极客笔记Python 通过将矩阵传递给函数来进行矩阵相乘
矩阵是一个由许多数字按行和列排列的二维数组。它被称为m X n矩阵，其中m和n是维度。
一般来说，两个矩阵的乘法只有在第一个矩阵的列数等于第二个矩阵的行数时才可能成立。
输入输出情况
假设我们有两个输入矩阵A和B，都有3行3列。那么结果矩阵也将有3行3列。
[a, b, c] [j, k, l] [(a*j+b*m+c*p), (a*k+b*n+c*q), (a*l+b*o+c*r)]
[d, e, f] * [m, n, o] = [(d*j+e*m+f*p), (d*k+e*n+f*q), (d*l+e*o+f*r)]
[g, h, i] [p, q, r] [(g*j+h*m+i*p), (g*k+h*n+i*q), (g*l+h*o+i*r)]
矩阵的逐元素乘法如下所示。在这种情况下，两个输入矩阵的行数和列数必须相同。
[a, b, c] [j, k, l] [(a*j), (b*k), (c*i)]
[d, e, f] * [m, n, o] = [(d*e), (e*n), (f*o)]
[g, h, i] [p, q, r] [(g*p), (h*q), (i*r)]
让我们通过将它们传递给一个函数来相乘两个矩阵
使用循环
我们将在python中使用def关键字定义一个用户定义的函数来相乘两个矩阵。在函数中，我们声明一个存储结果矩阵的零矩阵。通过使用for循环迭代两个矩阵的行和列，我们将相乘两个矩阵的元素，并将它们存储在结果矩阵中。
示例
在下面的示例中，我们将通过将它们传递给用户定义的函数来相乘两个矩阵。
def multiply(A,B):
result=[[0,0,0],[0,0,0],[0,0,0]]
#for rows
for i in range(len(A)):
#for columns
for j in range(len(B[0])):
#for rows of matrix B
for k in range(len(B)):
result[i][j] += A[i][k] * B[k][j]
for p in result:
print(p)
return
#function for displaying matrix
def display(matrix):
for row in matrix:
print(row)
print()
matrix_1 = [[2, 1, 2],[3, 2, 2], [1, 1, 2]]
matrix_2 = [[1, 5, 3],[4, 2, 1], [1, 2, 2]]
# Display two input matrices
print('The first matrix is defined as:')
display(matrix_1)
print('The second matrix is defined as:')
display(matrix_2)
print("Result: ")
multiply(matrix_1,matrix_2)
输出
The first matrix is defined as:
[2, 1, 2]
[3, 2, 2]
[1, 1, 2]
The second matrix is defined as:
[1, 5, 3]
[4, 2, 1]
[1, 2, 2]
Result:
[8, 16, 11]
[13, 23, 15]
[7, 11, 8]
在这里，我们将使用一些内置的NumPy函数来计算两个矩阵的乘积。
使用Numpy.matmul()函数
matmul()函数将执行将两个输入传递给函数的矩阵相乘。
示例
首先我们导入NumPy模块，并应用np.matmul()函数来计算两个矩阵的乘积。
import numpy as np
matrix_1 = np.array([[2, 1, 2],[3, 2, 2], [1, 1, 2]])
matrix_2 =np.array([[1, 5, 3],[4, 2, 1], [1, 2, 2]])
#function for displaying matrix
def display(matrix):
for row in matrix:
print(row)
print()
# Display two input matrices
print('The first matrix is defined as:')
display(matrix_1)
print('The second matrix is defined as:')
display(matrix_2)
print("Result: ")
print(np.matmul(matrix_1 ,matrix_2))
输出
The first matrix is defined as:
[2 1 2]
[3 2 2]
[1 1 2]
The second matrix is defined as:
[1 5 3]
[4 2 1]
[1 2 2]
Result:
[[ 8 16 11]
[13 23 15]
[ 7 11 8]]
使用Numpy.multiply()函数
它将执行两个输入矩阵的逐元素乘法操作。
示例
首先，我们将使用numpy.array()函数创建两个矩阵。然后，通过使用np.multiply()函数来计算两个矩阵的逐元素乘法。
import numpy as np
matrix_1 = np.array([[2, 1, 2],[3, 2, 2], [1, 1, 2]])
matrix_2 =np.array([[1, 5, 3],[4, 2, 1], [1, 2, 2]])
#function for displaying matrix
def display(matrix):
for row in matrix:
print(row)
print()
# Display two input matrices
print('The first matrix is defined as:')
display(matrix_1)
print('The second matrix is defined as:')
display(matrix_2)
print("Result: ")
print(np.multiply(matrix_1 ,matrix_2))
输出
The first matrix is defined as:
[2 1 2]
[3 2 2]
[1 1 2]
The second matrix is defined as:
[1 5 3]
[4 2 1]
[1 2 2]
Result:
[[ 2 5 6]
[12 4 2]
[ 1 2 4]]
使用Numpy.dot()函数
dot()函数将对两个输入矩阵执行点乘运算。
示例
我们将给np.dot()函数两个numpy数组，来执行两个输入的点乘运算。
import numpy as np
matrix_1 = np.array([[2, 1, 2],[3, 2, 2], [1, 1, 2]])
matrix_2 =np.array([[1, 5, 3],[4, 2, 1], [1, 2, 2]])
#function for displaying matrix
def display(matrix):
for row in matrix:
print(row)
print()
# Display two input matrices
print('The first matrix is defined as:')
display(matrix_1)
print('The second matrix is defined as:')
display(matrix_2)
print("Result: ")
print(np.dot(matrix_1 ,matrix_2))
输出
The first matrix is defined as:
[2 1 2]
[3 2 2]
[1 1 2]
The second matrix is defined as:
[1 5 3]
[4 2 1]
[1 2 2]
Result:
[[ 8 16 11]
[13 23 15]
[ 7 11 8]]