In this tutorial, you will learn how to access elements in a NumPy array using indexing techniques, including 1-D, 2-D, and 3-D arrays.

Indexing in 1-D Arrays

NumPy arrays use square bracket notation ([]) similar to Python lists for accessing elements.

Example:

import numpy as np

a = np.arange(0, 5)
print(a)         # [0 1 2 3 4]

print(a[0])      # 0 (first element)
print(a[1])      # 1 (second element)
print(a[-1])     # 4 (last element)
print(a[-2])     # 3 (second last element)

  • Positive indices start from 0.

  • Negative indices start from -1 (last element) and go backward.

Indexing in 2-D Arrays

For 2-D arrays, you need two indices: one for the row (first axis) and another for the column (second axis).

Example:

import numpy as np

a = np.array([
    [1, 2, 3],
    [4, 5, 6]
])

print(a.shape)     # (2, 3)

print(a[0])        # [1 2 3] - first row
print(a[1])        # [4 5 6] - second row

print(a[0, 0])     # 1
print(a[1, 0])     # 4
print(a[0, 2])     # 3
print(a[1, 2])     # 6
print(a[0, -1])    # 3 (last element in first row)
print(a[1, -1])    # 6 (last element in second row)

How it works:

  • a[0] returns the first row: [1 2 3]

  • a[0, 2] selects the third element from the first row: 3

  • a[1, -1] selects the last element from the second row: 6

Indexing in 3-D Arrays

For 3-D arrays, use three indices: one for each axis.

Example:

import numpy as np

a = np.array([
    [[1, 2], [3, 4], [5, 6]],
    [[5, 6], [7, 8], [9, 10]]
])

print(a.shape)     # (2, 3, 2)
print(a[0, 0, 1])   # 2

How it works:

  • a[0] returns:

    [[1, 2], [3, 4], [5, 6]]

  • a[0, 0] returns:

    [1, 2]

  • a[0, 0, 1] returns:

    2

Summary

  • Use square brackets [] to index NumPy arrays.

  • Positive indices count from the beginning (0-based).

  • Negative indices count from the end (-1 is the last element).

  • For multi-dimensional arrays, use a tuple of indices to access nested elements.

  • a[i, j] is used for 2-D arrays, and a[i, j, k] for 3-D arrays.

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