NumPy for Numerical Computation: A Comprehensive Guide

1. Introduction to NumPy

NumPy (Numerical Python) is the foundation of numerical computing in Python. It provides efficient and fast operations on large datasets using multi-dimensional arrays and mathematical functions. It is widely used in data science, machine learning, scientific computing, and financial analysis.

✅ Why Use NumPy?
✔ Faster than Python lists (uses C-based optimizations)
✔ Supports multi-dimensional arrays (ndarrays)
✔ Provides vectorized operations (avoids loops)
✔ Contains advanced mathematical and statistical functions
✔ Essential for machine learning, deep learning, and AI

📌 Use Cases of NumPy:

Mathematical and statistical operations (mean, median, variance, etc.)
Matrix operations (dot product, inverse, eigenvalues, etc.)
Image processing (pixels as numerical arrays)
Financial computations (stock prices, risk calculations)
Machine learning & AI (data preprocessing, model building)

2. Installing NumPy

To install NumPy, use the following command:

pip install numpy

📌 Verify Installation:

import numpy as np
print(np.__version__)

3. Creating NumPy Arrays

NumPy arrays (ndarrays) are more efficient than Python lists.

A. Creating a 1D Array

import numpy as np

# Creating a NumPy array from a list
arr = np.array([1, 2, 3, 4, 5])
print(arr)

📌 Key Features:
✔ Supports homogeneous data types
✔ Uses contiguous memory allocation (faster operations)

B. Creating Multi-Dimensional Arrays (2D & 3D)

# 2D Array (Matrix)
arr_2d = np.array([[1, 2, 3], [4, 5, 6]])
print(arr_2d)

# 3D Array
arr_3d = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
print(arr_3d)

📌 Shapes:
✔ 1D Array → (n,)
✔ 2D Array → (rows, columns)
✔ 3D Array → (depth, rows, columns)

C. Creating Arrays with Default Values

NumPy provides built-in functions to create arrays with predefined values:

# Array of zeros
zeros = np.zeros((3, 3))
print(zeros)

# Array of ones
ones = np.ones((2, 2))
print(ones)

# Identity Matrix
identity = np.eye(3)
print(identity)

# Random Numbers (0 to 1)
random_vals = np.random.rand(3, 3)
print(random_vals)

📌 Use Cases:
✔ Zeros & Ones → Placeholders for algorithms
✔ Identity Matrix → Used in linear algebra
✔ Random Numbers → Monte Carlo simulations, AI

4. NumPy Array Properties

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

# Shape of the array
print(arr.shape)  # (2, 3)

# Data type
print(arr.dtype)  # int32 or int64

# Number of elements
print(arr.size)   # 6

# Number of dimensions
print(arr.ndim)   # 2

📌 Key Insights:
✔ shape → Tells rows & columns
✔ dtype → Data type (int, float, etc.)
✔ size → Total elements
✔ ndim → Number of dimensions

5. Indexing & Slicing NumPy Arrays

A. Accessing Elements

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

# Accessing elements
print(arr[0])  # First element (10)
print(arr[-1]) # Last element (50)

B. Slicing Arrays

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

# Slicing
print(arr[1:4])   # [20, 30, 40]
print(arr[:3])    # [10, 20, 30]
print(arr[-3:])   # [30, 40, 50]

C. Indexing in 2D Arrays

arr_2d = np.array([[10, 20, 30], [40, 50, 60]])

# Access element at row index 1, column index 2
print(arr_2d[1, 2])  # 60

# Access entire row
print(arr_2d[0, :])  # [10, 20, 30]

# Access entire column
print(arr_2d[:, 1])  # [20, 50]

6. Mathematical Operations with NumPy

NumPy supports element-wise operations for fast computation.

A. Basic Arithmetic

arr = np.array([1, 2, 3, 4])

print(arr + 2)  # [3, 4, 5, 6]
print(arr * 3)  # [3, 6, 9, 12]
print(arr ** 2) # [1, 4, 9, 16]

B. Matrix Operations

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

# Matrix Addition
print(A + B)

# Matrix Multiplication
print(A @ B)

# Element-wise Multiplication
print(A * B)

📌 Use Cases:
✔ Matrix operations → Used in machine learning & AI
✔ Dot product → Essential in neural networks

7. Statistical Functions in NumPy

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

# Mean
print(np.mean(arr))  # 30.0

# Median
print(np.median(arr))  # 30.0

# Standard Deviation
print(np.std(arr))  # 14.14

# Variance
print(np.var(arr))  # 200.0

📌 Use Cases:
✔ Mean & Median → Measure of central tendency
✔ Standard Deviation & Variance → Measure of spread

8. Reshaping & Flattening NumPy Arrays

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

# Reshape (2x3 to 3x2)
reshaped = arr.reshape((3, 2))
print(reshaped)

# Flatten (convert to 1D array)
flattened = arr.flatten()
print(flattened)

📌 Reshaping is crucial for:
✔ Data preprocessing
✔ Feeding input into machine learning models

9. Saving & Loading NumPy Arrays

arr = np.array([1, 2, 3, 4])

# Save array
np.save("my_array.npy", arr)

# Load array
loaded_arr = np.load("my_array.npy")
print(loaded_arr)

📌 Why Save Arrays?
✔ Avoid recomputation
✔ Store large datasets efficiently

10. Summary

✔ NumPy is the backbone of numerical computing in Python.
✔ ndarrays are faster than Python lists.
✔ Supports mathematical, statistical, and matrix operations.
✔ Essential for data science, AI, and machine learning.

📌 Next Steps:
✅ Learn Pandas for data manipulation
✅ Use NumPy with Scikit-learn for machine learning
✅ Work on real-world datasets

Need hands-on exercises? Let me know!