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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.
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accumulaterepeat)bisectN)sha512Randomseedrandomuniformrandintchoicesample randrangeshuffle
normalvariatelognormvariate expovariatevonmisesvariate gammavariate
triangulargauss betavariate
paretovariateweibullvariategetstatesetstate getrandbitschoices SystemRandom g @ @ ? @5 c s$ e Zd ZdZdZd?ddZdd Zd@ fd d
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de> fd d ZeZd d ZdAd d!Zd"d# ZdBddd$d%d&Zd'd( ZdCd+d,Zd-d. Zd/d0 Zd1d2 Z d3d4 Z d5d6 Z d7d8 Z d9d: Z d;d< Z!d=d> Z" Z#S )Dr 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__c K sJ | j D ]>}d|jkr qFd|jkr.| j| _ qFd|jkr| j| _ qFqdS )a Control how subclasses generate random integers.
The algorithm a subclass can use depends on the random() and/or
getrandbits() implementation available to it and determines
whether it can generate random integers from arbitrarily large
ranges.
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None or no argument seeds from current time or from an operating
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,
bytes, or bytearray. For version 1 (provided for reproducing random
sequences from older versions of Python), the algorithm for str and
bytes generates a narrower range of seeds.
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z Random.seedc s | j t | jfS )z9Return internal state; can be passed to setstate() later.)VERSIONrT r& r3 r4 rW r6 r7 r& s zRandom.getstatec
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t|W 5 d}~X Y nX t | ntd|| jf dS )z:Restore internal state from object returned by getstate().r r2 r1 c s s | ]}|d V qdS )l Nr6 ).0r5 r6 r6 r7 <genexpr> s z"Random.setstate.<locals>.<genexpr>Nz?state with version %s passed to Random.setstate() of version %s)r3 rT r' tuple
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C s ||}||krt d|dkr:|dkr2| |S t d||}||krRt d|| }|dkrx|dkrx|| | S |dkrt d|||f ||}||krt d|dkr|| d | } n"|dk r|| d | } nt d | dkrt d||| | S )
zChoose a random item from range(start, stop[, step]).
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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()rB z(empty range for randrange() (%d, %d, %d)z non-integer step for randrange()zzero step for randrange())r^ r9 )
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zRandom.randrangec C s | ||d S )zJReturn random integer in range [a, b], including both end points.
rB )r r4 rU br6 r6 r7 r s zRandom.randintc C s, | j }| }||}||kr(||}q|S )zCReturn a random int in the range [0,n). Raises ValueError if n==0.)r(
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z"Random._randbelow_with_getrandbitsc C sn | j }||kr$td || | S |dkr4td|| }|| | }| }||kr^| }qN||| | S )zReturn a random int in the range [0,n). Raises ValueError if n==0.
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zUnderlying random() generator does not supply
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To remove the range limitation, add a getrandbits() method.r zBoundary cannot be zero)r _warnr^ )r4 rn rR maxsizer remlimitrs r6 r6 r7 r= s z%Random._randbelow_without_getrandbitsc C s: z| t|}W n tk
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random float in [0.0, 1.0); if it is the default None, the
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a= Chooses k unique random elements from a population sequence or set.
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 range as an argument.
This is especially fast and space efficient for sampling from a
large population: sample(range(10000000), 60)
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the selections are made with equal probability.
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r@ | Y S X ||krdd| }d| }|| }}||| t|| 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
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zRandom.triangularc C sP | j }| }d| }t|d | }|| d }|t| krqDq||| S )z\Normal distribution.
mu is the mean, and sigma is the standard deviation.
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zRandom.normalvariatec C s t | ||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 )r4 r r r6 r6 r7 r s zRandom.lognormvariatec C s t d| | 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.
r. )r r )r4 lambdr6 r6 r7 r s zRandom.expovariatec C s | j }|dkrt| S d| }|td|| }| }tt| }||| }| } | d|| k s| d| t| kr4qq4d| }
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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.
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| S dS ) 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
r z*gammavariate: alpha and beta must be > 0.0r. r, gHz>gP?r/ N)r^ r r LOG4r r
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zRandom.gammavariatec C s` | j }| j}d| _|dkrT| t }tdtd| }t|| }t|| | _||| 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.
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z Random.gaussc C s0 | |d}|dkrdS ||| |d S dS )zBeta distribution.
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Returned values range between 0 and 1.
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zRandom.betavariatec C s d| }d|d| S )z3Pareto distribution. alpha is the shape parameter.r. r )r4 r r r6 r6 r7 r$ s zRandom.paretovariatec C s" d| }|t| d| S )zfWeibull distribution.
alpha is the scale parameter and beta is the shape parameter.
r. )r r )r4 r r r r6 r6 r7 r% s zRandom.weibullvariate)N)Nr1 )N)N)r r. N)$__name__
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S ) r* zAlternate random number generator using sources provided
by the operating system (such as /dev/urandom on Unix or
CryptGenRandom on Windows).
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c C s t tddd? t S )z3Get the next random number in the range [0.0, 1.0).rC rF r2 )rR rS _urandom RECIP_BPFrZ r6 r6 r7 r s zSystemRandom.randomc C s< |dkrt d|d d }tt|d}||d | ? S )z:getrandbits(k) -> x. Generates an int with k random bits.r z(number of bits must be greater than zerorC rF )r^ rR rS r )r4 rr numbytesr5 r6 r6 r7 r( s
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