随机数是NumPy库中存在的模块。该模块包含用于生成随机数的功能。该模块包含一些简单的随机数据生成方法,一些排列和分布函数以及随机生成器函数。
随机模块中的所有功能如下:
简单随机数据具有以下功能:
1)p.random.rand(d0,d1,...,dn)
随机模块的此功能用于生成给定形状的随机数或值。
示例:
import numpy as np a=np.random.rand(5,2) a
输出:
array([[0.74710182, 0.13306399], [0.01463718, 0.47618842], [0.98980426, 0.48390004], [0.58661785, 0.62895758], [0.38432729, 0.90384119]])
2)np.random.randn(d0,d1,...,dn)
随机模块的此功能从"标准正态(standard normal)"分布返回样本。
示例:
import numpy as np a=np.random.randn(2,2) a
输出:
array([[ 1.43327469, -0.02019121], [ 1.54626422, 1.05831067]]) b=np.random.randn() b -0.3080190768904835
3)np.random.randint(low [high,size,dtype])
random模块的此功能用于生成从inclusive(low)到exclusive(high)的随机整数。
示例:
import numpy as np a=np.random.randint(3, size=10) a
输出:
array([1, 1, 1, 2, 0, 0, 0, 0, 0, 0])
4)np.random.random_integers(low [high,size])
随机模块的此功能用于生成介于低和高之间的np.int类型的随机整数。
示例:
import numpy as np a=np.random.random_integers(3) a b=type(np.random.random_integers(3)) b c=np.random.random_integers(5, size=(3,2)) c
输出:
2 <type 'numpy.int32'> array([[1, 1], [2, 5], [1, 3]])
5)np.random.random_sample([size])
随机模块的此功能用于在半开间隔[0.0,1.0)中生成随机浮点数。
示例:
import numpy as np a=np.random.random_sample() a b=type(np.random.random_sample()) b c=np.random.random_sample((5,)) c
输出:
0.09250360565571492 <type 'float'> array([0.34665418, 0.47027209, 0.75944969, 0.37991244, 0.14159746])
6)np.random.random([size])
随机模块的此功能用于在半开间隔[0.0,1.0)中生成随机浮点数。
示例:
import numpy as np a=np.random.random() a b=type(np.random.random()) b c=np.random.random((5,)) c
输出:
0.008786953974334155 <type 'float'> array([0.05530122, 0.59133394, 0.17258794, 0.6912388 , 0.33412534])
7)np.random.ranf([size])
随机模块的此功能用于在半开间隔[0.0,1.0)中生成随机浮点数。
示例:
import numpy as np a=np.random.ranf() a b=type(np.random.ranf()) b c=np.random.ranf((5,)) c
输出:
0.2907792098474542 <type 'float'> array([0.34084881, 0.07268237, 0.38161256, 0.46494681, 0.88071377])
8)np.random.sample([size])
随机模块的此功能用于在半开间隔[0.0,1.0)中生成随机浮点数。
示例:
import numpy as np a=np.random.sample() a b=type(np.random.sample()) b c=np.random.sample((5,)) c
输出:
0.012298209913766511 <type 'float'> array([0.71878544, 0.11486169, 0.38189074, 0.14303308, 0.07217287])
9)np.random.choice(a [size,replace,p])
随机模块的此功能用于从给定的一维数组生成随机样本。
示例:
import numpy as np a=np.random.choice(5,3) a b=np.random.choice(5,3, p=[0.2, 0.1, 0.4, 0.2, 0.1]) b
输出:
array([0, 3, 4]) array([2, 2, 2], dtype=int64)
10)np.random.bytes(length)
随机模块的此功能用于生成随机字节。
示例:
import numpy as np a=np.random.bytes(7) a
输出:
'nQ\x08\x83\xf9\xde\x8a'
有以下排列功能:
1)np.random.shuffle()
此功能用于通过改组其内容就地修改序列。
示例:
import numpy as np a=np.arange(12) a np.random.shuffle(a) a
输出:
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) array([10, 3, 2, 4, 5, 8, 0, 9, 1, 11, 7, 6])
2)np.random.permutation()
此函数随机置换序列或返回置换范围。
示例:
import numpy as np a=np.random.permutation(12) a
输出:
array([ 8, 7, 3, 11, 6, 0, 9, 10, 2, 5, 4, 1])
有以下排列功能:
1)Beta(a,b [,size])
此功能用于从Beta分布中抽取样本。
示例:
def setup(self): self.dist = dist.beta self.cargs = [] self.ckwd = dict(alpha=2, beta=3) self.np_rand_fxn = numpy.random.beta self.np_args = [2, 3] self.np_kwds = dict()
2)binomial(n,p [,size])
此函数用于从二项分布中抽取样本。
示例:
import numpy as np n, p = 10, .6 s1= np.random.binomial(n, p, 10) s1
输出:
array([6, 7, 7, 9, 3, 7, 8, 6, 6, 4])
3)chisquare(df [,size])
此函数用于从二项分布中抽取样本。
示例:
import numpy as np np.random.chisquare(2,4) sum(np.random.binomial(9, 0.1, 20000) == 0)/20000.
输出:
array([6, 7, 7, 9, 3, 7, 8, 6, 6, 4])
4)dirichlet(alpha [,size])
此函数用于从Dirichlet分布中抽取样本。
示例:
Import numpy as np import matplotlib.pyplot as plt s1 = np.random.dirichlet((10, 5, 3), 20).transpose() plt.barh(range(20), s1[0]) plt.barh(range(20), s1[1], left=s1[0], color='g') plt.barh(range(20), s1[2], left=s1[0]+s1[1], color='r') plt.title("Lengths of Strings") plt.show()
输出:
5)exponential([scale,size])
此函数用于从指数分布中提取样本。
示例:
def __init__(self, sourceid, targetid): self.__type = 'Transaction' self.id = uuid4() self.source = sourceid self.target = targetid self.date = self._datetime.date(start=2015, end=2019) self.time = self._datetime.time() if random() < 0.05: self.amount = self._numbers.between(100000, 1000000) self.amount = npr.exponential(10) if random() < 0.15: self.currency = self._business.currency_iso_code() else: self.currency = None
6)f(dfnum,dfden [size])
此函数用于从F分布中抽取样本。
示例:
import numpy as np dfno= 1. dfden = 48. s1 = np.random.f(dfno, dfden, 10) np.sort(s1)
输出:
array([0.00264041, 0.04725478, 0.07140803, 0.19526217, 0.23979 , 0.24023478, 0.63141254, 0.95316446, 1.40281789, 1.68327507])
7)gamma(shape[,scale,size])
此函数用于从Gamma分布中提取样本
示例:
import numpy as np shape, scale = 2., 2. s1 = np.random.gamma(shape, scale, 1000) import matplotlib.pyplot as plt import scipy.special as spss count, bins, ignored = plt.hist(s1, 50, density=True) a = bins**(shape-1)*(np.exp(-bins/scale) / (spss.gamma(shape)*scale**shape)) plt.plot(bins, a, linewidth=2, color='r') plt.show()
8)geometric(p [,size])
此功能用于从几何分布中提取样本。
示例:
import numpy as np a = np.random.geometric(p=0.35, size=10000) (a == 1).sum()/1000
输出:
3.
9)gumbel([loc,scale,size])
此功能用于从Gumbel分布中抽取样本。
示例:
import numpy as np lov, scale = 0, 0.2 s1 = np.random.gumbel(loc, scale, 1000) import matplotlib.pyplot as plt count, bins, ignored = plt.hist(s1, 30, density=True) plt.plot(bins, (1/beta)*np.exp(-(bins - loc)/beta)* np.exp( -np.exp( -(bins - loc) /beta) ),linewidth=2, color='r') plt.show()
输出:
10)hypergeometric(ngood,nba,nsample[,size])
此功能用于从超几何分布中提取样本。
示例:
import numpy as np good, bad, samp = 100, 2, 10 s1 = np.random.hypergeometric(good, bad, samp, 1000) plt.hist(s1) plt.show()
输出:
(array([ 13., 0., 0., 0., 0., 163., 0., 0., 0., 824.]), array([ 8. , 8.2, 8.4, 8.6, 8.8, 9. , 9.2, 9.4, 9.6, 9.8, 10. ]), <a list of 10 Patch objects>)
11)laplace([loc,scale,size])
此功能用于从Laplace或具有指定位置和比例的双指数分布中抽取样本。
示例:
import numpy as np location, scale = 0., 2. s = np.random.laplace(location, scale, 10) s
输出:
array([-2.77127948, -1.46401453, -0.03723516, -1.61223942, 2.29590691, 1.74297722, 1.49438411, 0.30325513, -0.15948891, -4.99669747])
12)logistic([loc,scale,size])
此功能用于从逻辑分布中抽取样本。
示例:
import numpy as np import matplotlib.pyplot as plt location, scale = 10, 1 s1 = np.random.logistic(location, scale, 10000) count, bins, ignored = plt.hist(s1, bins=50) count bins ignored plt.show()
输出:
array([1.000e+00, 1.000e+00, 1.000e+00, 0.000e+00, 1.000e+00, 1.000e+00, 1.000e+00, 5.000e+00, 7.000e+00, 1.100e+01, 1.800e+01, 3.500e+01, 5.300e+01, 6.700e+01, 1.150e+02, 1.780e+02, 2.300e+02, 3.680e+02, 4.910e+02, 6.400e+02, 8.250e+02, 9.100e+02, 9.750e+02, 1.039e+03, 9.280e+02, 8.040e+02, 6.530e+02, 5.240e+02, 3.380e+02, 2.470e+02, 1.650e+02, 1.150e+02, 8.500e+01, 6.400e+01, 3.300e+01, 1.600e+01, 2.400e+01, 1.400e+01, 4.000e+00, 5.000e+00, 2.000e+00, 2.000e+00, 1.000e+00, 1.000e+00, 0.000e+00, 1.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 1.000e+00]) array([ 0.50643911, 0.91891814, 1.33139717, 1.7438762 , 2.15635523, 2.56883427, 2.9813133 , 3.39379233, 3.80627136, 4.2187504 , 4.63122943, 5.04370846, 5.45618749, 5.86866652, 6.28114556, 6.69362459, 7.10610362, 7.51858265, 7.93106169, 8.34354072, 8.75601975, 9.16849878, 9.58097781, 9.99345685, 10.40593588, 10.81841491, 11.23089394, 11.64337298, 12.05585201, 12.46833104, 12.88081007, 13.2932891 , 13.70576814, 14.11824717, 14.5307262 , 14.94320523, 15.35568427, 15.7681633 , 16.18064233, 16.59312136, 17.00560039, 17.41807943, 17.83055846, 18.24303749, 18.65551652, 19.06799556, 19.48047459, 19.89295362, 20.30543265, 20.71791168, 21.13039072]) <a list of 50 Patch objects>
13)lognormal([mean,sigma,size])
此函数用于从对数正态分布中提取样本。
示例:
import numpy as np mu, sigma = 2., 1. s1 = np.random.lognormal(mu, sigma, 1000) import matplotlib.pyplot as plt count, bins, ignored = plt.hist(s1, 100, density=True, align='mid') a = np.linspace(min(bins), max(bins), 10000) pdf = (np.exp(-(np.log(a) - mu)**2/(2 * sigma**2))/ (a * sigma * np.sqrt(2 * np.pi))) plt.plot(a, pdf, linewidth=2, color='r') plt.axis('tight') plt.show()
输出:
14)logseries(p [size])
此函数用于从对数分布中提取样本。
示例:
import numpy as np x = .6 s1 = np.random.logseries(x, 10000) count, bins, ignored = plt.hist(s1) def logseries(k, p): return -p**k/(k*log(1-p)) plt.plot(bins, logseries(bins, x)*count.max()/logseries(bins, a).max(), 'r') plt.show()
输出:
15)multinomial(n,pvals [,size])
此函数用于从多项分布中提取样本。
示例:
import numpy as np np.random.multinomial(20, [1/6.]*6, size=1)
输出:
array([[4, 2, 5, 5, 3, 1]])
16)multivariate_normal(mean,cov [,size,...)
此函数用于从多元正态分布中提取样本。
示例:
import numpy as np mean = (1, 2) coveriance = [[1, 0], [0, 100]] import matplotlib.pyplot as plt a, b = np.random.multivariate_normal(mean, coveriance, 5000).T plt.plot(a, b, 'x') plt.axis('equal'023 030 ) plt.show()
输出:
17)negative_binomial(n,p [size])
此函数用于从负二项分布中抽取样本。
示例:
import numpy as np s1 = np.random.negative_binomial(1, 0.1, 100000) for i in range(1, 11): probability = sum(s1<i)/100000. print i, "wells drilled, probability of one success =", probability
输出:
1 wells drilled, probability of one success = 0 2 wells drilled, probability of one success = 0 3 wells drilled, probability of one success = 0 4 wells drilled, probability of one success = 0 5 wells drilled, probability of one success = 0 6 wells drilled, probability of one success = 0 7 wells drilled, probability of one success = 0 8 wells drilled, probability of one success = 0 9 wells drilled, probability of one success = 0 10 wells drilled, probability of one success = 0
18)noncentral_chisquare(df,nonc [size])
此函数用于从非中心卡方分布中抽取样本。
示例:
import numpy as np import matplotlib.pyplot as plt val = plt.hist(np.random.noncentral_chisquare(3, 25, 100000), bins=200, normed=True) plt.show()
输出:
19)normal([loc,scale,size])
此功能用于从正态分布中提取样本。
示例:
import numpy as np import matplotlib.pyplot as plt mu, sigma = 0, 0.2 # mean and standard deviation s1 = np.random.normal(mu, sigma, 1000) abs(mu - np.mean(s1)) < 0.01 abs(sigma - np.std(s1, ddof=1)) < 0.01 count, bins, ignored = plt.hist(s1, 30, density=True) plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *np.exp( - (bins - mu)**2/(2 * sigma**2) ), linewidth=2, color='r') plt.show()
输出:
20)pareto(a [,size])
此功能用于从Lomax或Pareto II中提取具有指定形状的样本。
示例:
import numpy as np import matplotlib.pyplot as plt b, m1 = 3., 2. # shape and mode s1 = (np.random.pareto(b, 1000) + 1) * m1 count, bins, _ = plt.hist(s1, 100, density=True) fit = b*m**b/bins**(b+1) plt.plot(bins, max(count)*fit/max(fit), linewidth=2, color='r') plt.show()
输出:
21)power(a [,size])
此函数用于从指数为a-1的幂分布中提取[0,1]中的样本。
示例:
import numpy as np x = 5. # shape samples = 1000 s1 = np.random.power(x, samples) import matplotlib.pyplot as plt count, bins, ignored = plt.hist(s1, bins=30) a = np.linspace(0, 1, 100) b = x*a**(x-1.) density_b = samples*np.diff(bins)[0]*b plt.plot(a, density_b) plt.show()
输出:
22)rayleigh([scale,size])
此功能用于从Rayleigh分布中提取样本。
示例:
val = hist(np.random.rayleigh(3, 100000), bins=200, density=True) meanval = 1 modeval = np.sqrt(2/np.pi) * meanval s1 = np.random.rayleigh(modeval, 1000000) 100.*sum(s1>3)/1000000.
输出:
0.087300000000000003
23)standard_cauchy([size])
此功能用于从模式= 0的标准柯西分布中提取样本。
示例:
import numpy as np import matplotlib.pyplot as plt s1 = np.random.standard_cauchy(1000000) s1 = s1[(s1>-25) & (s1
输出:
24)standard_exponential([size])
此函数用于从标准指数分布中抽取样本。
示例:
import numpy as np n = np.random.standard_exponential((2, 7000))
输出:
array([[0.53857931, 0.181262 , 0.20478701, ..., 3.66232881, 1.83882709, 1.77963295], [0.65163973, 1.40001955, 0.7525986 , ..., 0.76516523, 0.8400617 , 0.88551011]])
25)standard_gamma([size])
此功能用于从标准Gamma分布中提取样本。
示例:
import numpy as np shape, scale = 2., 1. s1 = np.random.standard_gamma(shape, 1000000) import matplotlib.pyplot as plt import scipy.special as sps count1, bins1, ignored1 = plt.hist(s, 50, density=True) y = bins1**(shape-1) * ((np.exp(-bins1/scale))/ (sps.gamma(shape) * scale**shape)) plt.plot(bins1, y, linewidth=2, color='r') plt.show()
输出:
26)standard_normal([size])
此功能用于从标准正态分布中抽取样本。
示例:
import numpy as np import matplotlib.pyplot as plt s1= np.random.standard_normal(8000) s1 q = np.random.standard_normal(size=(3, 4, 2)) q
输出:
array([-3.14907597, 0.95366265, -1.20100026, ..., 3.47180222, 0.9608679 , 0.0774319 ]) array([[[ 1.55635461, -1.29541713], [-1.50534663, -0.02829194], [ 1.03949348, -0.26128132], [ 1.51921798, 0.82136178]], [[-0.4011052 , -0.52458858], [-1.31803814, 0.37415379], [-0.67077365, 0.97447018], [-0.20212115, 0.67840888]], [[ 1.86183474, 0.19946562], [-0.07376021, 0.84599701], [-0.84341386, 0.32081667], [-3.32016062, -1.19029818]]])
27)standard_t(df [size])
此功能用于以df自由度从标准Student分布中抽取样本。
示例:
intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515,8230,8770]) s1 = np.random.standard_t(10, size=100000) np.mean(intake) intake.std(ddof=1) t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake))) h = plt.hist(s1, bins=100, density=True) np.sum(s1<t)/float(len(s1)) plt.show()
输出:
6677.5 1174.1101831694598 0.00864
28)triangular(left,mode,right[,size])
此函数用于从间隔内的三角形分布中抽取样本。
示例:
import numpy as np import matplotlib.pyplot as plt h = plt.hist(np.random.triangular(-4, 0, 8, 1000000), bins=300,density=True) plt.show()
输出:
29)uniform([low,heigh,size])
此功能用于从均匀分布中抽取样本。
示例:
import numpy as np import matplotlib.pyplot as plt s1 = np.random.uniform(-1,0,1000) np.all(s1 >= -1) np.all(s1
输出:
30)vonmises(m1,m2 [size])
此函数用于从von Mises分布中抽取样本。
示例:
import numpy as np import matplotlib.pyplot as plt m1, m2 = 0.0, 4.0 s1 = np.random.vonmises(m1, m2, 1000) from scipy.special import i0 plt.hist(s1, 50, density=True) x = np.linspace(-np.pi, np.pi, num=51) y = np.exp(m2*np.cos(x-m1))/(2*np.pi*i0(m2)) plt.plot(x, y, linewidth=2, color='r') plt.show()
输出:
31)wald(mean,scale[,size])
此函数用于从Wald或高斯逆分布中抽取样本。
示例:
import numpy as np import matplotlib.pyplot as plt h = plt.hist(np.random.wald(3, 3, 100000), bins=250, density=True) plt.show()
输出:
32)weibull(a [size])
此函数用于从Weibull分布中抽取样本。
示例:
import numpy as np import matplotlib.pyplot as plt from scipy import special x=2.0 s=np.random.weibull(x, 1000) a = np.arange(1, 100.)/50. def weib(x, n, a): return (a/n)*(x/n)**np.exp(-(x/n)**a) count, bins, ignored = plt.hist(np.random.weibull(5.,1000)) a= np.arange(1,100.)/50. scale = count.max()/weib(x, 1., 5.).max() scale = count.max()/weib(a, 1., 5.).max() plt.plot(x, weib(x, 1., 5.)*scale) plt.show()
输出:
33)zipf(a [size])
此函数用于从Zipf分布中抽取样本。
示例:
import numpy as np import matplotlib.pyplot as plt from scipy import special x=2.0 s=np.random.zipf(x, 1000) count, bins, ignored = plt.hist(s[s<50], 50, density=True) a = np.arange(1., 50.) b= a**(-x)/special.zetac(x) plt.plot(a, b/max(b), linewidth=2, color='r') plt.show()
输出:
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PPT设计进阶 · 从基础操作到高级创意 -〔李金宝(Bobbie)〕