随机抽样 (numpy.random)

简单的随机数据

rand(d0, d1, ..., dn)

随机值

>>> np.random.rand(3,2)

array([[ 0.14022471,  0.96360618],  #random

       [ 0.37601032,  0.25528411],  #random

       [ 0.49313049,  0.94909878]]) #random

randn(d0, d1, ..., dn)

返回一个样本，具有标准正态分布。

Notes

For random samples from N(\mu, \sigma^2), use:

sigma * np.random.randn(...) + mu

Examples

>>> np.random.randn()

2.1923875335537315 #random

Two-by-four array of samples from N(3, 6.25):

>>> 2.5 * np.random.randn(2, 4) + 3

array([[-4.49401501,  4.00950034, -1.81814867,  7.29718677],  #random

       [ 0.39924804,  4.68456316,  4.99394529,  4.84057254]]) #random

randint(low[, high, size])

返回随机的整数，位于半开区间 [low, high)。

>>> np.random.randint(2, size=10)

array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0])

>>> np.random.randint(1, size=10)

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

Generate a 2 x 4 array of ints between 0 and 4, inclusive:

>>> np.random.randint(5, size=(2, 4))

array([[4, 0, 2, 1],

       [3, 2, 2, 0]])

random_integers(low[, high, size])

返回随机的整数，位于闭区间 [low, high]。

Notes

To sample from N evenly spaced floating-point numbers between a and b, use:

a + (b - a) * (np.random.random_integers(N) - 1) / (N - 1.)

Examples

>>> np.random.random_integers(5)

>>> type(np.random.random_integers(5))

<type 'int'>

>>> np.random.random_integers(5, size=(3.,2.))

array([[5, 4],

       [3, 3],

       [4, 5]])

Choose five random numbers from the set of five evenly-spaced numbers between 0 and 2.5, inclusive (i.e., from the set {0, 5/8, 10/8, 15/8, 20/8}):

>>> 2.5 * (np.random.random_integers(5, size=(5,)) - 1) / 4.

array([ 0.625,  1.25 ,  0.625,  0.625,  2.5  ])

Roll two six sided dice 1000 times and sum the results:

>>> d1 = np.random.random_integers(1, 6, 1000)

>>> d2 = np.random.random_integers(1, 6, 1000)

>>> dsums = d1 + d2

Display results as a histogram:

>>> import matplotlib.pyplot as plt

>>> count, bins, ignored = plt.hist(dsums, 11, normed=True)

>>> plt.show()

random_sample([size])

返回随机的浮点数，在半开区间 [0.0, 1.0)。

To sample Unif[a, b), b > a multiply the output of random_sample by (b-a) and add a:

(b - a) * random_sample() + a

Examples

>>> np.random.random_sample()

0.47108547995356098

>>> type(np.random.random_sample())

<type 'float'>

>>> np.random.random_sample((5,))

array([ 0.30220482,  0.86820401,  0.1654503 ,  0.11659149,  0.54323428])

Three-by-two array of random numbers from [-5, 0):

>>> 5 * np.random.random_sample((3, 2)) - 5

array([[-3.99149989, -0.52338984],

       [-2.99091858, -0.79479508],

       [-1.23204345, -1.75224494]])

random([size])

返回随机的浮点数，在半开区间 [0.0, 1.0)。

（官网例子与random_sample完全一样）

ranf([size])

返回随机的浮点数，在半开区间 [0.0, 1.0)。

（官网例子与random_sample完全一样）

sample([size])

返回随机的浮点数，在半开区间 [0.0, 1.0)。

（官网例子与random_sample完全一样）

choice(a[, size, replace, p])

生成一个随机样本，从一个给定的一维数组

Examples

Generate a uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3)

array([0, 3, 4])

>>> #This is equivalent to np.random.randint(0,5,3)

Generate a non-uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0])

array([3, 3, 0])

Generate a uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False)

array([3,1,0])

>>> #This is equivalent to np.random.permutation(np.arange(5))[:3]

Generate a non-uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0])

array([2, 3, 0])

Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance:

>>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher']

>>> np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3])

array(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'],

      dtype='|S11')

bytes(length)

返回随机字节。

>>> np.random.bytes(10)

' eh\x85\x022SZ\xbf\xa4' #random

排列

shuffle(x)

现场修改序列，改变自身内容。（类似洗牌，打乱顺序）

>>> arr = np.arange(10)

>>> np.random.shuffle(arr)

>>> arr

[1 7 5 2 9 4 3 6 0 8]

This function only shuffles the array along the first index of a multi-dimensional array:

>>> arr = np.arange(9).reshape((3, 3))

>>> np.random.shuffle(arr)

>>> arr

array([[3, 4, 5],

       [6, 7, 8],

       [0, 1, 2]])

permutation(x)

返回一个随机排列

>>> np.random.permutation(10)

array([1, 7, 4, 3, 0, 9, 2, 5, 8, 6])

>>> np.random.permutation([1, 4, 9, 12, 15])

array([15,  1,  9,  4, 12])

>>> arr = np.arange(9).reshape((3, 3))

>>> np.random.permutation(arr)

array([[6, 7, 8],

       [0, 1, 2],

       [3, 4, 5]])

分布

beta(a, b[, size])

贝塔分布样本，在 [0, 1]内。

binomial(n, p[, size])

二项分布的样本。

chisquare(df[, size])

卡方分布样本。

dirichlet(alpha[, size])

狄利克雷分布样本。

exponential([scale, size])

指数分布

f(dfnum, dfden[, size])

F分布样本。

gamma(shape[, scale, size])

伽马分布

geometric(p[, size])

几何分布

gumbel([loc, scale, size])

耿贝尔分布。

hypergeometric(ngood, nbad, nsample[, size])

超几何分布样本。

laplace([loc, scale, size])

拉普拉斯或双指数分布样本

logistic([loc, scale, size])

Logistic分布样本

lognormal([mean, sigma, size])

对数正态分布

logseries(p[, size])

对数级数分布。

multinomial(n, pvals[, size])

多项分布

multivariate_normal(mean, cov[, size])

多元正态分布。

>>> mean = [0,0]

>>> cov = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis

>>> import matplotlib.pyplot as plt

>>> x, y = np.random.multivariate_normal(mean, cov, 5000).T

>>> plt.plot(x, y, 'x'); plt.axis('equal'); plt.show()

negative_binomial(n, p[, size])

负二项分布

noncentral_chisquare(df, nonc[, size])

非中心卡方分布

noncentral_f(dfnum, dfden, nonc[, size])

非中心F分布

normal([loc, scale, size])

正态(高斯)分布

Notes

The probability density for the Gaussian distribution is

p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }}

e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} },

where \mu is the mean and \sigma the standard deviation. The square of the standard deviation, \sigma^2, is called the variance.

The function has its peak at the mean, and its “spread” increases with the standard deviation (the function reaches 0.607 times its maximum at x + \sigma and x - \sigma [R217]).

Examples

Draw samples from the distribution:

>>> mu, sigma = 0, 0.1 # mean and standard deviation

>>> s = np.random.normal(mu, sigma, 1000)

Verify the mean and the variance:

>>> abs(mu - np.mean(s)) < 0.01

True

>>> abs(sigma - np.std(s, ddof=1)) < 0.01

True

Display the histogram of the samples, along with the probability density function:

>>> import matplotlib.pyplot as plt

>>> count, bins, ignored = plt.hist(s, 30, normed=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()

pareto(a[, size])

帕累托（Lomax）分布

poisson([lam, size])

泊松分布

power(a[, size])

Draws samples in [0, 1] from a power distribution with positive exponent a - 1.

rayleigh([scale, size])

Rayleigh 分布

standard_cauchy([size])

标准柯西分布

standard_exponential([size])

标准的指数分布

standard_gamma(shape[, size])

标准伽马分布

standard_normal([size])

标准正态分布 (mean=0, stdev=1).

standard_t(df[, size])

Standard Student’s t distribution with df degrees of freedom.

triangular(left, mode, right[, size])

三角形分布

uniform([low, high, size])

均匀分布

vonmises(mu, kappa[, size])

von Mises分布

wald(mean, scale[, size])

瓦尔德（逆高斯）分布

weibull(a[, size])

Weibull 分布

zipf(a[, size])

齐普夫分布

随机数生成器

RandomState

Container for the Mersenne Twister pseudo-random number generator.

seed([seed])

Seed the generator.

get_state()

Return a tuple representing the internal state of the generator.

set_state(state)

Set the internal state of the generator from a tuple.