ch8s1_WhatIsNumPy

**NumPy** (short for *Numerical Python*) is the core library for **numerical and scientific computing** in Python.

Chapter 8: Introduction to NumPy

Sub-Chapter: What is NumPy? — The Foundation of Numerical Computing

NumPy (short for Numerical Python) is the core library for numerical and scientific computing in Python.
It provides fast, memory-efficient multi-dimensional arrays (ndarray) and a rich set of mathematical, statistical, and linear algebra functions.

NumPy powers almost every data and scientific library in Python — including Pandas, Matplotlib, SciPy, and scikit-learn.

⚙️ 1. Why NumPy?

Python lists are flexible but slow and inefficient for numerical computation. NumPy arrays are:

• Fast (implemented in optimized C)
• Memory-efficient (homogeneous data types)
• Vectorized (no Python loops needed)

Example — List vs. NumPy Array

import numpy as np
import time

# Using Python list
data_list = list(range(1_000_000))
start = time.time()
sum_list = [x * 2 for x in data_list]
print("List time:", time.time() - start)

# Using NumPy array
data_array = np.arange(1_000_000)
start = time.time()
sum_array = data_array * 2
print("NumPy time:", time.time() - start)

🧠 NumPy performs element-wise operations using compiled code — up to 100x faster than Python lists.

🧩 2. Importing NumPy

By convention, NumPy is imported as np:

import numpy as np

🧱 3. Core Concept — The ndarray

An ndarray (n-dimensional array) is NumPy’s main data structure.
It stores homogeneous data in contiguous memory blocks.

arr = np.array([[1, 2, 3], [4, 5, 6]])
print(arr.ndim)   # Number of dimensions
print(arr.shape)  # Shape (2, 3)
print(arr.dtype)  # Data type

Visual Representation

[[1, 2, 3],
 [4, 5, 6]]
   ↑
  Rows → 2D array (2 × 3)

🧮 4. Creating Arrays

NumPy provides many functions to create arrays efficiently:

a = np.array([1, 2, 3])           # From list
zeros = np.zeros((2, 3))          # All zeros
ones = np.ones((3, 3))            # All ones
range_array = np.arange(0, 10, 2) # Like range()
linspace = np.linspace(0, 1, 5)   # 5 equally spaced values
identity = np.eye(3)              # Identity matrix
randoms = np.random.rand(2, 2)    # Random 2×2 array

🔢 5. Array Operations — Vectorization

NumPy supports vectorized operations, applying mathematical operations directly to arrays.

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

print(a + b)  # [5 7 9]
print(a * b)  # [4 10 18]
print(a ** 2) # [1 4 9]

Element-wise Operations

🧠 6. Universal Functions (ufuncs)

NumPy provides optimized vectorized functions that operate on entire arrays.

arr = np.array([0, np.pi/2, np.pi])

print(np.sin(arr))   # [0. 1. 0.]
print(np.log([1, np.e, np.e**2]))  # [0. 1. 2.]
print(np.sqrt([1, 4, 9]))          # [1. 2. 3.]

Ufuncs eliminate the need for loops and automatically handle broadcasting.

🔁 7. Indexing, Slicing, and Boolean Masking

You can extract elements, slices, or conditions from arrays efficiently.

matrix = np.array([[10, 20, 30], [40, 50, 60], [70, 80, 90]])

print(matrix[0, 1])     # 20
print(matrix[:, 2])     # [30 60 90]
print(matrix[1:, :2])   # [[40 50], [70 80]]

# Boolean masking
mask = matrix > 50
print(matrix[mask])     # [60 70 80 90]

📊 8. Broadcasting — Smart Arithmetic

NumPy allows operations between arrays of different shapes using broadcasting rules.

matrix = np.array([[1, 2, 3], [4, 5, 6]])
vector = np.array([10, 20, 30])

print(matrix + vector)

Output:

[[11 22 33]
 [14 25 36]]

Broadcasting Visualization

Matrix (2×3)
[[1, 2, 3],
 [4, 5, 6]]
+
Vector (1×3)
[10, 20, 30]
↓
[[11, 22, 33],
 [14, 25, 36]]

NumPy automatically expands smaller arrays to match dimensions.

🧮 9. Real-World Example — Normalizing Data

data = np.array([10, 20, 30, 40, 50])
mean = np.mean(data)
std = np.std(data)
normalized = (data - mean) / std

print(normalized)

🧾 10. Common Array Creation Functions

💡 11. Performance and Memory Efficiency

🧭 12. Summary

NumPy transforms Python into a high-performance mathematical platform. Mastering it unlocks the foundation for data science, AI, and scientific computing.

🧠 Practice Ideas

• Create and manipulate arrays with various shapes.
• Use ufuncs (np.exp, np.log, np.sqrt) for computation.
• Implement normalization and matrix operations.
• Visualize broadcasting behavior with different shapes.