The idea of writing Mastering SciPy arose but 2 months after publishing Learning SciPy for Numerical and Scientific Computing. During a presentation of that book at the University of South Carolina, I had the privilege of speaking about its contents to a heterogeneous audience of engineers, scientists, and students, each of them with very different research problems and their own set of preferred computational resources. In the weeks following that presentation, I helped a few professionals transition to a SciPy-based environment. During those sessions, we discussed how SciPy is, under the hood, the same set of algorithms (and often the same code) that they were already using. We experimented with some of their examples and systematically obtained comparable performance. We immediately saw the obvious benefit of a common environment based upon a robust scripting language. Through the SciPy stack, we discovered an easier way to communicate and share our results with colleagues, students, or employers. In all cases, the switch to the SciPy stack provided a faster setup for our groups, where newcomers could get up to speed quickly.
Everybody involved in the process went from novice to advanced user, and finally mastered the SciPy stack in no time. In most cases, the scientific background of the individuals with whom I worked made the transition seamless. The process toward mastering materialized when they were able to contrast the theory behind their research with the solutions offered. The aha moment always happened while replicating some of their experiments with a careful guidance and explanation of the process.
That is precisely the philosophy behind this book. I invite you to participate in similar sessions. Each chapter has been envisioned as a conversation with an individual with certain scientific needs expressed as numerical computations. Together, we discover relevant examples—the different possible ways to solve those problems, the theory behind them, and the pros and cons of each route.
The process of writing followed a similar path to obtain an engaging collection of examples. I entered into conversations with colleagues in several different fields. Each section clearly reflects these exchanges. This was crucial while engaged in the production of the most challenging chapters—the last four. To ensure the same quality throughout the book, always trying to commit to a rigorous set of standards, these chapters took much longer to be completed to satisfaction. Special mentions go to Aaron Dutle at NASA Langley Research Center, who helped shape parts of the chapter on computational geometry, and Parsa Bakhtary, a data analyst at Facebook, who inspired many of the techniques in the chapter on applications of statistical computing to data analysis.
It was an amazing journey that helped deepen my understanding of numerical methods, broadened my perspective in problem solving, and strengthened my scientific maturity. It is my wish that it has the same impact on you.
Chapter 1, Numerical Linear Algebra, presents an overview of the role of matrices to solve problems in scientific computing. It is a crucial chapter for understanding most of the processes and ideas of subsequent chapters. You will learn how to construct and store large matrices effectively in Python. We then proceed to reviewing basic manipulation and operations on them, followed by factorizations, solutions of matrix equations, and the computation of eigenvalues/eigenvectors.
Chapter 2, Interpolation and Approximation, develops advanced techniques to approximate functions, and their applications to scientific computing. This acts as a segway for the next two chapters.
Chapter 3, Differentiation and Integration, explores the different techniques to produce derivatives of functions and, more importantly, how to compute areas and volumes effectively by integration processes. This is the first of two chapters devoted to the core of numerical methods in scientific computing. This second part is also an introduction to Chapter 5, Initial Value Problems for Ordinary Differential Equations that mentions ordinary differential equations.
Chapter 4, Nonlinear Equations and Optimization, is a very technical chapter in which we discuss the best methods of obtaining the roots and extrema of systems of functions depending on the kinds of functions involved.
Chapter 5, Initial Value Problems for Ordinary Differential Equations, is the first of five chapters on applications to real-world problems. We show you, by example, the most popular techniques to solve systems of differential equations, as well as some applications.
Chapter 6, Computational Geometry, takes a tour of the most significant algorithms in this branch of computer science.
Chapter 7, Descriptive Statistics, is the first of two chapters on statistical computing and its applications to Data Analysis. In this chapter, we focus on probability and data exploration.
Chapter 8, Inference and Data Analysis, is the second chapter on Data Analysis. We focus on statistical inference, machine learning, and data mining.
Chapter 9, Mathematical Imaging, is the last chapter of this book. In it, we explore techniques for image compression, edition, restoration, and analysis.
To work with the examples and try out the code of this book, all you need is a recent version of Python (2.7 or higher) with the SciPy stack: NumPy, the SciPy library, matplotlib, IPython, pandas, and SymPy. Although recipes to install all these independently are provided throughout the book, we recommend that you perform a global installation through a scientific Python distribution such as Anaconda.
Although this book and technology are ultimately intended for applied mathematicians, engineers, and computer scientists, the material presented here is targeted at a broader audience. All that is needed is proficiency in Python, familiarity with iPython, some knowledge of the numerical methods in scientific computing, and a keen interest in developing serious applications in science, engineering, or data analysis.
In this book, you will find a number of text styles that distinguish between different kinds of information. Here are some examples of these styles and an explanation of their meaning.
Code words in text, database table names, folder names, filenames, file extensions, pathnames, dummy URLs, user input, and Twitter handles are shown as follows: "We can include other contexts through the use of the include directive."
Any command-line input or output is written as follows:
In [7]: %time eigvals, v = spspla.eigsh(A, 5, which='SM') CPU times: user 19.3 s, sys: 532 ms, total: 19.8 s Wall time: 16.7 s In [8]: print eigvals [ 10.565523 10.663114 10.725135 10.752737 10.774503]
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