Python中的幾種矩陣乘法

1. 同線(xiàn)性代數(shù)中矩陣乘法的定義： np.dot()

np.dot(A, B)：對(duì)于二維矩陣，計(jì)算真正意義上的矩陣乘積，同線(xiàn)性代數(shù)中矩陣乘法的定義。對(duì)于一維矩陣，計(jì)算兩者的內(nèi)積。見(jiàn)如下Python代碼：

import numpy as np

2-D array: 2 x 3

two_dim_matrix_one = np.array([[1, 2, 3], [4, 5, 6]])

2-D array: 3 x 2

two_dim_matrix_two = np.array([[1, 2], [3, 4], [5, 6]])

two_multi_res = np.dot(two_dim_matrix_one, two_dim_matrix_two)
print(‘two_multi_res: %s’ %(two_multi_res))

1-D array

one_dim_vec_one = np.array([1, 2, 3])
one_dim_vec_two = np.array([4, 5, 6])
one_result_res = np.dot(one_dim_vec_one, one_dim_vec_two)
print(‘one_result_res: %s’ %(one_result_res))

            
              1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

            
          

結(jié)果如下：

two_multi_res: [[22 28]
[49 64]]
one_result_res: 32

            
              1
2
3

            
          

2. 對(duì)應(yīng)元素相乘 element-wise product: np.multiply(), 或 *

在Python中，實(shí)現(xiàn)對(duì)應(yīng)元素相乘，有2種方式，一個(gè)是np.multiply()，另外一個(gè)是*。見(jiàn)如下Python代碼：

import numpy as np

2-D array: 2 x 3

two_dim_matrix_one = np.array([[1, 2, 3], [4, 5, 6]])
another_two_dim_matrix_one = np.array([[7, 8, 9], [4, 7, 1]])

對(duì)應(yīng)元素相乘 element-wise product

element_wise = two_dim_matrix_one * another_two_dim_matrix_one
print(‘element wise product: %s’ %(element_wise))

對(duì)應(yīng)元素相乘 element-wise product

element_wise_2 = np.multiply(two_dim_matrix_one, another_two_dim_matrix_one)
print(‘element wise product: %s’ % (element_wise_2))

            
              1
2
3
4
5
6
7
8
9
10
11
12
13

            
          

結(jié)果如下：

element wise product: [[ 7 16 27]
[16 35 6]]
element wise product: [[ 7 16 27]
[16 35 6]]