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by Robert Johansson
Numerical Python : A Practical Techniques Approach for Industry
Cover
Title
Copyright
Dedication
Contents at a Glance
Contents
About the Author
About the Technical Reviewer
Introduction
Chapter 1: Introduction to Computing with Python
1.1 Environments for Computing with Python
1.2 Python
1.2.1 Interpreter
1.3 IPython Console
1.3.1 Input and Output Caching
1.3.2 Autocompletion and Object Introspection
1.3.3 Documentation
1.3.4 Interaction with the System Shell
1.3.5 IPython Extensions
1.3.6 The IPython Qt Console
1.4 IPython Notebook
1.4.1 Cell Types
1.4.2 Editing Cells
1.4.3 Markdown Cells
1.4.4 nbconvert
1.5 Spyder: An Integrated Development Environment
1.5.1 Source Code Editor
1.5.2 Consoles in Spyder
1.5.3 Object Inspector
1.6 Summary
1.7 Further Reading
1.8 References
Chapter 2: Vectors, Matrices, and Multidimensional Arrays
2.1 Importing NumPy
2.2 The NumPy Array Object
2.2.1 Data Types
2.2.2 Order of Array Data in Memory
2.3 Creating Arrays
2.3.1 Arrays Created from Lists and Other Array-like Objects
2.3.2 Arrays Filled with Constant Values
2.3.3 Arrays Filled with Incremental Sequences
2.3.4 Arrays Filled with Logarithmic Sequences
2.3.5 Mesh-grid Arrays
2.3.6 Creating Uninitialized Arrays
2.3.7 Creating Arrays with Properties of Other Arrays
2.3.8 Creating Matrix Arrays
2.4 Indexing and Slicing
2.4.1 One-dimensional Arrays
2.4.2 Multidimensional Arrays
2.4.3 Views
2.4.4 Fancy Indexing and Boolean-valued Indexing
2.5 Reshaping and Resizing
2.6 Vectorized Expressions
2.6.1 Arithmetic Operations
2.6.2 Elementwise Functions
2.6.3 Aggregate Functions
2.6.4 Boolean Arrays and Conditional Expressions
2.6.5 Set Operations
2.6.6 Operations on Arrays
2.7 Matrix and Vector Operations
2.8 Summary
2.9 Further Reading
2.10 References
Chapter 3: Symbolic Computing
3.1 Importing SymPy
3.2 Symbols
3.2.1 Numbers
3.3 Expressions
3.4 Manipulating Expressions
3.4.1 Simplification
3.4.2 Expand
3.4.3 Factor, Collect, and Combine
3.4.4 Apart, Together, and Cancel
3.4.5 Substitutions
3.5 Numerical Evaluation
3.6 Calculus
3.6.1 Derivatives
3.6.2 Integrals
3.6.3 Series
3.6.4 Limits
3.6.5 Sums and Products
3.7 Equations
3.8 Linear Algebra
3.9 Summary
3.10 Further Reading
3.11 References
Chapter 4: Plotting and Visualization
4.1 Importing Matplotlib
4.2 Getting Started
4.2.1 Interactive and Noninteractive Modes
4.3 Figure
4.4 Axes
4.4.1 Plot Types
4.4.2 Line Properties
4.4.3 Legends
4.4.4 Text Formatting and Annotations
4.4.5 Axis Properties
4.5 Advanced Axes Layouts
4.5.1 Insets
4.5.2 Subplots
4.5.3 Subplot2grid
4.5.4 GridSpec
4.6 Colormap Plots
4.7 3D plots
4.8 Summary
4.9 Further Reading
4.10 References
Chapter 5: Equation Solving
5.1 Importing Modules
5.2 Linear Equation Systems
5.2.1 Square Systems
5.2.2 Rectangular Systems
5.3 Eigenvalue Problems
5.4 Nonlinear Equations
5.4.1 Univariate Equations
5.4.2 Systems of Nonlinear Equations
5.5 Summary
5.6 Further Reading
5.7 References
Chapter 6: Optimization
6.1 Importing Modules
6.2 Classification of Optimization Problems
6.3 Univariate Optimization
6.4 Unconstrained Multivariate Optimization
6.5 Nonlinear Least Square Problems
6.6 Constrained Optimization
6.6.1 Linear Programming
6.7 Summary
6.8 Further Reading
6.9 References
Chapter 7: Interpolation
7.1 Importing Modules
7.2 Interpolation
7.3 Polynomials
7.4 Polynomial Interpolation
7.5 Spline Interpolation
7.6 Multivariate Interpolation
7.7 Summary
7.8 Further Reading
7.9 References
Chapter 8: Integration
8.1 Importing Modules
8.2 Numerical Integration Methods
8.3 Numerical Integration with SciPy
8.3.1 Tabulated Integrand
8.4 Multiple Integration
8.5 Symbolic and Arbitrary-Precision Integration
8.6 Integral Transforms
8.7 Summary
8.8 Further Reading
8.9 References
Chapter 9: Ordinary Differential Equations
9.1 Importing Modules
9.2 Ordinary Differential Equations
9.3 Symbolic Solution to ODEs
9.3.1 Direction Fields
9.3.2 Solving ODEs using Laplace Transformations
9.4 Numerical Methods for Solving ODEs
9.5 Numerical Integration of ODEs using SciPy
9.6 Summary
9.7 Further Reading
9.8 References
Chapter 10: Sparse Matrices and Graphs
10.1 Importing Modules
10.2 Sparse Matrices in SciPy
10.2.1 Functions for Creating Sparse Matrices
10.2.2 Sparse Linear Algebra Functions
10.2.3 Linear Equation Systems
10.3
10.4 Summary
10.5 Further Reading
10.6 References
Chapter 11: Partial Differential Equations
11.1 Importing Modules
11.2 Partial Differential Equations
11.3 Finite-Difference Methods
11.4 Finite-Element Methods
11.4.1 Survey of FEM Libraries
11.5 Solving PDEs using FEniCS
11.6 Summary
11.7 Further Reading
11.8 References
Chapter 12: Data Processing and Analysis
Importing Modules
Introduction to Pandas
Series
DataFrame
Time Series
The Seaborn Graphics Library
Summary
Further Reading
References
Chapter 13: Statistics
Importing Modules
Review of Statistics and Probability
Random Numbers
Random Variables and Distributions
Hypothesis Testing
Nonparametric Methods
Summary
Further Reading
References
Chapter 14: Statistical Modeling
Importing Modules
Introduction to Statistical Modeling
Defining Statistical Models with Patsy
Linear Regression
Example Datasets
Discrete Regression
Logistic Regression
Poisson Model
Time Series
Summary
Further Reading
References
Chapter 15: Machine Learning
Importing Modules
Brief Review of Machine Learning
Regression
Classification
Clustering
Summary
Further Reading
References
Chapter 16: Bayesian Statistics
Importing Modules
Introduction to Bayesian Statistics
Model Definition
Sampling Posterior Distributions
Linear Regression
Summary
Further Reading
References
Chapter 17: Signal Processing
Importing Modules
Spectral Analysis
Fourier Transforms
Windowing
Spectogram
Signal Filters
Convolution Filters
FIR and IIR Filters
Summary
Further Reading
References
Chapter 18: Data Input and Output
Importing Modules
Comma-Separated Values
HDF5
h5py
PyTables
Pandas HDFStore
JSON
Serialization
Summary
Further Reading
References
Chapter 19: Code Optimization
Importing Modules
Numba
Cython
Summary
Further Reading
References
Appendix A Installation
Miniconda and Conda
A Complete Environment
Summary
Further Reading
Index
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Numerical Python
A Practical Techniques Approach for Industry
Robert Johansson
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