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- Herausgeber: Packt Publishing
- Kategorie: Fachliteratur
- Sprache: Englisch
The SciPy stack is a collection of open source libraries of the powerful scripting language Python, together with its interactive shells. This environment offers a cutting-edge platform for numerical computation, programming, visualization and publishing, and is used by some of the world’s leading mathematicians, scientists, and engineers. It works on any operating system that supports Python and is very easy to install, and completely free of charge! It can effectively transform into a data-processing and system-prototyping environment, directly rivalling MATLAB and Octave.
This book goes beyond a mere description of the different built-in functions coded in the libraries from the SciPy stack. It presents you with a solid mathematical and computational background to help you identify the right tools for each problem in scientific computing and visualization. You will gain an insight into the best practices with numerical methods depending on the amount or type of data, properties of the mathematical tools employed, or computer architecture, among other factors.
The book kicks off with a concise exploration of the basics of numerical linear algebra and graph theory for the treatment of problems that handle large data sets or matrices. In the subsequent chapters, you will delve into the depths of algorithms in symbolic algebra and numerical analysis to address modeling/simulation of various real-world problems with functions (through interpolation, approximation, or creation of systems of differential equations), and extract their representing features (zeros, extrema, integration or differentiation).
Lastly, you will move on to advanced concepts of data analysis, image/signal processing, and computational geometry.
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Seitenzahl: 428
Veröffentlichungsjahr: 2015
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Table of Contents
Mastering SciPy
Mastering SciPy
Copyright © 2015 Packt Publishing
All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior written permission of the publisher, except in the case of brief quotations embedded in critical articles or reviews.
Every effort has been made in the preparation of this book to ensure the accuracy of the information presented. However, the information contained in this book is sold without warranty, either express or implied. Neither the author, nor Packt Publishing, and its dealers and distributors will be held liable for any damages caused or alleged to be caused directly or indirectly by this book.
Packt Publishing has endeavored to provide trademark information about all of the companies and products mentioned in this book by the appropriate use of capitals. However, Packt Publishing cannot guarantee the accuracy of this information.
First published: November 2015
Production reference: 1301015
Published by Packt Publishing Ltd.
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Birmingham B3 2PB, UK.
ISBN 978-1-78398-474-9
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Credits
Author
Francisco J. Blanco-Silva
Reviewers
Raiyan Kamal
Kristen Thyng
Patrick Varilly
Jonathan Whitmore
Commissioning Editor
Kartikey Pandey
Acquisition Editor
Shaon Basu
Content Development Editor
Nikhil Potdukhe
Technical Editor
Bharat Patil
Copy Editors
Tani Kothari
Merilyn Pereira
Project Coordinator
Judie Jose
Proofreader
Safis Editing
Indexer
Tejal Soni
Production Coordinator
Aparna Bhagat
Cover Work
Aparna Bhagat
About the Author
Francisco J. Blanco-Silva is the owner of a scientific consulting company called Tizona Scientific Solutions, a faculty member of the Department of Mathematics, and an associate member of the Interdisciplinary Mathematics Institute at the University of South Carolina. He obtained his formal training as an applied mathematician from Purdue University. He enjoys problem solving, learning, and teaching alike. Being an avid programmer and blogger, when it comes to writing, he relishes finding the common denominator among his passions and skills and making it available to everyone.
He wrote the prequel to this book, Learning SciPy for Numerical and Scientific Computing, Packt Publishing, and coauthored Chapter 5 of the book, Modeling Nanoscale Imaging in Electron Microscopy, Springer.
I will always be indebted to Bradley J. Lucier and Rodrigo Bañuelos for being constant sources of inspiration and for their guidance and teachings. Special thanks to my editors, Sriram Neelakantam, Bharat Patil, Nikhil Potdukhe, Mohammad Rizvi, and the many colleagues who have contributed by giving me encouragement and participating in helpful discussions. In particular, I would like to mention Parsa Bakhtary, Aaron Dutle, Edsel Peña, Pablo Sprechmann, Adam Taylor, and Holly Watson.
The most special thanks, without a doubt, goes to my wife and daughter. Grace's love and smiles alone provided all the motivation, enthusiasm, and skills to overcome the difficulties encountered during the writing of this book and everything that life threw at me ever since she was born.
About the Reviewers
Raiyan Kamal is a strong proponent of the open source movement and everything related to Python. He holds a bachelor's degree in computer science from BUET, Dhaka, Bangladesh, and a master's degree from the University of Windsor, Ontario, Canada. He has been working in the software industry for several years, developing software for mobile, web, and desktop platforms. Although he is in his early thirties, Raiyan feels that his boyhood has not ended yet. He often looks for hidden treasures in science, engineering, programming, art, and nature. He is currently working at IOU Concepts, exploring different ways of saying thank you. When he isn't on a computer, he plants trees and composts kitchen scraps.
Kristen Thyng has worked on scientific computing for most of her career. She has a bachelor's degree in physics from Whitman College, master's degree in applied mathematics from the University of Washington, and PhD in mechanical engineering from the University of Washington. She uses Python on a daily basis for analysis and visualization in physical oceanography at Texas A&M University, where she works as an assistant research scientist.
Jonathan Whitmore is a data scientist at Silicon Valley Data Science. He has a diverse range of interests and is excited by the challenges in data science and data engineering. Before moving into the tech industry, he worked as an astrophysicist in Melbourne, Australia, researching whether the fundamental physical constants have changed over the lifespan of the universe. He has a long-standing commitment to the public's understanding of science and technology, and has contributed to FOSS projects. He co-starred in the 3D IMAX film Hidden Universe, which was playing in theaters around the world at the time of writing this book. Jonathan is a sought-after conference speaker on science and technical topics. He received his PhD in physics from the University of California, San Diego, and graduated magna cum laude from Vanderbilt University with a bachelor's degree in science. He is also a triple major in physics (with honors), philosophy, and mathematics.
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Preface
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.
What this book covers
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.
What you need for this book
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.
Who this book is for
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.
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