NumPy Norm of Vector

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  • Post category:NumPy / Python
  • Post last modified:September 20, 2022

NumPy norm of vector in python is used to get a matrix or vector norm we use numpy.linalg.norm() function. This function is used to calculate one of the eight different matrix norms or one of the vector norms, depending on the value of the ord parameter. In this article, I will explain how to use numpy.linalg.norm() function and using its syntax and parameters, and returns a norm of the matrix or vectors.

1. Quick Examples of Norm of Vector

If you are in a hurry, below are some quick examples of NumPy norm of vector.


# Below are a quick examples

# Example 1: use numpy.linalg.norm() function
arr = np.arange(12)
arr2 = np.linalg.norm(arr)

# Example 2: Get the linalg.norm() with 1-D array
arr = np.array([2, 4, 6, 8, 10, 12, 14])
arr2 = np.linalg.norm(arr)

# Example 3: Get the linalg.norm() with 2-D array 
arr = np.array([[3, 7, 9], [2, 6, 8]])
arr2 = np.linalg.norm(arr)

# Example 4: Get the linalg.norm() values over column 
# for each of 2 rows  
arr2 = np.linalg.norm(arr, axis = 1)

# Example 5: Get the linalg.norm() values over row 
# for each of 3 columns 
arr2 = np.linalg.norm(arr, axis = 0)

# Example 6: get numpy norm of vector with 2-d array along axis
arr2 = np.linalg.norm(arr,axis= (0,1))

# Example 7: use ord Parameter
arr2 = np.linalg.norm(arr, ord=1, axis=1)

2. Syntax of NumPy linalg.norm()

Following is the syntax to create numpy.linalg.norm() function.


# Syntax of numpy.linalg.norm()
linalg.norm(arr, ord=None, axis=None, keepdims=False)

2.1 Parameters of linalg.norm()

Following are the parameters of linalg.norm().

  • arr – Input array.
  • ord – {non-zero int, inf, -inf, ‘fro’, ‘nuc’}, optional: This stands for the order of the norm.
  • axis – None, int or 2-tuple of ints. Axis or axes is an integer, it specifies the axis of x along which to compute the vector norms. If an axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed.
  • keepdims – It is a boolean and optional. If this is set to True, the axes which are normed over are left in the result as dimensions with size one.

2.2 Return value of linalg.norm()

The linalg.norm() returns a norm of the matrix or vector(s).

3. Use numpy.linalg.norm() Function

We can use NumPy linalg.norm() function is used to calculate the norm of a vector or a matrix. This functions returns a float or an array of norm values accurately by passing the arr as a parameter.


import numpy as np
 
# initialize vector
arr = np.arange(12)
 
# use numpy.linalg.norm() function
arr2 = np.linalg.norm(arr)
print(arr2)

# Output
# 22.494443758403985

4. Get NumPy linalg.norm() With 1-D Array

Take a one-dimensional NumPy array and compute the norm of a vector or a matrix of the array using numpy.linalg.norm() function, for that let’s create an array using numpy.array(). For example,


# Create 1-D array 
arr = np.array([2, 4, 6, 8, 10, 12, 14])

# Get the linalg.norm() with 1-D array
arr2 = np.linalg.norm(arr)
print(arr2)

# Output
# 23.664319132398465

5. Get NumPy linalg.norm() With 2-D Array

Let’s norm of vector the two-dimensional NumPy array using numpy.linalg.norm(). This function takes a 2-D array as input and returns a float or an array of norm values.


# Create 2-D array
arr = np.array([[3, 7, 9], [2, 6, 8]])

# Get the linalg.norm() with 2-D array 
arr2 = np.linalg.norm(arr)
print(arr2)

# Output
# 15.588457268119896

6. Get NumPy Norm of Vector With 2-D Array Along Axis

We can also compute the matrix norm of a NumPy array along with a specified axis. If we want to compute the matrix norm of each row, we will pass the axis=0 parameter through the linalg.norm() function. Similarly, to compute the matrix norm of each column, use axis=1. We will pass the axis parameter as the 2- tuple of the integer value.


# Get the linalg.norm() values over column 
# for each of 2 rows  
arr2 = np.linalg.norm(arr, axis = 1)
print(arr2)

# Output
# [11.78982612 10.19803903]

# Get the linalg.norm() values over row 
# for each of 3 columns 
arr2 = np.linalg.norm(arr, axis = 0)
print(arr2)

# Output
# [ 3.60555128  9.21954446 12.04159458]

# get numpy norm of vector with 2-d array along axis
arr2 = np.linalg.norm(arr,axis= (0,1))
print(arr2)

# Output
# 15.588457268119896

7. Use ord Parameter

We can also compute the matrix norm of a NumPy array along with a specified ord Parameter and axis.


# use ord Parameter
arr2 = np.linalg.norm(arr, ord=1, axis=1)
print(arr2)

# Output
# [19. 16.]

8. Conclusion

In this article, I have explain the how to calculate the norm of a vector or a matrix of NumPy array along with the specified axis and multiple axes. Also explained how to use ord Parameter.

Happy Learning!!

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