使用NumPy获取多维矢量点积

给定两个多维矢量，任务是编写一个Python程序，使用NumPy得到两个多维矢量的点积。

例子：让我们取2个向量a = [2,5,3]和b = [6,3,1] 。

点积(ab) = (a[0] * b[0])+ (a[1] * b[1]) + (a[2] * b[2]) = (26)+ (53) + (3*1) = 30

点积是指在向量的每个位置上的元素的乘积之和。

一维矢量的点积。

现在让我们在python中实现这一点。但是我们不需要从头开始编码，这要感谢Numpy。Numpy模块有一个方法dot，它接收两个向量并返回它们的点积

# import numpy
import numpy as np
  
# initialize vectors
a = np.array([2,5,3])
b = np.array([6,3,1])
  
# calculating Dot product form np.dot
c = np.dot(a,b)
print("Dot product of a and b is: ",c)

输出:

Dot product of a and b is:  30

二维向量的点积。

二维向量的点积是简单的矩阵乘法。在一维向量中，每个向量的长度应该是相同的，但当涉及到二维向量时，我们将有两个方向的长度即行和列。二维向量的行和列不一定相同，但第一个向量的列数应与第二个向量的行数一致。

示例:

让我们用Python（Numpy模块）做同样的事情

# import numpy
import numpy as np
  
# initialize 2d vectors
a = np.array([[3, 9],
              [2, 5]])
b = np.array([[6, 1],
              [4, 8]])
  
# Checking the condition "No. of columns 
# of first vector == No. of rows of the
# second vector"
if a.shape[1] == b.shape[0]:
    
    # calculating Dot product using np.dot
    c = np.dot(a, b)
    print("Dot product of a and b is:\n", c)
else:
    print("No. of columns of first vector should match\
    with No. of rows of the second vector")

输出:

Dot product of a and b is:
 [[54 75]
 [32 42]]

示例:

在这个例子中，采用与上例相同的方法，我们要处理不同的数据点，并添加一个if语句，以防代码产生错误。

# import numpy
import numpy as np
  
# initialize vectors
a = np.array([[3,9,6],
              [2,5,2]])
b = np.array([[6,1],
              [4,8],
              [7,5]])
  
# Checking the condition "No. of columns
# of first vector == No. of rows of the 
# second vector"
if a.shape[1] == b.shape[0]:
    # calculating Dot product using np.dot
    c = np.dot(a,b)
    print("Dot product of a and b is:\n",c)
else:
    print("No. of columns of first vector should match with \
    No. of rows of the second vector")

输出:

Dot product of a and b is:
[[ 96 105]
[ 46  52]]

如果条件不满足，它将抛出一个错误，让我们删除我们的if块并计算不同形状的点积，看看什么是错误。

# import numpy
import numpy as np
  
# initialize vectors
a = np.array([[3,9],
              [2,5]])
b = np.array([[6,1],
              [4,8],
              [7,5]])
print("Shape of vector a: ",a.shape)
print("Shape of vector b: ",b.shape)
  
# calculating Dot product using np.dot
c = np.dot(a,b)
print("Dot product of a and b is:\n",c)

Shape of vector a: (2, 2)

Shape of vector b: (3, 2)

—————————————————————————

ValueError Traceback (most recent call last)

in

12

13 # calculating Dot product using np.dot

—> 14 c = np.dot(a,b)

15 print(“Dot product of a and b is:\n”,c)

<__array_function__ internals> in dot(*args, **kwargs)

ValueError: shapes (2,2) and (3,2) not aligned: 2 (dim 1) != 3 (dim 0)