NumPy Arrays and Operations

# CHAPTER 11

NumPy Arrays and Operations #

1. Chapter Introduction #

2. Array Indexing and Slicing (1D) #

Indexing a 1D NumPy array works exactly like a standard Python list. It is zero-indexed, and slicing uses the [start:stop:step] syntax.

import numpy as np

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

# Indexing
print(arr[0])   # 10
print(arr[-1])  # 50 (Last item)

# Slicing
print(arr[1:4]) # [20 30 40]
print(arr[:3])  # [10 20 30]

3. Matrix Indexing and Slicing (2D) #

Machine learning heavily utilizes 2D arrays (Rows and Columns). The syntax is matrix[rowindex, columnindex].

# Create a 3x3 matrix
matrix = np.array([
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
])

# 1. Accessing a single element (Row 0, Col 2)
print(matrix[0, 2]) # 3

# 2. Accessing a whole row (Row 1, All Columns)
print(matrix[1, :]) # [4 5 6]

# 3. Accessing a whole column (All Rows, Col 2)
print(matrix[:, 2]) # [3 6 9]

# 4. Slicing a sub-matrix (Rows 0-1, Cols 1-2)
print(matrix[0:2, 1:3])
# [[2 3]
#  [5 6]]

4. Boolean Indexing (Filtering) #

You can filter arrays using conditions. This is one of the most powerful features in data science.

ages = np.array([15, 22, 17, 30, 45, 12])

# Creates a boolean array: [False, True, False, True, True, False]
is_adult = ages >= 18

# Pass the boolean array back into the brackets to filter!
adults = ages[is_adult]

print(adults) # [22 30 45]

# Shorthand (Very common)
print(ages[ages >= 18]) 

5. Reshaping Arrays #

Machine learning models often require data in a very specific shape (e.g., a 1D list must be converted into a 2D column). We use .reshape().

# A 1D array of 6 items
arr_1d = np.array([1, 2, 3, 4, 5, 6])

# Reshape into 2 Rows, 3 Columns
arr_2d = arr_1d.reshape(2, 3)
print(arr_2d)

# Reshape into 6 Rows, 1 Column (-1 tells NumPy to calculate the rows automatically)
column_vector = arr_1d.reshape(-1, 1)
print(column_vector)

6. Mathematical and Aggregation Functions #

NumPy replaces the need for loops by providing highly optimized statistical functions.

data = np.array([
    [10, 20],
    [30, 40]
])

# Aggregate the ENTIRE matrix
print("Total Sum:", np.sum(data)) # 100
print("Mean:", np.mean(data))     # 25.0
print("Max:", np.max(data))       # 40

# Aggregate by Axis
# axis=0 means operate down the COLUMNS
print("Sum of Columns:", np.sum(data, axis=0)) # [40 60]

# axis=1 means operate across the ROWS
print("Sum of Rows:", np.sum(data, axis=1))    # [30 70]

7. Mini Project: Matrix Calculator #

Let's say we have an array of daily sales (Row 1 is Product A, Row 2 is Product B) over 3 days.

sales = np.array([
    [100, 150, 120], # Product A sales
    [200, 180, 210]  # Product B sales
])

# 1. Total revenue overall
print(f"Total Revenue: ${np.sum(sales)}")

# 2. Total revenue per product (sum across the rows)
prod_totals = np.sum(sales, axis=1)
print(f"Prod A Total: ${prod_totals[0]} | Prod B Total: ${prod_totals[1]}")

# 3. Best day overall (sum down the columns, then find max)
daily_totals = np.sum(sales, axis=0)
best_day_idx = np.argmax(daily_totals)
print(f"Best Day was Day {best_day_idx + 1} with ${daily_totals[best_day_idx]}")

8. Common Mistakes #

• Confusing axis=0 and axis=1: Remember: axis=0 crushes the rows (calculating down the columns). axis=1 crushes the columns (calculating across the rows).

• Reshaping to impossible dimensions: If you have an array of 5 items, you cannot .reshape(2, 3) because 2*3=6. The total number of elements must remain identical.

9. MCQs #

10. Interview Questions #

• Q: Explain how Boolean Indexing works in NumPy. Write a line of code to extract all negative numbers from an array.

• Q: You have a 2D matrix. Explain the difference between np.sum(matrix, axis=0) and np.sum(matrix, axis=1).

11. Summary #

12. Next Chapter Recommendation #