【学习笔记】100道NumPy练习题（61-80题）

100道NumPy练习题（61-80题）

七、随机数与统计

61.生成10个0-1之间的随机数

import numpy as np
a = np.random.rand(10)
print(a)

[0.28613361 0.37749818 0.46263267 0.26107433 0.28591036 0.04154898
 0.76444883 0.93588597 0.07605215 0.58587586]

62.生成10个符合正态分布的随机数

import numpy as np
a = np.random.randn(10)
print(a)

[ 0.49453002 -0.11759588 -0.64466301  0.59821977  0.48681156  0.22169839
  1.34682773 -0.18080486 -1.41018212  0.53211155]

63.生成10个整数随机数（范围1-100）

import numpy as np
a = np.random.randint(1,101,10)
print(a)

[64 54 96 77 88 93 86 56 82 90]

64.随机打乱一个数组

import numpy as np
a = np.array([1,2,3,4,5,6,7,8,9,10])
np.random.shuffle(a)
print(a)

[ 9  8  3 10  2  6  1  4  7  5]

65.从数组中进行随机抽样

import numpy as np
a = np.array([1,2,3,4,5,6,7,8,9,10])
b = np.random.choice(a,size = 3,replace = False)
print(b)

[6 5 1]

66.计算数组的百分位数

import numpy as np
a = np.array([1,2,3,4,5,6,7,8,9,10])
print(np.percentile(a,[25,50,75]))

[3.25 5.5  7.75]

67.计算数组的协方差矩阵

import numpy as np
a = np.array([[1,2,3],[4,5,6],[7,8,9]])
print(np.cov(a))

[[1. 1. 1.]
 [1. 1. 1.]
 [1. 1. 1.]]

68.计算数组的相关系数矩阵

import numpy as np
a = np.array([[1,2,3],[4,5,6],[7,8,9]])
print(np.corrcoef(a))

[[1. 1. 1.]
 [1. 1. 1.]
 [1. 1. 1.]]

69.计算数组的直方图

import numpy as np
data = np.random.normal(0,1,1000)
x,y = np.histogram(data,bins = 10)
print(x)
print(y)

[ 15  50 124 233 254 205 100  16   2   1]
[-3.00513691 -2.30296978 -1.60080264 -0.89863551 -0.19646838  0.50569876
  1.20786589  1.91003303  2.61220016  3.31436729  4.01653443]

70.计算数组的累积分布函数

import numpy as np
data = np.random.normal(0,1,100)
so = np.sort(data)
df = np.arange(1,len(so)+1) / len(so)
print(df)

[0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1  0.11 0.12 0.13 0.14
 0.15 0.16 0.17 0.18 0.19 0.2  0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28
 0.29 0.3  0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4  0.41 0.42
 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5  0.51 0.52 0.53 0.54 0.55 0.56
 0.57 0.58 0.59 0.6  0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7
 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8  0.81 0.82 0.83 0.84
 0.85 0.86 0.87 0.88 0.89 0.9  0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
 0.99 1.  ]

八、线性代数运算

71.计算矩阵的行列式

import numpy as np
a = np.array([[1,2],[3,4]])
data = np.linalg.det(a)
print(data)

-2.0000000000000004

72.计算矩阵的逆

import numpy as np
a = np.array([[1,2],[3,4]])
data = np.linalg.inv(a)
print(data)

[[-2.   1. ]
 [ 1.5 -0.5]]

73.计算矩阵的特征值和特征向量

import numpy as np
a = np.array([[1,2],[3,4]])
b = np.linalg.eig(a)
print(b)

EigResult(eigenvalues=array([-0.37228132,  5.37228132]), eigenvectors=array([[-0.82456484, -0.41597356],
       [ 0.56576746, -0.90937671]]))

74.解线性方程组

import numpy as np
a = np.array([[1,2],[3,4]])
b = np.array([5,6])
x = np.linalg.solve(a,b)
print(x)

[-4.   4.5]

75.计算矩阵的奇异值分解

import numpy as np
a = np.array([[1,2],[3,4]])
u,s,v = np.linalg.svd(a)
print(u)
print(s)
print(v)

[[-0.40455358 -0.9145143 ]
 [-0.9145143   0.40455358]]
[5.4649857  0.36596619]
[[-0.57604844 -0.81741556]
 [ 0.81741556 -0.57604844]]

76.计算矩阵的QR分解

import numpy as np
a = np.array([[1,2],[3,4]])
q,r = np.linalg.qr(a)
print(q)
print(r)

[[-0.31622777 -0.9486833 ]
 [-0.9486833   0.31622777]]
[[-3.16227766 -4.42718872]
 [ 0.         -0.63245553]]

77.计算矩阵的Cholesky分解

import numpy as np
a = np.array([[2,-1],[-1,2]])
k = np.linalg.cholesky(a)
print(k)

[[ 1.41421356  0.        ]
 [-0.70710678  1.22474487]]

78.计算矩阵的迹

import numpy as np
a = np.array([[1,2],[3,4]])
print(np.trace(a))

5

79.计算矩阵的范数

import numpy as np
a = np.array([[1,2],[3,4]])
b = np.linalg.norm(a)
print(b)

5.477225575051661

80.计算矩阵的秩

import numpy as np
a = np.array([[1,2],[3,4]])
b = np.linalg.matrix_rank(a)
print(b)

2

特别说明，上述题目已在jupyter notebook上运行过了。