如何得到 NumPy 中矢量的大小？

原文:https://www . geeksforgeeks . org/如何获得数字矢量幅度/

线性代数的基本特征是向量，向量是既有方向又有大小的对象。在 Python 中，NumPy 数组可以用来描述一个向量。

矢量大小的获取主要有两种方式:

• By defining an explicit function which computes the magnitude of a given vector based on the below mathematical formula:

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

  ```

  下面是一些按照上述方法计算矢量大小的程序:

  ```py

  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:

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

  ```

  下面是采用相同方法的另一个示例:

  ```py

  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:

  ```py Magnitude of the Vector: 3.7416573867739413

  ```

• By using the norm() method in linalg module of NumPy library. The Linear Algebra module of NumPy offers various methods to apply linear algebra on any NumPy array. Below are some programs which use numpy.linalg.norm() to compute the magnitude of a vector:

  ```py

  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:

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

  ```

  一个额外的参数ord可以用来计算向量的第 n 阶norm()。

  ```py

  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:

  ```py 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

  ```

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