机器学习利器之Numpy

PS：机器学习相关代码：https://nbviewer.jupyter.org/github/coderzc/machine_learning/tree/master/jupyter

GitHub源码：https://github.com/coderzc/machine_learning

等有时间整理一下，发出来

Numpy 创建N维数组

import numpy as np

''' 创建10行10列的数值为浮点0的矩阵 '''
>>> print("np.zeros\n", np.zeros([10, 10]))
np.zeros
 [[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]

''' 创建10行10列的数值为浮点1的矩阵 '''
>>> print("np.ones\n", np.ones([10, 10]))
np.ones
 [[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]


''' 创建10行10列的数值为浮点1的对角矩阵 '''
>>> print("np.eye\n", np.eye(10, 10))
np.eye
 [[1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]]

''' 从数值范围创建数组 开始，结束，步长，输出元素类型 '''
>>> print("np.arange\n", np.arange(0, 100, 2, float))
np.arange
 [ 0.  2.  4.  6.  8. 10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32. 34.
 36. 38. 40. 42. 44. 46. 48. 50. 52. 54. 56. 58. 60. 62. 64. 66. 68. 70.
 72. 74. 76. 78. 80. 82. 84. 86. 88. 90. 92. 94. 96. 98.]

'''生产随机数组 5行5列 范围0～1'''
>>> np.random.rand(5, 5)
array([[0.79909192, 0.40687012, 0.05833267, 0.90631693, 0.85774438],
       [0.65685319, 0.99620959, 0.64195711, 0.28694344, 0.54805126],
       [0.87347445, 0.20443748, 0.45883044, 0.90017425, 0.17487183],
       [0.4833086 , 0.59498315, 0.75053456, 0.93725983, 0.79870607],
       [0.8908418 , 0.49860926, 0.44097606, 0.53744394, 0.21089092]])


''' 生成在半开半闭区间 [low,high)上离散均匀分布的整数值;若high=None，则取值区间变为[0,low) ; size维度 '''
>>> np.random.randint(4,10,size=(5, 5))
array([[6, 6, 6, 7, 9],
       [4, 8, 6, 7, 7],
       [6, 8, 6, 5, 7],
       [7, 8, 8, 4, 5],
       [7, 6, 5, 5, 7]])


''' 给定均值/标准差/维度的正态分布 '''
>>> np.random.normal(1.75, 0.1, (3, 4))
array([[1.83246388, 1.73186179, 1.78198763, 1.76844117],
       [1.69089184, 1.69620751, 1.78018062, 1.68086896],
       [1.86462936, 1.61972878, 1.95645574, 1.66104741]])


''' 将列表转换为np数组 '''
>>> array = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
>>> np_array = np.array(array, dtype=float)  # copy,新数组
>>> print("np.array:\n", np_array)
np.array:
 [[ 1.  2.  3.  4.]
 [ 5.  6.  7.  8.]
 [ 9. 10. 11. 12.]]

>>> np_array2 = np.asarray(array, dtype=float)  # view,会改变原数组
>>> print("np.asarray:\n", np_array2)
np.asarray:
 [[ 1.  2.  3.  4.]
 [ 5.  6.  7.  8.]
 [ 9. 10. 11. 12.]]

查看数组属性

# 数组元素个数
>>> print("数组元素个数 size:", np_array.size)
数组元素个数 size: 12
# 数组形状
>>> print("数组形状 shape:", np_array.shape)
数组形状 shape: (3, 4)
# 数组维度
>>> print("数组维度 ndim:", np_array.ndim)
数组维度 ndim: 2
# 数组元素类型
>>> print("数组元素类型 dtype:", np_array.dtype)
数组元素类型 dtype: float64
# 数组中每个元素的字节大小
>>> print("数组元素类型 itemsize:", np_array.itemsize)
数组元素类型 itemsize: 8

shape操作

>>> array = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
>>> n1 = np.asarray(array)

# 改变数组的格式
>>> n2 = n1.reshape(6, 2)
>>> print(n1)
[[ 1  2  3  4]
 [ 5  6  7  8]
 [ 9 10 11 12]]
>>> print(n2)
[[ 1  2]
 [ 3  4]
 [ 5  6]
 [ 7  8]
 [ 9 10]
 [11 12]]

# 将多维降到1维展开
>>> print("flatten():", n2.flatten())  # copy,新数组
flatten(): [ 1  2  3  4  5  6  7  8  9 10 11 12]
>>> print("ravel():", n2.ravel())  # view，会改变原数组,却不会改变shape
ravel(): [ 1  2  3  4  5  6  7  8  9 10 11 12]

# 转置
>>> n3 = np.arange(12)
>>> n3 = n3.reshape(3, 4)
>>> print("n3:", n3)
n3: [[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]]

>>> print("n3.T:", n3.T)
n3.T: [[ 0  4  8]
 [ 1  5  9]
 [ 2  6 10]
 [ 3  7 11]]

# reshape一些特殊值
>>> n4 = np.arange(10, 130, 10)
>>> print("n4:", n4.reshape(4, 3))
n4: [[ 10  20  30]
 [ 40  50  60]
 [ 70  80  90]
 [100 110 120]]

#   -1 一维展开 与 ravel()作用相似
>>> print(n4.reshape(-1))
[ 10  20  30  40  50  60  70  80  90 100 110 120]

#   (-1,1) n行，1列
>>> print(n4.reshape(-1, 1))
[[ 10]
 [ 20]
 [ 30]
 [ 40]
 [ 50]
 [ 60]
 [ 70]
 [ 80]
 [ 90]
 [100]
 [110]
 [120]]

#   (1,-1) 1行，n列但任然是二维矩阵
>>> print(n4.reshape(1, -1))
[[ 10  20  30  40  50  60  70  80  90 100 110 120]]

数组索引和迭代

>>> print('\n\n')
>>> n5 = np.arange(30)
>>> print('n5:', n5)
n5: [ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
 24 25 26 27 28 29]

# 获取第一个元素
>>> print(n5[0])
0

# 获取倒数第一个元素
>>> print(n5[-1])
29

# 取前十个数
>>> print(n5[:10])
[0 1 2 3 4 5 6 7 8 9]

# 取后十个数
>>> print(n5[-10:])
[20 21 22 23 24 25 26 27 28 29]

# 取前11-20个数，左闭右开
>>> print(n5[10:20])
[10 11 12 13 14 15 16 17 18 19]

# 前十个数中，每2个数取一个
>>> print(n5[:10:2])
[0 2 4 6 8]

# 第6-15个数中，每3个数取一个
>>> print(n5[5:15:3])
[ 5  8 11 14]

# 所有的数中，每10个数取一个
>>> print(n5[::10])
[ 0 10 20]

# 什么都不写，可以原样复制一个数组
>>> print(n5[:])
[ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
 24 25 26 27 28 29]


############### 多维数组索引与切片 ###############
>>> n6 = n5.reshape(5, 6)
>>> print('n6:', n6)
n6: [[ 0  1  2  3  4  5]
 [ 6  7  8  9 10 11]
 [12 13 14 15 16 17]
 [18 19 20 21 22 23]
 [24 25 26 27 28 29]]

#   索引第二行第三列的元素
>>> print('n6[1, 2]:', n6[1, 2])
n6[1, 2]: 8

#   在第一维取前两行，第二维每+2取一个元素
>>> print('n6[:2, ::2]:\n', n6[:2, ::2])
n6[:2, ::2]:
 [[ 0  2  4]
 [ 6  8 10]]

# 取第一列
>>> print('n6[:, 0]]:\n', n6[:, 0])
n6[:, 0]]:
 [ 0  6 12 18 24]

# 取第2、3列
>>> print('n6[:, 3:5]]:\n', n6[:, 3:5])
n6[:, 3:5]]:
 [[ 3  4]
 [ 9 10]
 [15 16]
 [21 22]
 [27 28]]

拼接、分割

>>> A=np.arange(10,20).reshape(5,2)
>>> print(A)
[[10 11]
 [12 13]
 [14 15]
 [16 17]
 [18 19]]

>>> B=np.arange(20,30).reshape(5,2)
>>> print(B)
[[20 21]
 [22 23]
 [24 25]
 [26 27]
 [28 29]]

# 垂直拼接
>>> C=np.vstack([A,B]) #C=np.r_[A,B]
>>> print(C)
[[10 11]
 [12 13]
 [14 15]
 [16 17]
 [18 19]
 [20 21]
 [22 23]
 [24 25]
 [26 27]
 [28 29]]

# 自我堆叠
>>> v=np.asarray([1,2])
>>> a=np.vstack([v]*2)
>>> print(a)
[[1 2]
 [1 2]]
# 横向堆叠两次，纵向堆叠一次
>>> b=np.tile(v,(2,1))
>>> print(b)
[[1 2]
 [1 2]]

# 水平拼接
>>> C=np.hstack([A,B]) #C=np.c_[A,B]
>>> print(C)
[[10 11 20 21]
 [12 13 22 23]
 [14 15 24 25]
 [16 17 26 27]
 [18 19 28 29]]

#列组合column_stack([A,B]) 一维数组：按列方向组合  二维数组：同hstack一样
>>> A=np.arange(10,20)
>>> print(A)
[10 11 12 13 14 15 16 17 18 19]
#行组合row_stack([A,B]) 一维数组：按行方向组合  二维数组：同vstack一样

基础运算

>>> n7 = np.asarray([10, 20, 30,40])
>>> n8 = np.arange(4)
>>> print(n7)
[10 20 30 40]
>>> print(n8)
[0 1 2 3]

# 计算立方
>>> print(n7**3)
[ 1000  8000 27000 64000]

# 三角函数
>>> print(np.sin(n7))
[-0.54402111  0.91294525 -0.98803162  0.74511316]

# 指定轴最大/小值
>>> print(np.amax(n7, axis=0))
40
>>> print(np.amin(n7, axis=0))
10

# 平均值
>>> print(np.mean(n7, axis=0))
25.0

# 中位数
>>> print(np.median(n7))
25.0

# 方差
>>> print(n7.var())
125.0

# 标准差
>>> print(np.std(n7, axis=0))
11.180339887498949

# 差值
>>> print("n7-n8:",n7-n8)
n7-n8: [10 19 28 37]


# 逐个相乘非矩阵乘法
>>> n9 = np.asarray([[1,1],[0,1]])
>>> print(n9)
[[1 1]
 [0 1]]
>>> n10=np.arange(4).reshape((2,2))
>>> print(n10)
[[0 1]
 [2 3]]
>>> print(n9 * n10) 
[[0 1]
 [0 3]]

矩阵计算

# Ax=B 求解x
>>> A = np.array([[2, 1, -2], [3, 0, 1], [1, 1, -1]])
>>> B = np.transpose(np.array([[-3, 5, -2]]))
>>> x = np.linalg.solve(A, B)
>>> print('x:\n', x)
x:
 [[ 1.]
 [-1.]
 [ 2.]]

# 矩阵相乘 C=AB  求解C
>>> A = np.array([[3, 2, -2], [3, 1, 4], [3, 1, -2]])
>>> B = np.arange(9).reshape((3,3))
>>> C = np.dot(A, B)
>>> print('C:\n',C)
C:
 [[-6 -3  0]
 [27 35 43]
 [-9 -7 -5]]


# 矩阵乘向量
>>> v=np.asarray([1,2])
>>> print(v)
[1 2]
>>> A=np.arange(1,5).reshape(2,2)
>>> print(A)
[[1 2]
 [3 4]]
>>> D=v.dot(A)
>>> print(D)
[ 7 10]
# 自动将v转换为列向量，结果有自动转化为行向量
>>> C=A.dot(v)
>>> print(C)
[ 5 11]


# 矩阵的逆
>>> A=np.arange(1,5).reshape(2,2)
>>> print(A)
[[1 2]
 [3 4]]
>>> invA=np.linalg.inv(A)
>>> print(invA)
[[-2.   1. ]
 [ 1.5 -0.5]]
#   矩阵乘以矩阵的逆等于单位矩阵对角线都为1,其他为0，这里有浮点误差
>>> print(A.dot(invA))
[[1.00000000e+00 1.11022302e-16]
 [0.00000000e+00 1.00000000e+00]]

# 对于非方阵求伪逆矩阵
>>> A=np.arange(1,11).reshape(2,5)
>>> print(A)
[[ 1  2  3  4  5]
 [ 6  7  8  9 10]]
>>> pinvA=np.linalg.pinv(A)
>>> print(pinvA)
[[-0.36  0.16]
 [-0.2   0.1 ]
 [-0.04  0.04]
 [ 0.12 -0.02]
 [ 0.28 -0.08]]
>>> print(A.dot(pinvA))
[[ 1.00000000e+00 -1.11022302e-16]
 [-8.88178420e-16  1.00000000e+00]]

排序与arg

>>> x=np.asarray([2,6,7,1,4,5,8,3,10,9])
>>> print(x)
[ 2  6  7  1  4  5  8  3 10  9]

# argxxx 索引函数
>>> print(np.argmax(x)) #最大数的索引为8
8
>>> print(np.argmin(x))
3

# 排序
>>> print(np.sort(x))
[ 1  2  3  4  5  6  7  8  9 10]

# x原地排序
>>> x.sort()
>>> print(x)
[ 1  2  3  4  5  6  7  8  9 10]

#打乱顺序
>>> np.random.shuffle(x)
>>> print(x)
[ 9  3  5  6  2  1  8  4  7 10]

# 返回排序索引
>>> print(np.argsort(x))
[5 4 1 7 2 3 8 6 0 9]

# 划分大于3和小于3 （快排子过程）
>>> print(np.partition(x,3))
[ 2  1  3  4  5  6  8  7  9 10]

FancyIndexing与np比较

>>> x=np.arange(16)
>>> print(x)
[ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15]

# FancyIndexing
>>> a=[3,5,8]
>>> print(x[a])
[3 5 8]

# np数组比较
>>> x<3
array([ True,  True,  True, False, False, False, False, False, False,
       False, False, False, False, False, False, False])

>>> 2*x==24-4*x
array([False, False, False, False,  True, False, False, False, False,
       False, False, False, False, False, False, False])

# 小于等于3的元素Ture/False序列
>>> i=(x<=3)
>>> print(i)
[ True  True  True  True False False False False False False False False
 False False False False]
>>> print(x[i])
[0 1 2 3]
>>> np.sum(i) # 对值Ture累加记数
4

# 是否含有零元素
>>> np.any(x==0)
True

# 是否都等于零
>>> np.all(x==0)
False

# 判断两个数组是否相等
>>> np.all(x==x)
True

读取数据

>>> np.genfromtxt("http://aima.cs.berkeley.edu/data/iris.csv", delimiter=",",skip_header=0,dtype="f8,f8,f,i4,|S8")
array([(5.1, 3.5, 1.4, 0, b'setosa'), (4.9, 3. , 1.4, 0, b'setosa'),
       (4.7, 3.2, 1.3, 0, b'setosa'), (4.6, 3.1, 1.5, 0, b'setosa'),
       (5. , 3.6, 1.4, 0, b'setosa'), (5.4, 3.9, 1.7, 0, b'setosa'),
       (4.6, 3.4, 1.4, 0, b'setosa'), (5. , 3.4, 1.5, 0, b'setosa'),
       (4.4, 2.9, 1.4, 0, b'setosa'), (4.9, 3.1, 1.5, 0, b'setosa'),
       (5.4, 3.7, 1.5, 0, b'setosa'), (4.8, 3.4, 1.6, 0, b'setosa'),
  ......
  ......
       (5.8, 2.7, 5.1, 1, b'virginic'), (6.8, 3.2, 5.9, 2, b'virginic'),
       (6.7, 3.3, 5.7, 2, b'virginic'), (6.7, 3. , 5.2, 2, b'virginic'),
       (6.3, 2.5, 5. , 1, b'virginic'), (6.5, 3. , 5.2, 2, b'virginic'),
       (6.2, 3.4, 5.4, 2, b'virginic'), (5.9, 3. , 5.1, 1, b'virginic')],
      dtype=[('f0', '<f8'), ('f1', '<f8'), ('f2', '<f8'), ('f3', '<i4'), ('f4', 'S8')])