如何在 NumPy 中获取向量的大小？

线性代数的基本特征是向量，它们是具有方向和大小的对象。在Python中，NumPy 数组可用于描述向量。

获取向量的大小主要有两种方式：

• 通过定义一个显式函数，该函数根据以下数学公式计算给定向量的大小：

  if V is vector such that, V = (a, b, c)
  then ||V|| = ?(a*a + b*b + c*c)
  

  以下是一些按照上述方法计算向量大小的程序：

  # program to compute magnitude of a vector
    
  # importing required libraries
  import numpy
  import math
    
  # function defination to compute magnitude o f the vector
  def magnitude(vector): 
      return math.sqrt(sum(pow(element, 2) for element in vector))
    
  # displaying the original vector
  v = numpy.array([0, 1, 2, 3, 4])
  print('Vector:', v)
    
  # computing and displaying the magnitude of the vector
  print('Magnitude of the Vector:', magnitude(v))
  

  输出：

  Vector: [0 1 2 3 4]
  Magnitude of the Vector: 5.477225575051661
  

  以下是使用相同方法的另一个示例：

  # program to compute magnitude of a vector
    
  # importing required libraries
  import numpy
  import math
    
  # function defination to compute magnitude o f the vector
  def magnitude(vector): 
      return math.sqrt(sum(pow(element, 2) for element in vector))
    
  # computing and displaying the magnitude of the vector
  print('Magnitude of the Vector:', magnitude(numpy.array([1, 2, 3])))
  

  输出：

  Magnitude of the Vector: 3.7416573867739413
  

• 通过使用NumPy库的linalg模块中的norm()方法。 NumPy的线性代数模块提供了在任何NumPy数组上应用线性代数的各种方法。下面是一些使用numpy.linalg.norm()计算向量大小的程序：

  # program to compute magnitude of a vector
    
  # importing required libraries
  import numpy
    
  # displaying the original vector
  v = numpy.array([1, 2, 3])
  print('Vector:', v)
    
  # computing and displaying the magnitude of
  # the vector using norm() method
  print('Magnitude of the Vector:', numpy.linalg.norm(v))
  

  输出：

  Vector: [1 2 3]
  Magnitude of the Vector: 3.7416573867739413
  

  额外的参数ord可用于计算向量的norm()的第 n 阶。

  # program to compute the nth order of the 
  # magnitude of a vector
    
  # importing required libraries
  import numpy
    
  # displaying the original vector
  v = numpy.array([0, 1, 2, 3, 4])
  print('Vector:', v)
    
  # computing and displaying the magnitude of the vector
  print('Magnitude of the Vector:', numpy.linalg.norm(v))
    
  # Computing the nth order of the magnitude of vector
  print('ord is 0: ', numpy.linalg.norm(v, ord = 0))
  print('ord is 1: ', numpy.linalg.norm(v, ord = 1))
  print('ord is 2: ', numpy.linalg.norm(v, ord = 2))
  print('ord is 3: ', numpy.linalg.norm(v, ord = 3))
  print('ord is 4: ', numpy.linalg.norm(v, ord = 4))
  

  输出：

  Vector: [0 1 2 3 4]
  Magnitude of the Vector: 5.477225575051661
  ord is 0:  4.0
  ord is 1:  10.0
  ord is 2:  5.477225575051661
  ord is 3:  4.641588833612778
  ord is 4:  4.337613136533361