NUMERICAL PYTHON : scientific computing and data science applications with numpy, scipy and... matplotlib

Learn how to leverage the scientific computing and data analysis capabilities of Python, its standard library, and popular open-source numerical Python packages like NumPy, SymPy, SciPy, matplotlib, and more. This book demonstrates how to work with mathematical modeling and solve problems with numerical, symbolic, and visualization techniques. It explores applications in science, engineering, data analytics, and more. Numerical Python, Third Edition, presents many case study examples of applications in fundamental scientific computing disciplines, as well as in data science and statistics. This fully revised edition, updated for each library's latest version, demonstrates Python's power for rapid development and exploratory computing due to its simple and high-level syntax and many powerful libraries and tools for computation and data analysis. After reading this book, readers will be familiar with many computing techniques, including array-based and symbolic computing, visualization and numerical file I/O, equation solving, optimization, interpolation and integration, and domain-specific computational problems, such as differential equation solving, data analysis, statistical modeling, and machine learning. What You'll Learn• Work with vectors and matrices using NumPy• Review Symbolic computing with SymPy• Plot and visualize data with Matplotlib• Perform data analysis tasks with Pandas and SciPy• Understand statistical modeling and machine learning with statsmodels and scikit-learn• Optimize Python code using Numba and Cython Who This Book Is ForDevelopers who want to understand how to use Python and its ecosystem of libraries for scientific computing and data analysis. Table of Contents About the Author About the Technical Reviewer Introduction Chapter 1: Introduction to Computing with Python Environments for Computing with Python Python Interpreter IPython Console Input and Output Caching Autocompletion and Object Introspection Documentation Interaction with the System Shell IPython Extensions File System Navigation Running Scripts from the IPython Console Debugger Reset Timing and Profiling Code Interpreter and Text Editor as Development Environment Jupyter The Jupyter QtConsole The Jupyter Notebook Jupyter Lab Cell Types Editing Cells Markdown Cells Rich Output Display nbconvert HTML PDF Python Spyder: An Integrated Development Environment Source Code Editor Consoles in Spyder Object Inspector Summary Further Reading Chapter 2: Vectors, Matrices, and Multidimensional Arrays Importing the Modules The NumPy Array Object Data Types Real and Imaginary Parts Order of Array Data in Memory Creating Arrays Arrays Created from Lists and Other Array-Like Objects Arrays Filled with Constant Values Arrays Filled with Incremental Sequences Arrays Filled with Logarithmic Sequences Meshgrid Arrays Creating Uninitialized Arrays Creating Arrays with Properties of Other Arrays Creating Matrix Arrays Indexing and Slicing One-Dimensional Arrays Multidimensional Arrays Views Fancy Indexing and Boolean-Valued Indexing Reshaping and Resizing Vectorized Expressions Arithmetic Operations Elementwise Functions Aggregate Functions Boolean Arrays and Conditional Expressions Set Operations Operations on Arrays Matrix and Vector Operations Summary Further Reading Chapter 3: Symbolic Computing Importing SymPy Symbols Numbers Integer Float Rational Constants and Special Symbols Functions Expressions Manipulating Expressions Simplification Expand Factor, Collect, and Combine Apart, Together, and Cancel Substitutions Numerical Evaluation Calculus Derivatives Integrals Series Limits Sums and Products Equations Linear Algebra Summary Further Reading Chapter 4: Plotting and Visualization Importing Modules Getting Started Interactive and Noninteractive Modes Figure Axes Plot Types Line Properties Legends Text Formatting and Annotations Axis Properties Axis Labels and Titles Axis Range Axis Ticks, Tick Labels, and Grids Log Plots Twin Axes Spines Advanced Axes Layouts Insets Subplots Subplot2grid GridSpec Colormap Plots 3D Plots Summary Further Reading Chapter 5: Equation Solving Importing Modules Linear Equation Systems Square Systems Rectangular Systems Eigenvalue Problems Nonlinear Equations Univariate Equations Systems of Nonlinear Equations Summary Further Reading Chapter 6: Optimization Importing Modules Classification of Optimization Problems Univariate Optimization Unconstrained Multivariate Optimization Nonlinear Least Square Problems Constrained Optimization Linear Programming Summary Further Reading Chapter 7: Interpolation Importing Modules Interpolation Polynomials Polynomial Interpolation Spline Interpolation Multivariate Interpolation Summary Further Reading Chapter 8: Integration Importing Modules Numerical Integration Methods Numerical Integration with SciPy Tabulated Integrand Multiple Integration Symbolic and Arbitrary-Precision Integration Line Integrals Integral Transforms Summary Further Reading Chapter 9: Ordinary Differential Equations Importing Modules Ordinary Differential Equations Symbolic Solution to ODEs Direction Fields Solving ODEs Using Laplace Transformations Numerical Methods for Solving ODEs Numerical Integration of ODEs Using SciPy Summary Further Reading Chapter 10: Sparse Matrices and Graphs Importing Modules Sparse Matrices in SciPy Functions for Creating Sparse Matrices Sparse Linear Algebra Functions Linear Equation Systems Eigenvalue Problems Graphs and Networks Summary Further Reading Chapter 11: Partial Differential Equations Importing Modules Partial Differential Equations Finite-Difference Methods Finite-Element Methods Survey of FEM Libraries Solving PDEs Using FEniCS Summary Further Reading Chapter 12: Data Processing and Analysis Importing Modules Introduction to Pandas Series DataFrame Time Series The Seaborn Graphics Library Summary Further Reading Chapter 13: Statistics Importing Modules Review of Statistics and Probability Random Numbers Random Variables and Distributions Hypothesis Testing Nonparametric Methods Summary Further Reading 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 Chapter 15: Machine Learning Importing Modules Brief Review of Machine Learning Regression Classification Clustering Summary Further Reading Chapter 16: Bayesian Statistics Importing Modules Introduction to Bayesian Statistics Model Definition Sampling Posterior Distributions Linear Regression Summary Further Reading Chapter 17: Signal Processing Importing Modules Spectral Analysis Fourier Transforms Frequency-Domain Filter Windowing Spectrogram Signal Filters Convolution Filters FIR and IIR Filters Summary Further Reading Chapter 18: Data Input and Output Importing Modules Comma-Separated Values HDF5 h5py Files Groups Datasets Attributes PyTables Pandas HDFStore Parquet JSON Serialization Summary Further Reading Chapter 19: Code Optimization Importing Modules Numba Cython Summary Further Reading Appendix: Installation Miniconda and Conda Jupyter Notebook Kernel Registration A Complete Environment Summary Further Reading Index Learn how to leverage the scientific computing and data analysis capabilities of Python, its standard library, and popular open-source numerical Python packages like NumPy, SymPy, SciPy, matplotlib, and more. This book demonstrates how to work with mathematical modeling and solve problems with numerical, symbolic, and visualization techniques. It explores applications in science, engineering, data analytics, and more. Numerical Python, Third Edition , presents many case study examples of applications in fundamental scientific computing disciplines, as well as in data science and statistics. This fully revised edition, updated for each library's latest version, demonstrates Python's power for rapid development and exploratory computing due to its simple and high-level syntax and many powerful libraries and tools for computation and data analysis. After reading this book, readers will be familiar with many computing techniques, including array-based and symbolic computing, visualization and numerical file I/O, equation solving, optimization, interpolation and integration, and domain-specific computational problems, such as differential equation solving, data analysis, statistical modeling, and machine learning. What You'll Learn Work with vectors and matrices using NumPy Review Symbolic computing with SymPy Plot and visualize data with Matplotlib Perform data analysis tasks with Pandas and SciPy Understand statistical modeling and machine learning with statsmodels and scikit-learn Optimize Python code using Numba and Cython Who This Book Is For Developers who want to understand how to use Python and its ecosystem of libraries for scientific computing and data analysis.