python之numpy库中数组和矩阵的各种乘法区别(*,dot,multiply)

numpy库中两种对象，数组和矩阵(ndarray,matrix)，两者都有三种不同的乘法，分别是 * , dot 和multiply 三种类型。以下分别进行介绍。

1.数组(ndarray）

先不废话，直接上实例：

import numpy as np

a = np.array([[1,2,3]])
b = np.array([(1,2,3), 
              (4,5,6)])
print(type(a),type(b))

print("a=\n",a,"\n")
print("b=\n",b,"\n")
print("a*b=\n",a*b,"\n")
print("a.dot(b.T)=\n",a.dot(b.T),"\n")
print("b.dot(a.T)=\n",b.dot(a.T),"\n")
print("np.multiply(a,b)=\n",np.multiply(a,b),"\n")
print("np.multiply(b,a)=\n",np.multiply(b,a),"\n")

结果如下：

a=
 [[1 2 3]] 

b=
 [[1 2 3]
 [4 5 6]] 

<class 'numpy.ndarray'> <class 'numpy.ndarray'>

a*b=
 [[ 1  4  9]
 [ 4 10 18]] 

a.dot(b.T)=
 [[14 32]] 

b.dot(a.T)=
 [[14]
 [32]] 

np.multiply(a,b)=
 [[ 1  4  9]
 [ 4 10 18]] 

np.multiply(b,a)=
 [[ 1  4  9]
 [ 4 10 18]]

2.矩阵(matrix）

也不废话，继续上实例：

a = np.mat([[1,2,3]])
b = np.mat([(1,2,3), 
            (4,5,6)])
print(type(a),type(b))

print("a=\n",a,"\n")
print("b=\n",b,"\n")

# print("a*b=\n",a*b,"\n") 注意，此处报错，因为不符合矩阵乘法规则，注[1]
print("a*b.T=\n",a*b.T,"\n")
print("b*a.T=\n",b*a.T,"\n")

print("a.dot(b.T)=\n",a.dot(b.T),"\n")
print("b.dot(a.T)=\n",b.dot(a.T),"\n")
print("np.multiply(a,b)=\n",np.multiply(a,b),"\n")
print("np.multiply(b,a)=\n",np.multiply(b,a),"\n")

注[1]：矩阵相乘应满足矩阵乘法规则，即前矩阵的列数（column）和后矩阵的行数（row）相同时才有意义。

结果如下：

a=
 [[1 2 3]] 

b=
 [[1 2 3]
 [4 5 6]] 

<class 'numpy.matrix'> <class 'numpy.matrix'>

a*b.T=
 [[14 32]] 

b*a.T=
 [[14]
 [32]] 

a.dot(b.T)=
 [[14 32]] 

b.dot(a.T)=
 [[14]
 [32]] 

np.multiply(a,b)=
 [[ 1  4  9]
 [ 4 10 18]] 

np.multiply(b,a)=
 [[ 1  4  9]
 [ 4 10 18]]