9.6. random — 生成伪随机数 ¶

9.6.1. 簿记函数 ¶

random. seed ( a=None , version=2 ) ¶

初始化随机数生成器。

若 a 被省略或 None , the current system time is used. If randomness sources are provided by the operating system, they are used instead of the system time (see the os.urandom() function for details on availability).

若 a 是 int，它会被直接使用。

With version 2 (the default), a str , bytes ，或 bytearray object gets converted to an int and all of its bits are used.

With version 1 (provided for reproducing random sequences from older versions of Python), the algorithm for str and bytes generates a narrower range of seeds.

3.2 版改变： Moved to the version 2 scheme which uses all of the bits in a string seed.

random. getstate ( ) ¶

Return an object capturing the current internal state of the generator. This object can be passed to setstate() to restore the state.

random. setstate ( state ) ¶

state should have been obtained from a previous call to getstate() ，和 setstate() restores the internal state of the generator to what it was at the time getstate() was called.

random. getrandbits ( k ) ¶

Returns a Python integer with k random bits. This method is supplied with the MersenneTwister generator and some other generators may also provide it as an optional part of the API. When available, getrandbits() enables randrange() to handle arbitrarily large ranges.

9.6.2. 整数函数 ¶

random. randrange ( stop ) ¶

random. randrange ( start , stop [ , step ] )

返回随机选中的元素，从 range(start, stop, step) 。这相当于 choice(range(start, stop, step)) , but doesn’t actually build a range object.

The positional argument pattern matches that of range() . Keyword arguments should not be used because the function may use them in unexpected ways.

3.2 版改变： randrange() is more sophisticated about producing equally distributed values. Formerly it used a style like int(random()*n) which could produce slightly uneven distributions.

random. randint ( a , b ) ¶

返回随机整数 N 这样 a <= N <= b . Alias for randrange(a, b+1) .

9.6.3. 序列函数 ¶

random. choice ( seq ) ¶

返回随机元素，从非空序列 seq 。若 seq 为空，引发 IndexError .

random. choices ( population , weights=None , * , cum_weights=None , k=1 ) ¶

返回 k 尺寸的元素列表，选取自 population with replacement. If the population 为空，引发 IndexError .

若 weights sequence is specified, selections are made according to the relative weights. Alternatively, if a cum_weights sequence is given, the selections are made according to the cumulative weights (perhaps computed using itertools.accumulate() ). For example, the relative weights [10, 5, 30, 5] are equivalent to the cumulative weights [10, 15, 45, 50] . Internally, the relative weights are converted to cumulative weights before making selections, so supplying the cumulative weights saves work.

若 weights nor cum_weights are specified, selections are made with equal probability. If a weights sequence is supplied, it must be the same length as the population sequence. It is a TypeError to specify both weights and cum_weights .

weights or cum_weights can use any numeric type that interoperates with the float values returned by random() (that includes integers, floats, and fractions but excludes decimals).

3.6 版新增。

random. shuffle ( x [ , random ] ) ¶

洗牌序列 x 原位。

可选自变量 random is a 0-argument function returning a random float in [0.0, 1.0); by default, this is the function random() .

To shuffle an immutable sequence and return a new shuffled list, use sample(x, k=len(x)) 代替。

Note that even for small len(x) , the total number of permutations of x can quickly grow larger than the period of most random number generators. This implies that most permutations of a long sequence can never be generated. For example, a sequence of length 2080 is the largest that can fit within the period of the Mersenne Twister random number generator.

random. sample ( population , k ) ¶

返回 k length list of unique elements chosen from the population sequence or set. Used for random sampling without replacement.

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 from a range of integers, use a range() object as an argument. This is especially fast and space efficient for sampling from a large population: sample(range(10000000), k=60) .

If the sample size is larger than the population size, a ValueError 被引发。

9.6.4. 实值分布 ¶

The following functions generate specific real-valued distributions. Function parameters are named after the corresponding variables in the distribution’s equation, as used in common mathematical practice; most of these equations can be found in any statistics text.

random. random ( ) ¶

Return the next random floating point number in the range [0.0, 1.0).

random. uniform ( a , b ) ¶

Return a random floating point number N 这样 a <= N <= b for a <= b and b <= N <= a for b < a .

The end-point value b may or may not be included in the range depending on floating-point rounding in the equation a + (b-a) * random() .

random. triangular ( low , high , mode ) ¶

Return a random floating point number N 这样 low <= N <= high and with the specified mode between those bounds. The low and high bounds default to zero and one. The mode argument defaults to the midpoint between the bounds, giving a symmetric distribution.

random. betavariate ( alpha , beta ) ¶

Beta distribution. Conditions on the parameters are alpha > 0 and beta > 0 . Returned values range between 0 and 1.

random. expovariate ( lambd ) ¶

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.

random. gammavariate ( alpha , beta ) ¶

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
										

random. gauss ( mu , sigma ) ¶

Gaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function defined below.

random. lognormvariate ( mu , sigma ) ¶

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.

random. normalvariate ( mu , sigma ) ¶

Normal distribution. mu is the mean, and sigma is the standard deviation.

random. vonmisesvariate ( mu , kappa ) ¶

mu is the mean angle, expressed in radians between 0 and 2* pi ，和 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 .

random. paretovariate ( alpha ) ¶

Pareto distribution. alpha is the shape parameter.

random. weibullvariate ( alpha , beta ) ¶

Weibull distribution. alpha is the scale parameter and beta is the shape parameter.

9.6.5. 替代生成器 ¶

class random. SystemRandom ( [ seed ] ) ¶

Class that uses the os.urandom() function for generating random numbers from sources provided by the operating system. Not available on all systems. Does not rely on software state, and sequences are not reproducible. Accordingly, the seed() method has no effect and is ignored. getstate() and setstate() methods raise NotImplementedError if called.

9.6.6. Notes on Reproducibility ¶

Sometimes it is useful to be able to reproduce the sequences given by a pseudo random number generator. By re-using a seed value, the same sequence should be reproducible from run to run as long as multiple threads are not running.

Most of the random module’s algorithms and seeding functions are subject to change across Python versions, but two aspects are guaranteed not to change:

• If a new seeding method is added, then a backward compatible seeder will be offered.
• 生成器的 random() method will continue to produce the same sequence when the compatible seeder is given the same seed.

9.6.7. 范例和配方 ¶

基本范例：

>>> random()                             # Random float:  0.0 <= x < 1.0
0.37444887175646646
>>> uniform(2.5, 10.0)                   # Random float:  2.5 <= x < 10.0
3.1800146073117523
>>> expovariate(1 / 5)                   # Interval between arrivals averaging 5 seconds
5.148957571865031
>>> randrange(10)                        # Integer from 0 to 9 inclusive
7
>>> randrange(0, 101, 2)                 # Even integer from 0 to 100 inclusive
26
>>> choice(['win', 'lose', 'draw'])      # Single random element from a sequence
'draw'
>>> deck = 'ace two three four'.split()
>>> shuffle(deck)                        # Shuffle a list
>>> deck
['four', 'two', 'ace', 'three']
>>> sample([10, 20, 30, 40, 50], k=4)    # Four samples without replacement
[40, 10, 50, 30]
								

Simulations:

>>> # Six roulette wheel spins (weighted sampling with replacement)
>>> choices(['red', 'black', 'green'], [18, 18, 2], k=6)
['red', 'green', 'black', 'black', 'red', 'black']
>>> # Deal 20 cards without replacement from a deck of 52 playing cards
>>> # and determine the proportion of cards with a ten-value
>>> # (a ten, jack, queen, or king).
>>> deck = collections.Counter(tens=16, low_cards=36)
>>> seen = sample(list(deck.elements()), k=20)
>>> seen.count('tens') / 20
0.15
>>> # Estimate the probability of getting 5 or more heads from 7 spins
>>> # of a biased coin that settles on heads 60% of the time.
>>> trial = lambda: choices('HT', cum_weights=(0.60, 1.00), k=7).count('H') >= 5
>>> sum(trial() for i in range(10000)) / 10000
0.4169
>>> # Probability of the median of 5 samples being in middle two quartiles
>>> trial = lambda : 2500 <= sorted(choices(range(10000), k=5))[2]  < 7500
>>> sum(trial() for i in range(10000)) / 10000
0.7958
								

Example of statistical bootstrapping using resampling with replacement to estimate a confidence interval for the mean of a sample of size five:

# http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htm
from statistics import mean
from random import choices
data = 1, 2, 4, 4, 10
means = sorted(mean(choices(data, k=5)) for i in range(20))
print(f'The sample mean of {mean(data):.1f} has a 90% confidence '
      f'interval from {means[1]:.1f} to {means[-2]:.1f}')
								

Example of a resampling permutation test to determine the statistical significance or p-value of an observed difference between the effects of a drug versus a placebo:

# Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson
from statistics import mean
from random import shuffle
drug = [54, 73, 53, 70, 73, 68, 52, 65, 65]
placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46]
observed_diff = mean(drug) - mean(placebo)
n = 10000
count = 0
combined = drug + placebo
for i in range(n):
    shuffle(combined)
    new_diff = mean(combined[:len(drug)]) - mean(combined[len(drug):])
    count += (new_diff >= observed_diff)
print(f'{n} label reshufflings produced only {count} instances with a difference')
print(f'at least as extreme as the observed difference of {observed_diff:.1f}.')
print(f'The one-sided p-value of {count / n:.4f} leads us to reject the null')
print(f'hypothesis that there is no difference between the drug and the placebo.')
								

Simulation of arrival times and service deliveries in a single server queue:

from random import expovariate, gauss
from statistics import mean, median, stdev
average_arrival_interval = 5.6
average_service_time = 5.0
stdev_service_time = 0.5
num_waiting = 0
arrivals = []
starts = []
arrival = service_end = 0.0
for i in range(20000):
    if arrival <= service_end:
        num_waiting += 1
        arrival += expovariate(1.0 / average_arrival_interval)
        arrivals.append(arrival)
    else:
        num_waiting -= 1
        service_start = service_end if num_waiting else arrival
        service_time = gauss(average_service_time, stdev_service_time)
        service_end = service_start + service_time
        starts.append(service_start)
waits = [start - arrival for arrival, start in zip(arrivals, starts)]
print(f'Mean wait: {mean(waits):.1f}. Stdev wait: {stdev(waits):.1f}.')
print(f'Median wait: {median(waits):.1f}.  Max wait: {max(waits):.1f}.')