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初版
2024-08-19 17:05:14 +08:00
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*åf_‹ãó^—dZddlmZddlmZmZm Z
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l5m6Z7gd¢Z:ded«zed«z Z;ed«Z<ded«zZ=dZ>de> zZ?dZ@Gd„de4j‚«ZAGd„deA«ZBeA«ZCeCjˆZDeCjŠZEeCjŒZFeCjŽZGeCj�ZHeCj’ZIeCj”ZJeCj–ZKeCj˜ZLeCjšZMeCjœZNeCjžZOeCj ZPeCj¢ZQeCj¤ZReCj¦ZSeCj¨ZTeCjªZUeCj¬ZVeCj®ZWeCj°ZXeCj²ZYeCj´ZZeCj¶Z[d„Z\d!d„Z]e^e3d«re3j¾eCjˆ¬«e`d k(re]«y y #e8$r
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l9m6Z7Y�ŒÅwxYw)"aERandom variable generators.
bytes
-----
uniform bytes (values between 0 and 255)
integers
--------
uniform within range
sequences
---------
pick random element
pick random sample
pick weighted random sample
generate random permutation
distributions on the real line:
------------------------------
uniform
triangular
normal (Gaussian)
lognormal
negative exponential
gamma
beta
pareto
Weibull
distributions on the circle (angles 0 to 2pi)
---------------------------------------------
circular uniform
von Mises
discrete distributions
----------------------
binomial
General notes on the underlying Mersenne Twister core generator:
* The period is 2**19937-1.
* It is one of the most extensively tested generators in existence.
* The random() method is implemented in C, executes in a single Python step,
and is, therefore, threadsafe.
é)Úwarn)ÚlogÚexpÚpiÚeÚceil)ÚsqrtÚacosÚcosÚsin)ÚtauÚfloorÚisfinite)ÚlgammaÚfabsÚlog2)Úurandom)ÚSequence)Úindex)Ú
accumulateÚrepeat)ÚbisectN)Úsha512)ÚRandomÚ SystemRandomÚ betavariateÚbinomialvariateÚchoiceÚchoicesÚ expovariateÚ gammavariateÚgaussÚ getrandbitsÚgetstateÚlognormvariateÚ
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paretovariateÚ randbytesÚrandintÚrandomÚ randrangeÚsampleÚseedÚsetstateÚshuffleÚ
triangularÚuniformÚvonmisesvariateÚweibullvariateégà¿ç@ç@çð?ç@é5éécó‡—eZdZdZdZd$d„Zd%ˆfd„ Zˆfd„Zˆfd„Zd„Z d „Z
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dœd„Zd„Zd&d„Zd'd„Zd'd„Zd„Zd(d„Zd„Zd„Z d „Z!d!„Z"d"„Z#d)d#„Z$ˆxZ%S)*raãRandom number generator base class used by bound module functions.
Used to instantiate instances of Random to get generators that don't
share state.
Class Random can also be subclassed if you want to use a different basic
generator of your own devising: in that case, override the following
methods: random(), seed(), getstate(), and setstate().
Optionally, implement a getrandbits() method so that randrange()
can cover arbitrarily large ranges.
éNcó4—|j|«d|_y)zeInitialize an instance.
Optional argument x controls seeding, as for Random.seed().
N)r-Ú
gauss_next)ÚselfÚxs úBC:\Users\RCi\AppData\Local\Programs\Python\Python312\Lib\random.pyÚ__init__zRandom.__init__~s€ð
� ‰ �!Œ ؈�óc 󜕗|dk(r†t|ttf«rpt|t«r|jd«n|}|rt |d«dznd}t t|«D]
}d|z|z dz}Œ|t
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|_y
) a\Initialize internal state from a seed.
The only supported seed types are None, int, float,
str, bytes, and bytearray.
None or no argument seeds from current time or from an operating
system specific randomness source if available.
If *a* is an int, all bits are used.
For version 2 (the default), all of the bits are used if *a* is a str,
bytes, or bytearray. For version 1 (provided for reproducing random
sequences from older versions of Python), the algorithm for str and
bytes generates a narrower range of seeds.
r;zlatin-1réiCBlÿÿÿÿéÿÿÿÿéþÿÿÿr:NzOThe only supported seed types are: None,
int, float, str, bytes, and bytearray.)Ú
isinstanceÚstrÚbytesÚdecodeÚordÚmapÚlenÚ bytearrayÚencodeÚintÚ
from_bytesÚ_sha512ÚdigestÚtypeÚfloatÚ TypeErrorÚsuperr-r?)r@ÚaÚversionrAÚcÚ __class__s €rBr-z Random.seed‡sø€ð$ �aŠ<œJ q¬3´¨,Ô7Ü'1°!´UÔ';�—‘˜Ô#ÀˆAÙ"#”�A�a‘D“ ˜Q’¨ˆAÜœ˜a“[ò
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¬C´¼¼UÄIÐNÔOÜðEóFð
Fô ‰‰ �QŒØˆ�rDcóN•—|jt‰|� «|jfS)z9Return internal state; can be passed to setstate() later.)ÚVERSIONrYr$r?)r@r]s €rBr$zRandom.getstate­s ø€à�|‰|œU™WÑ-Ó/°·±Ð@Ð@rDcó•—|d}|dk(r|\}}|_t‰|� |«y|dk(r.|\}}|_ td„|D««}t‰|� |«yt d|›d|j ›�«‚#t$r }t
|‚d}~wwxYw)z:Restore internal state from object returned by getstate().rr=r:c3ó&K—|] }|dz–—Œ y­w)lN©)Ú.0rAs rBú <genexpr>z"Random.setstate.<locals>.<genexpr>¾sèø€Ò%K¸ a¨7¥mÑ%Kùs‚Nzstate with version z( passed to Random.setstate() of version )r?rYr.ÚtupleÚ
ValueErrorrXr_)r@Ústater[Ú
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có"—|j«S©N)r$©r@s rBÚ __getstate__zRandom.__getstate__Òs€Ø�}‰}‹ÐrDcó&—|j|«yrj)r.)r@rgs rBÚ __setstate__zRandom.__setstate__Õs€Ø �
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__reduce__zRandom.__reduce__Øs€Ø�~‰~˜r 4§=¡=£?Ð2Ð2rDc óÊ—|jD]T}d|jvryd|jvr|j|_yd|jvsŒC|j|_yy)aControl 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.
Ú
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|z }|«}||k\r
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t||z«|zS)z‹Return a random int in the range [0,n). Defined for n > 0.
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z¤Underlying random() generator does not supply
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Oô™&›( Q™,Ó'Ð 'ؘ‰kˆØ˜3‘ 'Ñ)ˆÙ ‹HˆØ�5ŠjÙ“ˆAð�5‹jä�a˜'‘kÓ" QÑ&Ð&rDcóJ—|j|dz«j|d«S)úGenerate n random bytes.éÚlittle)r#Úto_bytes©r@r|s rBr(zRandom.randbytess$€à×Ñ  A¡Ó&×/Ñ/°°8Ó<Ð<rDc óÖ—t|«}|€4|tur td«‚|dkDr|j|«St d«‚t|«}||z
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|z}n|dkr ||zdz|z}n t d«‚|dkrt d|›d|›d|›d�«‚|||j|«zzS) zãChoose a random item from range(stop) or range(start, stop[, step]).
Roughly equivalent to ``choice(range(start, stop, step))`` but
supports arbitrarily large ranges and is optimized for common cases.
z Missing a non-None stop argumentrzempty range for randrange()r;zempty range in randrange(z, ú)zzero step for randrange())Ú_indexÚ_ONErXrrrf) r@ÚstartÚstopÚstepÚistartÚistopÚwidthÚistepr|s rBr+zRandom.randrange#s'€ô˜“ˆØ ˆ<ðœ4ÑÜÐ BÓCÐCؘŠzØ—‘ vÓ.Ð.ÜÐ:Ó;Ð ;ô�t“ ˆØ˜‘ˆÜ�t“ ˆà �AŠ:Ø�qŠyØ §¡°Ó 6Ñ6Ð6ÜÐ8¸¸¸rÀ$ÀÀqÐIÓJÐ Jð �1Š9ؘ‘ Ñ" uÑ,‰AØ
�QŠYؘ‘ Ñ" uÑ,‰AäÐ8Ó9Ð 9Ø �Š6ÜÐ8¸¸¸rÀ$ÀÀrÈ$ÈÈqÐQÓRÐ Rؘ §¡°Ó 2Ñ2Ñ2Ð2rDcó,—|j||dz«S)zJReturn random integer in range [a, b], including both end points.
r;)r+©r@rZÚbs rBr)zRandom.randintLs€ð�~‰~˜a  1¡Ó%Ð%rDcóh—t|«s td«‚||jt|««S)z2Choose a random element from a non-empty sequence.z$Cannot choose from an empty sequence)rOÚ
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d«‚|j«}t|t«s td«‚|dkr t
d«‚|jt|«|¬«}t}|D� cgc]} |||| «‘Œc} S|j}
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||«||| |<Œ-| Scc} w)afChooses 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.
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)
zAPopulation must be a sequence. For dicts or sets, use sorted(d).Nz2The number of counts does not match the populationzCounts must be integersrz)Total of counts must be greater than zero)r}z,Sample larger than population or is negativeéér4r=r;)rIÚ _SequencerXrOÚlistÚ _accumulaterfÚpoprRr,ržÚ_bisectrrÚ_ceilÚ_logÚsetÚadd)r@Ú
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d|›�«d‚wxYwcc}w) zÑReturn a k sized list of population elements chosen with replacement.
If the relative weights or cumulative weights are not specified,
the selections are made with equal probability.
Nçz4The number of choices must be a keyword argument: k=z2Cannot specify both weights and cumulative weightsz3The number of weights does not match the populationrGz*Total of weights must be greater than zerozTotal of weights must be finiter;r) r*rOr�Ú_repeatr§r¨rXrIrRrfÚ _isfiniterª) r@r¯Úweightsr¹r}r*r|rr r±rÚhis rBrzRandom.choicesÆs[€ð—‘ˆÜ �
‹OˆØ Р؈Ü�Ø�S‘�ÜAHÈÈqÓAQÖR¸A˜
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ÜÐPÓQÐ QÜ ˆ{Ó ˜qÒ ÜÐRÓSÐ SؘB‘ #Ñ%ˆØ �CŠ<ÜÐIÓJÐ JܘÔÜÐ>Ó?Ð ?܈Ø
�‰Uˆä   qÓ)ö+Øð™6 +©v«x¸%Ñ/?ÀÀBÓGÓHò+ð +ùò+Søôò
Ü! '¬3Ô/ØØ�ÜØKÈÈÐMóàðð 
üò$+sµC5ÁC:ÃD)Ã:,D&có4—|||z
|j«zzS)zåGet a random number in the range [a, b) or [a, b] depending on rounding.
The mean (expected value) and variance of the random variable are:
E[X] = (a + b) / 2
Var[X] = (b - a) ** 2 / 12
©r*r—s rBr1zRandom.uniformîs€ð�A˜‘E˜TŸ[™[›]Ñ*Ñ*Ð*rDcó¸—|j«} |€dn
||z
||z
z }||kDrd|z
}d|z
}||}}|||z
t||z«zzS#t$r|cYSwxYw)a­Triangular distribution.
Continuous distribution bounded by given lower and upper limits,
and having a given mode value in-between.
http://en.wikipedia.org/wiki/Triangular_distribution
The mean (expected value) and variance of the random variable are:
E[X] = (low + high + mode) / 3
Var[X] = (low**2 + high**2 + mode**2 - low*high - low*mode - high*mode) / 18
çà?r7)r*ÚZeroDivisionErrorÚ_sqrt)r@ÚlowÚhighÚmodeÚur\s rBr0zRandom.triangularùs‚€ð
�K‰K‹Mˆð Ø�|‘¨$°©*¸À¹Ñ)DˆAð
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!ò ØŠJð ús’A Á AÁAcóž—|j} |«}d|«z
}t|dz
z|z }||zdz }|t|« krnŒ9|||zzS)z\Normal distribution.
mu is the mean, and sigma is the standard deviation.
r7rÃr6)r*Ú
NV_MAGICCONSTr¬)r@ÚmuÚsigmar*Úu1Úu2ÚzÚzzs rBr&zRandom.normalvariatesg€ð—‘ˆØÙ“ˆBØ‘v“x‘ˆBÜ  c¡Ñ*¨RÑ/ˆAØ�Q‘˜‘ˆBØ”d˜2“h�YŠØð
ð�A˜‘I‰~ÐrDcóð—|j}|j}d|_|€N|«tz}tdt d|«z
«z«}t |«|z}t
|«|z|_|||zzS)zØGaussian 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.
NgÀr7)r*r?ÚTWOPIrÅr¬Ú_cosÚ_sin)r@rÌrÍr*rÐÚx2piÚg2rads rBr"z Random.gauss'st€ð6—‘ˆØ �O‰OˆØˆŒØ ˆ9Ù“8œeÑ#ˆDܘ$¤ c©F«H¡nÓ!5Ñ5Ó6ˆEÜ�T“
˜UÑ"ˆAÜ" 4›j¨5Ñ0ˆDŒOà�A˜‘I‰~ÐrDcó8—t|j||««S)zûLog normal distribution.
If you take the natural logarithm of this distribution, you'll get a
normal distribution with mean mu and standard deviation sigma.
mu can have any value, and sigma must be greater than zero.
)Ú_expr&)r@rÌrÍs rBr%zRandom.lognormvariateMs€ô�D×&Ñ& r¨5Ó1Ó2Ð2rDcóB—td|j«z
« |z S)aìExponential distribution.
lambd is 1.0 divided by the desired mean. It should be
nonzero. (The parameter would be called "lambda", but that is
a reserved word in Python.) Returned values range from 0 to
positive infinity if lambd is positive, and from negative
infinity to 0 if lambd is negative.
The mean (expected value) and variance of the random variable are:
E[X] = 1 / lambd
Var[X] = 1 / lambd ** 2
r7)r¬r*)r@Úlambds rBr zRandom.expovariateWs"€ô$�S˜4Ÿ;™;›=Ñ(Ó)Ð)¨EÑ1Ð1rDcó —|j}|dkrt|«zSd|z }|td||zz«z} |«}tt|z«}|||zz }|«} | d||zz
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S)aFCircular 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�íµ ÷Æ°>rÃr7)r*rÓrÅrÔÚ_pirÙÚ_acos)r@rÌÚkappar*r³r~rÎrÐÚdrÏÚqÚfÚu3Úthetas rBr2zRandom.vonmisesvariateksù€ð —‘ˆØ �DŠ=Ü™6›8Ñ#Ð #à �%‰KˆØ
”�c˜A ™E‘kÓ"Ñ "ˆàÙ“ˆBÜ”S˜2‘X“ˆAà�Q˜‘U‘ ˆAÙ“ˆBØ�C˜!˜a™%‘KÒ 2¨#°©'´T¸!³WÑ)<Ò#<Øðð
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�Š8Øœ% ›(‘]¤eÑ+ˆEðˆ ðœ% ›(‘]¤eÑ+ˆEàˆ rDcóš—|dks|dkr td«‚|j}|dkDrštd|zdz
«}|tz
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|zSŒo)aîGamma 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
The mean (expected value) and variance of the random variable are:
E[X] = alpha * beta
Var[X] = alpha * beta ** 2
r»z*gammavariate: alpha and beta must be > 0.0r7r5gH¯¼šò×z>gËPÊÿÿï?r8)rfr*rÅÚLOG4r¬rÙÚ
SG_MAGICCONSTÚ_e)r@ÚalphaÚbetar*ÚainvÚbbbÚcccrÎrÏÚvrArÐr~rÉr˜Úps rBr!zRandom.gammavariate•s¦€ð( �CŠ<˜4 3š;ÜÐIÓJÐ Jà—‘ˆØ �3Š;ô ˜˜u™ sÑ*Ó+ˆDØœ$‘,ˆCؘ$‘,ˆCàÙ“X�ؘbÔ, 9Ô,ØØ™6›8‘^�ܘ˜s R™x™Ó)¨DÑ0�ØœD ›G‘O�ؘ‘G˜b‘L�ؘ# ™'‘M AÑ%�Ø”}Ñ$ s¨Q¡wÑ.°#Ò5¸¼dÀ1»gºØ˜t™8�Oðð�cŠ\䘙v›x™Ó(Ð(¨4Ñ/Ð /ð
Ù“H�ܘ%‘Z¤2Ñ%�ؘ‘E�ؘ’8ؘc E™kÑ*‘Aä˜q 1™u¨™oÓ.Ð.�AÙ“X�Ø�s’7ؘQ 5¨3¡;Ñ/Ò/Øð�t‘8ˆOðœ4  ›8’^ØØ�t‘8ˆOðrDcó\—|j|d«}|r|||j|d«zz Sy)aQBeta distribution.
Conditions on the parameters are alpha > 0 and beta > 0.
Returned values range between 0 and 1.
The mean (expected value) and variance of the random variable are:
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