NumPy Mastery

A Complete Guide to Numerical Computing in Python

Introduction

Chapter 1: Why NumPy - The Foundation of Scientific Python

1. The Problem with Python Lists for Numbers
2. Enter NumPy - A Brief History from Numeric to NumPy
3. Installing and Verifying Your Setup
4. Your First Array - A Taste of What’s Coming
5. How This Book Is Organized

Chapter 2: The ndarray - Understanding NumPy’s Core Data Structure

1. What Is an ndarray?
2. Dimensions, Shape and Rank
3. Data Types - The dtype System
4. Memory Layout - Contiguous Arrays in C
5. Views Versus Copies - A Critical Distinction
6. Inspecting Your Arrays

Chapter 3: Creating Arrays - From Scratch and From Data

1. From Python Lists and Tuples
2. Generating Sequences with arange and linspace
3. Filled Arrays - zeros, ones, empty, full
4. Random Initialization Basics
5. Identity Matrices and Diagonal Arrays
6. From Files and External Data
7. Converting Between Types and Shapes During Creation

Chapter 4: Indexing and Slicing - Accessing Array Elements

1. Basic Integer Indexing
2. Slicing - The start:stop:step Pattern
3. Multi-dimensional Indexing and Slicing
4. Boolean Indexing and Masking
5. Fancy Indexing with Arrays of Indices
6. Combining Indexing Strategies
7. Common Pitfalls and Gotchas

Chapter 5: Reshaping, Stacking and Splitting - Rearranging Data

1. Reshape and resize
2. Flatten, Ravel and Squeeze
3. Transpose and Axis Swapping
4. Stacking Arrays - vstack, hstack, concatenate
5. Splitting and Partitioning Arrays
6. Broadcasting - The Key to Elegant Array Code
7. When Operations Return Views Versus Copies

Chapter 6: Vectorization and Universal Functions - Writing Fast NumPy Code

1. The Cost of Python Loops
2. What Is Vectorization?
3. Universal Functions - Element-wise Operations
4. Arithmetic and Comparison Ufuncs
5. Logical Operations on Arrays
6. Reducing Dimensionality with Aggregations
7. Writing Your Own Vectorized Code

Chapter 7: Mathematical and Statistical Computing

1. Basic Arithmetic and Powers
2. Trigonometric and Exponential Functions
3. Rounding, Clipping and Modulo Operations
4. Summarizing Data - Mean, Median, Variance, Standard Deviation
5. Correlation and Covariance
6. Percentiles and Quantiles
7. Handling Numerical Precision

Chapter 8: Sorting, Searching and Set Operations

1. Sorting Arrays - sort and argsort
2. Partial Sorting with Partition
3. Searching for Values - where, argwhere, searchsorted
4. Finding Unique Elements
5. Set Operations - union, intersection, difference
6. Comparing Arrays for Equality and Approximation

Chapter 9: Random Number Generation - The np.random Module

1. Why Randomness Matters in Scientific Computing
2. The Modern Generator API - default_rng
3. Seeding for Reproducibility
4. Common Distributions - Uniform, Normal, Poisson
5. Discrete and Specialized Distributions
6. Generating Random Samples Without Replacement
7. Best Practices and Common Mistakes

Chapter 10: Linear Algebra with NumPy

1. Matrix Multiplication - dot, matmul and the @ Operator
2. Transpose, Conjugate and Special Matrices
3. Solving Linear Systems
4. Determinants, Trace and Rank
5. Eigendecomposition
6. Singular Value Decomposition (SVD)
7. Condition Numbers and Numerical Stability

Chapter 11: Handling Missing Data and Special Values

1. What Are NaN and Infinity?
2. Detecting Special Values
3. nan-aware Functions - nansum, nanmean, etc.
4. Masked Arrays for Complex Missing Data Patterns
5. Replacing and Cleaning Special Values
6. Design Decisions Behind NumPy’s Approach

Chapter 12: Performance Optimization and Memory Efficiency

1. Understanding Strides and Memory Layout
2. C-contiguous Versus Fortran-contiguous Arrays
3. Avoiding Unnecessary Copies
4. In-place Operations
5. Vectorization Strategies for Complex Problems
6. Profiling NumPy Code
7. When to Use Numba or Cython Alongside NumPy

Chapter 13: Advanced Topics and Power User Patterns

1. Structured Arrays and Record Arrays
2. Memory-mapped Files for Huge Datasets
3. Advanced Indexing Patterns
4. Subclassing ndarray
5. Type Annotations with NumPy Arrays
6. The NumPy API Design Philosophy

Chapter 14: NumPy in the Ecosystem - Working with Other Libraries

1. NumPy and pandas - Arrays Underneath DataFrames
2. NumPy and SciPy - From Foundations to Specialized Functions
3. NumPy and Matplotlib - Plotting Arrays Directly
4. NumPy and scikit-learn - The Array Interface
5. Interoperability Patterns Across Libraries
6. Choosing the Right Tool for the Job

Conclusion

References