🏠 NumPy Indexing & Slicing: Finding Things in Your Treasure Chest

Imagine you have a treasure chest with many compartments. Each compartment holds a gem. To find a specific gem, you need to know where it lives in the chest.

That’s exactly what indexing and slicing do in NumPy! They help you find and grab data from your arrays.

🎯 The Big Picture

📍 Positive Indexing: Counting From the Front Door

Think of a row of houses on a street. The first house is number 0, the next is 1, and so on.

import numpy as np

gems = np.array(['Ruby', 'Emerald', 'Diamond', 'Sapphire'])
#                  0        1          2          3

print(gems[0])   # Ruby
print(gems[2])   # Diamond

Remember: Python starts counting from 0, not 1!

graph TD
    A["gems array"] --> B["Index 0: Ruby"]
    A --> C["Index 1: Emerald"]
    A --> D["Index 2: Diamond"]
    A --> E["Index 3: Sapphire"]

🔙 Negative Indexing: Counting From the Back Door

What if you want the last gem but don’t know how many gems there are?

Use negative numbers! They count from the end.

• -1 = last item
• -2 = second-to-last
• -3 = third-to-last

gems = np.array(['Ruby', 'Emerald', 'Diamond', 'Sapphire'])
#                 -4       -3         -2         -1

print(gems[-1])  # Sapphire (last)
print(gems[-2])  # Diamond (second-to-last)

Super useful when you just want “the last one” without counting!

🏢 Multi-Dimensional Indexing: Finding Rooms in a Building

A 2D array is like a building with floors and rooms.

• First number = which floor (row)
• Second number = which room (column)

building = np.array([
    [101, 102, 103],  # Floor 0
    [201, 202, 203],  # Floor 1
    [301, 302, 303]   # Floor 2
])

print(building[1, 2])  # 203
# Floor 1, Room 2

graph TD
    A["building[1, 2]"] --> B["Go to Floor 1"]
    B --> C["Go to Room 2"]
    C --> D["Found: 203"]

Mix positive and negative too!

print(building[0, -1])  # 103
# Floor 0, last room

✨ Ellipsis: The Magic Shortcut

When you have many dimensions, typing all those commas gets tiring.

The ellipsis (...) means “fill in whatever I skipped.”

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

# These are the same:
print(cube[0, :, :])  # Explicit
print(cube[0, ...])   # With ellipsis
# Both give: [[1, 2], [3, 4]]

Think of ... as saying “and all the rest.”

✂️ Basic Slicing: Grabbing a Range

Slicing lets you grab multiple items at once.

Syntax: array[start:stop]

• start = where to begin (included)
• stop = where to end (NOT included)

numbers = np.array([10, 20, 30, 40, 50, 60])

print(numbers[1:4])  # [20, 30, 40]
# Starts at index 1, stops BEFORE index 4

graph LR
    A["[10, 20, 30, 40, 50, 60]"] --> B["numbers[1:4]"]
    B --> C["[20, 30, 40]"]

Shortcuts:

numbers[:3]   # [10, 20, 30] - from start
numbers[3:]   # [40, 50, 60] - to end
numbers[:]    # Everything!

🦘 Slicing with Step: Skip Like a Kangaroo

Want to grab every other item? Add a step!

Syntax: array[start:stop:step]

numbers = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

print(numbers[::2])    # [0, 2, 4, 6, 8]
# Every 2nd item

print(numbers[1::2])   # [1, 3, 5, 7, 9]
# Every 2nd, starting from index 1

print(numbers[::3])    # [0, 3, 6, 9]
# Every 3rd item

Reverse an array with step -1:

print(numbers[::-1])   # [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]

🏢 Multi-Dimensional Slicing: Slicing the Building

Apply slicing to each dimension separately!

grid = np.array([
    [1, 2, 3, 4],
    [5, 6, 7, 8],
    [9, 10, 11, 12]
])

# Get rows 0-1, columns 1-2
print(grid[0:2, 1:3])
# [[2, 3],
#  [6, 7]]

# All rows, every other column
print(grid[:, ::2])
# [[1, 3],
#  [5, 7],
#  [9, 11]]

graph TD
    A["grid[0:2, 1:3]"] --> B["Rows 0 to 2"]
    B --> C["Columns 1 to 3"]
    C --> D["Result: 2x2 block"]

🧪 Real-World Example

Imagine you have test scores for 4 students across 5 tests:

scores = np.array([
    [85, 90, 78, 92, 88],  # Student 0
    [79, 85, 90, 87, 91],  # Student 1
    [92, 88, 84, 90, 86],  # Student 2
    [76, 82, 79, 85, 88]   # Student 3
])

# Last test for everyone
print(scores[:, -1])   # [88, 91, 86, 88]

# First 2 students, first 3 tests
print(scores[:2, :3])
# [[85, 90, 78],
#  [79, 85, 90]]

# Every other student, all tests
print(scores[::2, :])
# [[85, 90, 78, 92, 88],
#  [92, 88, 84, 90, 86]]

🎓 Quick Summary

💡 Remember This!

1. Indexing starts at 0 — always!
2. Negative indices count backward — -1 is the last
3. Slicing excludes the stop — [1:4] gives indices 1, 2, 3
4. Step lets you skip — [::2] grabs every other
5. Ellipsis = “and all the rest” — saves typing in many dimensions

You now have the keys to unlock any treasure in your NumPy arrays! 🗝️