� | 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+ ( ( s /usr/lib64/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 ( ( s /usr/lib64/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.
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__reduce__� s i l c C s� | | � } | | 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 r� | d k r� | | k r� | | | j | � � S| | | | j � | � � S| d k r!t d | | | f � n | | � }
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| | 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
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c C s | j | | d � S( sJ Return random integer in range [a, b], including both end points.
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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.
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enough bits to choose from a population range this large( R& t AttributeErrort typeR t _warn(
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c C s | t | j � t | � � S( s2 Choose a random element from a non-empty sequence.( R> R t len( R* t seq( ( s /usr/lib64/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( ( s /usr/lib64/python2.7/random.pyR s
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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
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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 ( ( s /usr/lib64/python2.7/random.pyR c s g g �?c C sx | j � } | d k r d n | | | | } | | k r` d | } d | } | | } } n | | | | | d S( s� 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( R R( ( R* t lowt hight modet ut c( ( s /usr/lib64/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.
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NV_MAGICCONSTRV ( R* t mut sigmaR t u1t u2t zt zz( ( s /usr/lib64/python2.7/random.pyR | s
c C s t | j | | � � S( s� 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 ( ( s /usr/lib64/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 �?( RV R ( R* t lambd( ( s /usr/lib64/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 | }
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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.
g���ư>g �?g �?( R t TWOPIt _sqrtt _cost _piR} t _acos( R* Rw t kappaR RC R[ Ry R{ t dRz t qt ft u3t theta( ( s /usr/lib64/python2.7/random.pyR � s&
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| 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 �?g @gH�����z>g�P���?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( ( s /usr/lib64/python2.7/random.pyR � sJ
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c C s� | j } | j } d | _ | d k rw | � t } t d t d | � � � } t | � | } t | � | | _ n | | | S( s� 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 �?N( R R) R( R R� RV R� t _sin( R* Rw Rx R R{ t x2pit g2rad( ( s /usr/lib64/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 �?i g N( R ( R* R� R� t y( ( s /usr/lib64/python2.7/random.pyR a s
c C s% d | j � } d t | d | � S( s3 Pareto distribution. alpha is the shape parameter.g �?( R t pow( R* R� Rt ( ( s /usr/lib64/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 �?( R R� RV ( R* R� R� Rt ( ( s /usr/lib64/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! ( ( ( s /usr/lib64/python2.7/random.pyR H s: ?
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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( 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.
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 i����Ni i<v ibv irv i ( R( R- R. R/ R0 R1 Ri R> t hasht divmodt _seedR) ( R* R3 R1 R+ R� R{ ( ( s /usr/lib64/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 i� isv g @��@g ���@g ���@g �?( R� ( R* R+ R� R{ ( ( s /usr/lib64/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* ( ( s /usr/lib64/python2.7/random.pyR" � 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: ( ( s /usr/lib64/python2.7/random.pyR# � 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(
s� 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 i� isv N( R7 R� R> R� ( R* RB R+ R� R{ ( ( s /usr/lib64/python2.7/random.pyR$ � 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 o� | k o� | 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)i����Ni��� i i (
RT R> R8 R7 R1 R- R� R� R( R) ( R* R+ R� R{ R1 t t( ( s /usr/lib64/python2.7/random.pyt __whseed� s 9T' $c C s� | d k r | j � d St | � } t | d � \ } } t | d � \ } } t | d � \ } } | | d pv d } | | d p� d } | | d p� d } | j | | | � d S( sb Seed from hashable object's hash code.
None or no argument seeds from current time. It is not guaranteed
that objects with distinct hash codes lead to distinct internal
states.
This is obsolete, provided for compatibility with the seed routine
used prior to Python 2.1. Use the .seed() method instead.
Ni i ( R( t _WichmannHill__whseedR� R� ( R* R3 R+ R� R{ ( ( s /usr/lib64/python2.7/random.pyt whseed s
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RS( s� Alternate random number generator using sources provided
by the operating system (such as /dev/urandom on Unix or
CryptGenRandom on Windows).
Not available on all systems (see os.urandom() for details).
c C s! t t t d � � d � d ?t S( s3 Get the next random number in the range [0.0, 1.0).i i i ( R- R. R/ t RECIP_BPF( R* ( ( s /usr/lib64/python2.7/random.pyR ' s c C su | d k r t d � � n | t | � k r< t d � � n | d d } t t t | � � d � } | | d | ?S( s> getrandbits(k) -> x. Generates a long int with k random bits.i s( number of bits must be greater than zeros# number of bits should be an integeri i i ( R7 R> R8 R- R. R/ ( R* RZ t bytesR+ ( ( s /usr/lib64/python2.7/random.pyR& + s c O s d S( s< Stub method. Not used for a system random number generator.N( R( ( R* t argst kwds( ( s /usr/lib64/python2.7/random.pyt _stub5 s c O s t d � � d S( sA Method should not be called for a system random number generator.s* System entropy source does not have state.N( R0 ( R* R� R� ( ( s /usr/lib64/python2.7/random.pyt _notimplemented: s ( R� R� R� R R& R� R R$ R� R" R# ( ( ( s /usr/lib64/python2.7/random.pyR' s
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