How to normalize an array in NumPy in Python?

Last Updated : 21 Nov, 2022

In this article, we are going to discuss how to normalize 1D and 2D arrays in Python using NumPy. Normalization refers to scaling values of an array to the desired range.

Normalization of 1D-Array

Suppose, we have an array = [1,2,3] and to normalize it in range [0,1] means that it will convert array [1,2,3] to [0, 0.5, 1] as 1, 2 and 3 are equidistant.

Array [1,2,4] -> [0, 0.3, 1]

This can also be done in a Range i.e. instead of [0,1], we will use [3,7].

Now,

Array [1,2,3] -> [3,5,7]

and

Array [1,2,4] -> [3,4.3,7]

Let's see examples with code

Example 1:

Python3

# import module
import numpy as np

# explicit function to normalize array
def normalize(arr, t_min, t_max):
    norm_arr = []
    diff = t_max - t_min
    diff_arr = max(arr) - min(arr)    
    for i in arr:
        temp = (((i - min(arr))*diff)/diff_arr) + t_min
        norm_arr.append(temp)
    return norm_arr

# gives range starting from 1 and ending at 3  
array_1d = np.arange(1,4) 
range_to_normalize = (0,1)
normalized_array_1d = normalize(array_1d, 
                                range_to_normalize[0], 
                                range_to_normalize[1])

# display original and normalized array
print("Original Array = ",array_1d)
print("Normalized Array = ",normalized_array_1d)

Output:

Example 2:

Now, Lets input array is [1,2,4,8,10,15] and range is again [0,1]

Python3

# import module
import numpy as np

# explicit function to normalize array
def normalize(arr, t_min, t_max):
    norm_arr = []
    diff = t_max - t_min
    diff_arr = max(arr) - min(arr)
    for i in arr:
        temp = (((i - min(arr))*diff)/diff_arr) + t_min
        norm_arr.append(temp)
    return norm_arr

# assign array and range
array_1d = [1, 2, 4, 8, 10, 15]
range_to_normalize = (0, 1)
normalized_array_1d = normalize(
    array_1d, range_to_normalize[0], 
  range_to_normalize[1])

# display original and normalized array
print("Original Array = ", array_1d)
print("Normalized Array = ", normalized_array_1d)

Output:

Normalization of 2D-Array

To normalize a 2D-Array or matrix we need NumPy library. For matrix, general normalization is using The Euclidean norm or Frobenius norm.

The formula for Simple normalization is

Here, v is the matrix and |v| is the determinant or also called The Euclidean norm. v-cap is the normalized matrix.

Below are some examples to implement the above:

Example 1:

Python3

# import module
import numpy as np

# explicit function to normalize array
def normalize_2d(matrix):
    norm = np.linalg.norm(matrix)
    matrix = matrix/norm  # normalized matrix
    return matrix

# gives and array starting from -2
# and ending at 13
array = np.arange(16) - 2

# converts 1d array to a matrix
matrix = array.reshape(4, 4)
print("Simple Matrix \n", matrix)
normalized_matrix = normalize_2d(matrix)
print("\nSimple Matrix \n", normalized_matrix)

Output:

Example 2:

We can also use other norms like 1-norm or 2-norm

Python3

# import module
import numpy as np

def normalize_2d(matrix):
    # Only this is changed to use 2-norm put 2 instead of 1
    norm = np.linalg.norm(matrix, 1)
    # normalized matrix
    matrix = matrix/norm  
    return matrix

# gives and array starting from -2 and ending at 13
array = np.arange(16) - 2  
# converts 1d array to a matrix
matrix = array.reshape(4, 4)  
print("Simple Matrix \n", matrix)
normalized_matrix = normalize_2d(matrix)
print("\nSimple Matrix \n", normalized_matrix)