random

2023-05-16 13:45| 来源: 网络整理| 查看: 265

random --- 生成伪随机数¶

源码： Lib/random.py

该模块实现了各种分布的伪随机数生成器。

对于整数，从范围中有统一的选择。对于序列，存在随机元素的统一选择、用于生成列表的随机排列的函数、以及用于随机抽样而无需替换的函数。

在实数轴上，有计算均匀、正态（高斯）、对数正态、负指数、伽马和贝塔分布的函数。为了生成角度分布，可以使用 von Mises 分布。

Almost all module functions depend on the basic function random(), which generates a random float uniformly in the half-open range 0.0 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]

模拟:

>>> # 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: ten, jack, queen, or king. >>> dealt = sample(['tens', 'low cards'], counts=[16, 36], k=20) >>> dealt.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. >>> def trial(): ... return choices('HT', cum_weights=(0.60, 1.00), k=7).count('H') >= 5 ... >>> sum(trial() for i in range(10_000)) / 10_000 0.4169 >>> # Probability of the median of 5 samples being in middle two quartiles >>> def trial(): ... return 2_500 > sum(trial() for i in range(10_000)) / 10_000 0.7958

statistical bootstrapping 的示例，使用重新采样和替换来估计一个样本的均值的置信区间:

# https://www.thoughtco.com/example-of-bootstrapping-3126155 from statistics import fmean as mean from random import choices data = [41, 50, 29, 37, 81, 30, 73, 63, 20, 35, 68, 22, 60, 31, 95] means = sorted(mean(choices(data, k=len(data))) for i in range(100)) print(f'The sample mean of {mean(data):.1f} has a 90% confidence ' f'interval from {means[5]:.1f} to {means[94]:.1f}')

使用重新采样排列测试来确定统计学显著性或者使用 p-值来观察药物与安慰剂的作用之间差异的示例:

# Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson from statistics import fmean as 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 = 10_000 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.')

多服务器队列的到达时间和服务交付模拟:

from heapq import heapify, heapreplace from random import expovariate, gauss from statistics import mean, quantiles average_arrival_interval = 5.6 average_service_time = 15.0 stdev_service_time = 3.5 num_servers = 3 waits = [] arrival_time = 0.0 servers = [0.0] * num_servers # time when each server becomes available heapify(servers) for i in range(1_000_000): arrival_time += expovariate(1.0 / average_arrival_interval) next_server_available = servers[0] wait = max(0.0, next_server_available - arrival_time) waits.append(wait) service_duration = max(0.0, gauss(average_service_time, stdev_service_time)) service_completed = arrival_time + wait + service_duration heapreplace(servers, service_completed) print(f'Mean wait: {mean(waits):.1f} Max wait: {max(waits):.1f}') print('Quartiles:', [round(q, 1) for q in quantiles(waits)])

参见

Statistics for Hackers Jake Vanderplas 撰写的视频教程，使用一些基本概念进行统计分析，包括模拟、抽样、洗牌和交叉验证。

Economics Simulation a simulation of a marketplace by Peter Norvig that shows effective use of many of the tools and distributions provided by this module (gauss, uniform, sample, betavariate, choice, triangular, and randrange).

A Concrete Introduction to Probability (using Python) a tutorial by Peter Norvig covering the basics of probability theory, how to write simulations, and how to perform data analysis using Python.

例程¶

These recipes show how to efficiently make random selections from the combinatoric iterators in the itertools module:

def random_product(*args, repeat=1): "Random selection from itertools.product(*args, **kwds)" pools = [tuple(pool) for pool in args] * repeat return tuple(map(random.choice, pools)) def random_permutation(iterable, r=None): "Random selection from itertools.permutations(iterable, r)" pool = tuple(iterable) r = len(pool) if r is None else r return tuple(random.sample(pool, r)) def random_combination(iterable, r): "Random selection from itertools.combinations(iterable, r)" pool = tuple(iterable) n = len(pool) indices = sorted(random.sample(range(n), r)) return tuple(pool[i] for i in indices) def random_combination_with_replacement(iterable, r): "Choose r elements with replacement. Order the result to match the iterable." # Result will be in set(itertools.combinations_with_replacement(iterable, r)). pool = tuple(iterable) n = len(pool) indices = sorted(random.choices(range(n), k=r)) return tuple(pool[i] for i in indices)

默认的 random() 返回在 0.0 ≤ x < 1.0 范围内 2⁻⁵³ 的倍数。所有这些数值间隔相等并能精确表示为 Python 浮点数。但是在此间隔上有许多其他可表示浮点数是不可能的选择。例如，0.05954861408025609 就不是 2⁻⁵³ 的整数倍。

以下规范程序采取了一种不同的方式。在间隔上的所有浮点数都是可能的选择。它们的尾数取值来自 2⁵² ≤ 尾数 < 2⁵³ 范围内整数的均匀分布。指数取值则来自几何分布，其中小于 -53 的指数的出现频率为下一个较大指数的一半。

from random import Random from math import ldexp class FullRandom(Random): def random(self): mantissa = 0x10_0000_0000_0000 | self.getrandbits(52) exponent = -53 x = 0 while not x: x = self.getrandbits(32) exponent += x.bit_length() - 32 return ldexp(mantissa, exponent)

该类中所有的实值分布都将使用新的方法:

>>> fr = FullRandom() >>> fr.random() 0.05954861408025609 >>> fr.expovariate(0.25) 8.87925541791544

该规范程序在概念上等效于在 0.0 ≤ x < 1.0 范围内对所有 2⁻¹⁰⁷⁴ 的倍数进行选择的算法。所有这样的数字间隔都相等，但大多必须向下舍入为最接近的 Python 浮点数表示形式。（2⁻¹⁰⁷⁴ 这个数值是等于 math.ulp(0.0) 的未经正规化的最小正浮点数。）

参见

生成伪随机浮点数值为 Allen B. Downey 所撰写的描述如何生成相比通过 random() 正常生成的数值更细粒度浮点数的论文。

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