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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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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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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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whether it can generate random integers from arbitrarily large
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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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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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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.
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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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)�_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
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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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to a uniform random angle over the range 0 to 2*pi.
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Conditions on the parameters are alpha > 0 and beta > 0.
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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.
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