Python NumPy nonzero() Function

In NumPy, the nonzero() function is used to return the indices (the index numbers or index positions) of the elements that are non-zero in a given array. It is particularly useful when you want to find the indices of non-zero elements in an array without actually iterating through the array manually. It returns a tuple of arrays, one for each dimension of arr, containing the indices of the non-zero elements in that dimension.

1. Quick Examples of NumPy nonzero() Function

If you are in a hurry, below are some quick examples of how to use Python NumPy nonzero() function. For more creators of ndarray refer NumPy Tutorial.

# Quick examples of nonzero() function

# Example 1: Indices of non zero elements 
arr = np.array([8, 23, 45, 0, 60, 0, 85, 0, 101])
arr2 = np.nonzero(arr)

# Example 2: All nonzero elements
arr3 = arr[arr2]

# Example 3: Index of all elements 
# Which are greater than 50
arr2 = np.nonzero(arr > 50)

# Example 4: Use nonzero() function to 2-d array 
arr = np.array([[4, 0, 0], [0, 6, 0], [-7, 15, 0]])
arr2 = np.nonzero(arr)

# Example 5: Get the corresponding non-zero number                
arr3 = arr[np.nonzero(arr)]

# Example 6: Use numpy.transpose() function
# To indices of non-zero number 
arr = np.array([[4, 0, 0], [0, 6, 0], [-7, 15, 0]])             
arr3 = np.transpose(np.nonzero(arr))

2. Syntax of NumPy nonzero()

Following is the syntax to create numpy.nonzero() function.

# Python numpy.nonzero() Syntax
numpy.nonzero(arr)

2.1 Parameters of NumPy nonzeros()

• arr : This is the input array. It can be a 1-dimensional or multi-dimensional array.

2.2 Return Value

It returns Indices of elements that are non-zero.

3. Get Indices of nonzero Elements Use nonzero()

If you want to directly get the indices of non-zero elements using numpy.nonzero() function. Here, arr2 is a tuple containing one array, which represents the indices of the non-zero elements in the original array arr. The output indicates that non-zero elements are at positions 0, 1, 2, 4, 6, and 8 in the array. You can also use NumPy nonzero() function to get the index of all elements which are non-zero.

# Import numpy
import numpy as np

# Create one-dimensional array with nonzero
arr = np.array([8, 23, 45, 0, 60, 0, 85, 0, 101])
print("Original array:\n",arr)

# Indices of non zero elements  
arr2 = np.nonzero(arr)
print("Indices of non-zero elements:\n",arr2)

# Output:
# Original array:
#  [  8  23  45   0  60   0  85   0 101]
# Indices of non-zero elements:
# (array([0, 1, 2, 4, 6, 8], dtype=int64),)

# All nonzero elements
arr3 = arr[arr2]
print("All nonzero elements:\n", arr3)

Yields below output.

To find the indices of elements in a NumPy array that are greater than 50, you can use boolean indexing. Here, arr2 is a tuple containing one array, which represents the indices of elements in the original array arr that are greater than 50. The output indicates that elements greater than 50 are at positions 4, 6, and 8 in the array.

# Index of all elements which are greater than 50
arr2 = np.nonzero(arr > 50)
print("Indices of elements greater than 50:\n",arr2)

# Output:
# Indices of elements greater than 50:
# (array([4, 6, 8], dtype=int64),)

4. Use nonzero() Function to 2-D Array

You can use the numpy.nonzero() function to find the indices of non-zero elements in a two-dimensional NumPy array. For instance, the first array represents the row indices, and the second array represents the column indices of the non-zero elements in the original two-dimensional array arr.

import numpy as np

# Create two-dimensional array with nonzero
arr = np.array([[4, 0, 0], [0, 6, 0], [-7, 15, 0]])

# Use nonzero() function to 2-d array 
arr2 = np.nonzero(arr)
print("Indices of non-zero elements:\n",arr2)

# Output:
Indices of non-zero elements:
(array([0, 1, 2, 2], dtype=int64), array([0, 1, 0, 1], dtype=int64))

# Get the corresponding non-zero number                
arr3 = arr[np.nonzero(arr)]
print("All nonzero elements:\n", arr3) 

# Output:
# All nonzero elements:
#  [ 4  6 -7 15]

If you want to access the non-zero elements directly, you can use these indices. Now, arr3 contains the values of the non-zero elements in the original two-dimensional array.

5. Use numpy.transpose() Function to Indices of non-zero Number

To use numpy.transpose() to get the indices of non-zero elements in a 2D array, you can first use numpy.nonzero() to obtain the indices and then transpose the result.

In the below example, arr2 is a tuple containing two arrays representing the row and column indices of non-zero elements. Using numpy.transpose(), you transpose these indices, so each row now represents a pair of (row, column) indices for the non-zero elements in the original array.

# Create two-dimensional array with nonzero
arr = np.array([[4, 0, 0], [0, 6, 0], [-7, 15, 0]])

# Use numpy.transpose() function to indices of non-zero number 
arr2 = np.transpose(np.nonzero(arr))
print("Transposed indices of non-zero elements:\n",arr2)

# Output:
# Transposed indices of non-zero elements:
#  [[0 0]
#  [1 1]
#  [2 0]
#  [2 1]]

Frequently Asked Questions

Conclusion

In this article, I have explained how to use Python NumPy nonzero() function using indices of elements that are non-zero with examples.

Happy Learning!!

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References

• https://numpy.org/doc/stable/reference/generated/numpy.nonzero.html