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S )"a� Random variable generators.
bytes
-----
uniform bytes (values between 0 and 255)
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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Used to instantiate instances of Random to get generators that don't
share state.
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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.
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a\ Initialize internal state from a seed.
The only supported seed types are None, int, float,
str, bytes, and bytearray.
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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__reduce__� s zRandom.__reduce__c K sJ | j D ]>}d|jv r qFd|jv r.| j| _ qFd|jv r| j| _ qFqdS )a Control how subclasses generate random integers.
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whether it can generate random integers from arbitrarily large
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z"Random._randbelow_with_getrandbitsr< c C sj | j }||kr$td� t|� | �S |dkr0dS || }|| | }|� }||krZ|� }qJt|| �| S )z�Return a random int in the range [0,n). Returns 0 if n==0.
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v �r�||�} �q||| � �| || < �qp|S )am Chooses k unique random elements from a population sequence or set.
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in selection order so that all sub-slices will also be valid random
samples. This allows raffle winners (the sample) to be partitioned
into grand prize and second place winners (the subslices).
Members of the population need not be hashable or unique. If the
population contains repeats, then each occurrence is a possible
selection in the sample.
Repeated elements can be specified one at a time or with the optional
counts parameter. For example:
sample(['red', 'blue'], counts=[4, 2], k=5)
is equivalent to:
sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5)
To choose a sample from a range of integers, use range() for the
population argument. This is especially fast and space efficient
for sampling from a large population:
sample(range(10000000), 60)
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�zRandom.choicesc C s ||| | � � S )zHGet a random number in the range [a, b) or [a, b] depending on rounding.�r$ r| r9 r9 r: r+ � s zRandom.uniformr� r1 c C sz | � � }z |du rdn|| || }W n ty> | Y S 0 ||krbd| }d| }|| }}||| t|| � S )z�Triangular distribution.
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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.
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mu is the mean, and sigma is the standard deviation. This is
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)�_expr )r7 r� r� r9 r9 r: r 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.
r1 )r� r$ )r7 Zlambdr9 r9 r: r \ s zRandom.expovariatec C s� | j }|dkrt|� S d| }|td|| � }|� }tt| �}||| }|� } | d|| k s�| d| t|� kr4q�q4d| }
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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
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r1 r� )r )r7 r� r� �yr9 r9 r: r � s zRandom.betavariatec C s d| � � }d|d| S )z3Pareto distribution. alpha is the shape parameter.r1 r� )r7 r� r� r9 r9 r: r! � s zRandom.paretovariatec C s" d| � � }|t|� d| S )zfWeibull distribution.
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