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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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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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zRandom.__init__c K sJ | j D ]>}d|jkr qFd|jkr.| j| _ qFd|jkr| j| _ qFqdS )a Control how subclasses generate random integers.
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getrandbits() implementation available to it and determines
whether it can generate random integers from arbitrarily large
ranges.
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� �|� d | _d S ) a 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 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�Choose a random item from range(start, stop[, step]).
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zRandom.randrangec C s | � ||d �S )zJReturn random integer in range [a, b], including both end points.
rB )r �r4 rT �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 )z�Return a random int in the range [0,n). Raises ValueError if n==0.
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a= Chooses k unique random elements from a population sequence or set.
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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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r@ | Y S X ||krdd| }d| }|| }}||| t|| � S )z�Triangular distribution.
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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.
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zRandom.normalvariatec C s t | �||��S )z�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.
)�_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 Zlambdr6 r6 r7 r � s zRandom.expovariatec C s� | j }|dkrt|� S d| }|td|| � }|� }tt| �}||| }|� } | d|| k s�| d| t|� kr4q�q4d| }
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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
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zRandom.gammavariatec C s` | j }| j}d| _|dkrT|� t }tdtd|� � �}t|�| }t|�| | _||| S )z�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.
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z Random.gaussc C s0 | � |d�}|dkrdS ||| � |d� S dS )z�Beta 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.
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c C s t �td�d�d? t S )z3Get the next random number in the range [0.0, 1.0).rC rF r2 )rQ rR �_urandom� RECIP_BPFrY r6 r6 r7 r � s zSystemRandom.randomc C s< |dkrt d��|d d }t�t|�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] rQ rR r� )r4 rm Znumbytesr5 r6 r6 r7 r( � s
zSystemRandom.getrandbitsc O s dS )z<Stub method. Not used for a system random number generator.Nr6 �r4 �args�kwdsr6 r6 r7 r � s zSystemRandom.seedc O s t d��dS )zAMethod should not be called for a system random number generator.z*System entropy source does not have state.N)�NotImplementedErrorr� r6 r6 r7 �_notimplemented� s z SystemRandom._notimplementedN)
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