NumPy: Reshaping and Dimensions 🧱

The LEGO Brick Analogy

Imagine you have a box of LEGO bricks. You can arrange them in a single long line, stack them in a flat rectangle, or build a tall tower. The same bricks, just arranged differently!

NumPy arrays work exactly like this. You can reshape them—change how they’re organized—without changing the actual data inside.

1. Reshaping with reshape() 🔄

What is it? reshape() lets you rearrange your array into a new shape. Think of it as taking your LEGO line and reorganizing it into rows and columns.

The Golden Rule: The total number of elements must stay the same!

import numpy as np

# 12 bricks in a line
bricks = np.array([1, 2, 3, 4, 5, 6,
                   7, 8, 9, 10, 11, 12])

# Reshape into 3 rows, 4 columns
grid = bricks.reshape(3, 4)
print(grid)

Output:

[[ 1  2  3  4]
 [ 5  6  7  8]
 [ 9 10 11 12]]

Why does this work? 12 bricks = 3 rows × 4 columns = 12. The math checks out!

graph TD
    A["[1,2,3,4,5,6,7,8,9,10,11,12]"] --> B["reshape#40;3,4#41;"]
    B --> C["3 rows × 4 columns"]

2. The Magic -1: Let NumPy Figure It Out 🧙‍♂️

What if you’re lazy? (We all are!)

Use -1 and NumPy will calculate that dimension for you.

# 12 elements, want 4 columns
# How many rows? Let NumPy decide!
result = bricks.reshape(-1, 4)
print(result.shape)  # (3, 4)

# Want 3 rows, unknown columns?
result2 = bricks.reshape(3, -1)
print(result2.shape)  # (3, 4)

Think of -1 as saying: “Hey NumPy, you’re smart. Figure out this part for me!”

Important: You can only use ONE -1 per reshape. NumPy can solve for one unknown, not two!

3. Flattening Arrays: Back to a Line 📏

Sometimes you want to undo all that shaping and get back to a simple line of numbers.

Three Ways to Flatten:

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

# Method 1: flatten() - always a copy
flat1 = grid.flatten()
print(flat1)  # [1 2 3 4 5 6]

# Method 2: ravel() - usually a view
flat2 = grid.ravel()
print(flat2)  # [1 2 3 4 5 6]

# Method 3: reshape(-1)
flat3 = grid.reshape(-1)
print(flat3)  # [1 2 3 4 5 6]

When to use what?

• Need a safe copy? Use flatten()
• Need speed? Use ravel() or reshape(-1)

4. Transposing Arrays: Flip the Grid! 🔃

Transpose swaps rows and columns. What was a row becomes a column!

matrix = np.array([[1, 2, 3],
                   [4, 5, 6]])
print("Original shape:", matrix.shape)
# (2, 3) - 2 rows, 3 columns

transposed = matrix.T
print("Transposed shape:", transposed.shape)
# (3, 2) - 3 rows, 2 columns

print(transposed)

Output:

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

graph TD
    A["Original: 2×3"] --> B[".T"]
    B --> C["Transposed: 3×2"]
    D["Rows ↔ Columns"]

Three ways to transpose:

matrix.T           # Shortcut
matrix.transpose() # Full method
np.transpose(matrix)  # Function

5. Swapping and Moving Axes 🎯

For arrays with 3 or more dimensions, you might want to rearrange specific axes.

swapaxes() - Swap Two Axes

# 3D array: 2 layers, 3 rows, 4 columns
cube = np.arange(24).reshape(2, 3, 4)
print("Original:", cube.shape)  # (2, 3, 4)

# Swap axis 0 and axis 2
swapped = cube.swapaxes(0, 2)
print("Swapped:", swapped.shape)  # (4, 3, 2)

moveaxis() - Move One Axis to New Position

# Move axis 0 to position 2
moved = np.moveaxis(cube, 0, 2)
print("Moved:", moved.shape)  # (3, 4, 2)

Real-world example: Image data often comes as (batch, height, width, channels). Some libraries want (batch, channels, height, width). Use moveaxis to convert!

6. Adding Dimensions: Make It Bigger! 📦

Sometimes you need to add an extra dimension to your array. It’s like putting your LEGO creation in a box.

Method 1: np.newaxis

line = np.array([1, 2, 3])
print("Original:", line.shape)  # (3,)

# Add dimension at start
row = line[np.newaxis, :]
print("Row vector:", row.shape)  # (1, 3)

# Add dimension at end
column = line[:, np.newaxis]
print("Column vector:", column.shape)  # (3, 1)

Method 2: np.expand_dims()

line = np.array([1, 2, 3])

# Add axis at position 0
expanded = np.expand_dims(line, axis=0)
print(expanded.shape)  # (1, 3)

# Add axis at position 1
expanded2 = np.expand_dims(line, axis=1)
print(expanded2.shape)  # (3, 1)

Why add dimensions?

• Broadcasting requires matching dimensions
• Neural networks expect specific input shapes
• Matrix multiplication rules

7. Squeeze: Remove Extra Dimensions 🧹

The opposite of adding dimensions! squeeze() removes dimensions that have size 1.

# Array with unnecessary dimensions
bulky = np.array([[[1, 2, 3]]])
print("Bulky shape:", bulky.shape)  # (1, 1, 3)

# Remove all size-1 dimensions
slim = bulky.squeeze()
print("Slim shape:", slim.shape)  # (3,)

# Remove specific axis
specific = np.squeeze(bulky, axis=0)
print("Specific:", specific.shape)  # (1, 3)

graph TD
    A["#40;1, 1, 3#41;"] --> B["squeeze#40;#41;"]
    B --> C["#40;3,#41;"]
    D["Removes size-1 dims"]

Warning: squeeze() won’t remove dimensions larger than 1!

Quick Summary Table 📊

The Big Picture 🎯

Think of your NumPy array as clay:

1. Reshape = Mold it into different forms
2. Flatten = Roll it back into a snake
3. Transpose = Flip it over
4. Swap/Move axes = Rotate in 3D space
5. Add dimensions = Put it in a box
6. Squeeze = Take it out of the box

The data stays the same. Only the organization changes!

Practice Challenge 🏆

Can you predict the output?

arr = np.arange(24)
result = arr.reshape(2, 3, -1)
print(result.shape)

Answer: (2, 3, 4) because 24 ÷ (2 × 3) = 4!

You now have the power to reshape any NumPy array. Go forth and mold your data! 🚀