numpy教程

阅读该教程，您需要python基础的预备知识

矩阵基础

注意:矩阵必须满足所有行的元素个数相等,像b=np.array([[5,6,3,4],[2,4,7]])是不合法的

import numpy as np
arr=np.array([[1,2,3],
              [2,3,4]])
print(arr)
print([[1,2,3],
       [4,5,6]])
print(f"arr是{arr.ndim}维矩阵")
print(f"行数和列数为{arr.shape}")
print(f"arr中的元素总数为{arr.size}")

[[1 2 3]
 [2 3 4]]
[[1, 2, 3], [4, 5, 6]]
arr是2维矩阵
行数和列数为(2, 3)
arr中的元素总数为6

dtype元素的类型

定义矩阵时可以用dtype声明元素的类型,常见包括

• int64 64位整数
• int32 32位整数
• float32
• float64
• float16

了解更多numpy的数据类型,请阅读

import numpy as np
arr=np.array([2,2333,3,4],np.dtype(np.float64))
print(arr.dtype)
print(arr)

float64
[2.000e+00 2.333e+03 3.000e+00 4.000e+00]

zeros 全零矩阵

import numpy as np
a=np.zeros((3,4))
print(a)
print(a.dtype)

[[0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]]
float64

ones 全一矩阵

import numpy as np
a=np.ones((3,4))
print(a)
print(a.dtype)

[[1. 1. 1. 1.]
 [1. 1. 1. 1.]
 [1. 1. 1. 1.]]
float64

empty 元素都几乎接近0的矩阵

import numpy as np
a=np.empty((3,4))
print(a)
print(a.dtype)

[[6.95322371e-310 0.00000000e+000 0.00000000e+000 0.00000000e+000]
 [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000]
 [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000]]
float64

arrange 某一区间的数列

np.arrange(a,b,c)等价于matlab中的a:c:b

import numpy as np
a=np.arange(12)
print(a)
b=np.arange(2,10)
print(b)
c=np.arange(4,15,2)
print(c)

[ 0  1  2  3  4  5  6  7  8  9 10 11]
[2 3 4 5 6 7 8 9]
[ 4  6  8 10 12 14]

reshape 改变矩阵形状

import numpy as np
a=np.arange(12)
a=a.reshape((3,4))
print(a)

[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]]

linspace(开始,结尾,分几段)

import numpy as np
a=np.linspace(1,5,9)
print(a.reshape(3,3))
print(a)

[[1.  1.5 2. ]
 [2.5 3.  3.5]
 [4.  4.5 5. ]]
[1.  1.5 2.  2.5 3.  3.5 4.  4.5 5. ]

随机矩阵

import numpy as np
a=np.random.random((3,2))
print(a)

[[0.81661957 0.66981303]
 [0.50054947 0.85381138]
 [0.36714028 0.16603213]]

矩阵运算

矩阵和标量的基本运算

import numpy as np
a=np.array([1,2,3,4,5])
print(a)
print(a+2)
print(a-3)
print(a*5)
print(a/4)
print(a//4)
print(a**2)
print(a*np.sin(a))

[1 2 3 4 5]
[3 4 5 6 7]
[-2 -1  0  1  2]
[ 5 10 15 20 25]
[0.25 0.5  0.75 1.   1.25]
[0 0 0 1 1]
[ 1  4  9 16 25]
[ 0.84147098  1.81859485  0.42336002 -3.02720998 -4.79462137]

矩阵元素的判断

import numpy as np
a=np.array([1,2,3,4,5])
print(a)
print(a<=3)

[1 2 3 4 5]
[ True  True  True False False]

元素乘法和矩阵乘法

import numpy as np
a=np.array([[1,1],
            [0,1]])
b=np.array([[0,1],
            [2,3]])
c=a*b  # 逐个元素相乘
print(c)
c_dot=np.dot(a,b) # 矩阵乘法
print(c_dot)
c_dot_2=a.dot(b)  #矩阵乘法的另一种写法
print(c_dot_2)

[[0 1]
 [0 3]]
[[2 4]
 [2 3]]
[[2 4]
 [2 3]]

求和sum,最小值min,最大值max

import numpy as np
a=np.random.random((3,2))
print(a)
print(np.sum(a))
print(np.min(a))
print(np.max(a))

[[0.16496185 0.9437828 ]
 [0.81840345 0.89624578]
 [0.26440633 0.74531292]]
3.833113133002955
0.16496184822955373
0.9437827991060538

使用axis axis的意义是维度数

import numpy as np
a=np.array([[1,2,3,4],
            [2,3,4,5],
            [3,4,5,6]])
print(np.sum(a,axis=0))  # 对列求和
print(np.sum(a,axis=1))  # 对行求和

[ 6  9 12 15]
[10 14 18]

min,max,mean也适用axis

argmin,argmax矩阵中最小最大值的索引

import numpy as np
a=np.arange(2,14).reshape((3,4))
print(np.argmin(a))
print(np.argmax(a))

0
11

mean平均值 median中位数

import numpy as np
a=np.arange(2,14).reshape((3,4))
print(np.mean(a))
print(np.average(a))
print(a.mean())
print(np.median(a))

7.5
7.5
7.5
7.5

cumsum累加数组 diff数组差分

import numpy as np
a=np.arange(2,14).reshape((3,4))
print(a)
print(np.cumsum(a))
print(np.diff(a))

[[ 2  3  4  5]
 [ 6  7  8  9]
 [10 11 12 13]]
[ 2  5  9 14 20 27 35 44 54 65 77 90]
[[1 1 1]
 [1 1 1]
 [1 1 1]]

sort排序每行

import numpy as np
a=np.arange(14,2,-1).reshape((3,4))
print(a)
print(np.sort(a))

[[14 13 12 11]
 [10  9  8  7]
 [ 6  5  4  3]]
[[11 12 13 14]
 [ 7  8  9 10]
 [ 3  4  5  6]]

矩阵转置

import numpy as np
a=np.arange(14,2,-1).reshape((3,4))
print(a)
print(np.transpose(a))
print(a.T)

[[14 13 12 11]
 [10  9  8  7]
 [ 6  5  4  3]]
[[14 10  6]
 [13  9  5]
 [12  8  4]
 [11  7  3]]
[[14 10  6]
 [13  9  5]
 [12  8  4]
 [11  7  3]]

clip(矩阵,矩阵中保留数的下限,矩阵中保留数的上限)

import numpy as np
a=np.arange(14,2,-1).reshape((3,4))
print(a)
print(np.clip(a,5,9))

[[14 13 12 11]
 [10  9  8  7]
 [ 6  5  4  3]]
[[9 9 9 9]
 [9 9 8 7]
 [6 5 5 5]]

矩阵索引

下标从0开始算

对于行向量,a[i]会取出下标为i的元素

import numpy as np
a=np.arange(3,15)
print(a)
print(a[3])

[ 3  4  5  6  7  8  9 10 11 12 13 14]
6

对于3行4列的矩阵,a[i]取出第i行

import numpy as np
a=np.arange(3,15).reshape(3,4)
print(a)
print(a[2])

[[ 3  4  5  6]
 [ 7  8  9 10]
 [11 12 13 14]]
[11 12 13 14]

import numpy as np
a=np.arange(3,15).reshape(3,4)
print(a)
print(a[2][1])
print(a[2,1])

[[ 3  4  5  6]
 [ 7  8  9 10]
 [11 12 13 14]]
12
12

利用冒号

注意:取出来的都是行向量

import numpy as np
a=np.arange(3,15).reshape(3,4)
print(a)
print(a[2,:])  # 第2行所有的数
print(a[:,1])  # 第1列所有的数
print(a[1,1:3]) # 取第1行1~2列（不包括下标为3）
print(a[0,0:4:2])  #第0行，从第0列开始，每隔2个数取一次，直到下标为4（不包括下标为4）

[[ 3  4  5  6]
 [ 7  8  9 10]
 [11 12 13 14]]
[11 12 13 14]
[ 4  8 12]
[8 9]
[3 5]

flat和flatten

import numpy as np
a=np.arange(3,15).reshape(3,4)
print(a.flat)  # 这是一个迭代器
print(a.flatten())  #展开矩阵

<numpy.flatiter object at 0x0000021DAA7D7CE0>
[ 3  4  5  6  7  8  9 10 11 12 13 14]

for循环遍历

import numpy as np
a=np.arange(3,15).reshape(3,4)
print(a)
for row in a:
    print(row)  # 取出所有行
for col in a.T:
    print(col)  # 取出所有列

[[ 3  4  5  6]
 [ 7  8  9 10]
 [11 12 13 14]]
[3 4 5 6]
[ 7  8  9 10]
[11 12 13 14]
[ 3  7 11]
[ 4  8 12]
[ 5  9 13]
[ 6 10 14]

遍历所有元素

import numpy as np
a=np.arange(3,15).reshape(3,4)
print(a)
for item in a.flat:
    print(item,end=" ")

[[ 3  4  5  6]
 [ 7  8  9 10]
 [11 12 13 14]]
3 4 5 6 7 8 9 10 11 12 13 14 

矩阵的合并

import numpy as np
a=np.array([1,1,1])
b=np.array([2,2,2])
c=np.vstack((a,b))  # vertical stack
d=np.hstack((a,b))  # horizontal stack
print(c)
print(d)

[[1 1 1]
 [2 2 2]]
[1 1 1 2 2 2]

转置合并

import numpy as np
a=np.array([1,1,1])[:,np.newaxis]
b=np.array([2,2,2])[:,np.newaxis]
d=np.hstack((a,b))
print(d)

[[1 2]
 [1 2]
 [1 2]]

newaxis的使用

newaxis用于增加维度

import numpy as np
a=np.array([1,1,1])
print(a.shape)
c=a[:,np.newaxis]
print(c)
print(c.shape)
d=a[np.newaxis,:]
print(d)
print(d.shape)

(3,)
[[1]
 [1]
 [1]]
(3, 1)
[[1 1 1]]
(1, 3)

concatenate矩阵拼接

import numpy as np
a=np.array([1,1,1])[:,np.newaxis]
b=np.array([2,2,2])[:,np.newaxis]
print(np.concatenate((a,b,b,a),axis=0))
print(np.concatenate((a,b,b,a),axis=1))

[[1]
 [1]
 [1]
 [2]
 [2]
 [2]
 [2]
 [2]
 [2]
 [1]
 [1]
 [1]]
[[1 2 2 1]
 [1 2 2 1]
 [1 2 2 1]]

深浅拷贝

import numpy as np
a=np.arange(4)
b=a
print(b is a)

True

等号复制是浅拷贝

import numpy as np
a=np.arange(4)
b=a
print(a)
a[0]=11
print(a)
print(b)

[0 1 2 3]
[11  1  2  3]
[11  1  2  3]

利用copy深拷贝

import numpy as np
a=np.arange(4)
b=a.copy()
print(b is a)
print(a)
a[1:3]=[22,33]
print(a)
print(b)

False
[0 1 2 3]
[ 0 22 33  3]
[0 1 2 3]