Mastering Python Scientific Computing: A complete guide for Python programmers to master scientific computing using Python APIs and tools

Table of Contents

Mastering Python Scientific Computing

Credits

About the Author

About the Reviewers

www.PacktPub.com

Support files, eBooks, discount offers, and more

Why subscribe?

Free access for Packt account holders

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Downloading the example code

Downloading the color images of this book

Errata

Piracy

Questions

1. The Landscape of Scientific Computing – and Why Python?

Definition of scientific computing

A simple flow of the scientific computation process

Examples from scientific/engineering domains

A strategy for solving complex problems

Approximation, errors, and associated concepts and terms

Error analysis

Conditioning, stability, and accuracy

Backward and forward error analysis

Is it okay to ignore these errors?

Computer arithmetic and floating-point numbers

The background of the Python programming language

The guiding principles of the Python language

Why Python for scientific computing?

Compact and readable code

Holistic language design

Free and open source

Language interoperability

Portable and extensible

Hierarchical module system

Graphical user interface packages

Data structures

Python's testing framework

Available libraries

The downsides of Python

Summary

2. A Deeper Dive into Scientific Workflows and the Ingredients of Scientific Computing Recipes

Mathematical components of scientific computations

A system of linear equations

A system of nonlinear equations

Optimization

Interpolation

Extrapolation

Numerical integration

Numerical differentiation

Differential equations

The initial value problem

The boundary value problem

Random number generator

Python scientific computing

Introduction to NumPy

The SciPy library

The SciPy Subpackage

Data analysis using pandas

A brief idea of interactive programming using IPython

IPython parallel computing

IPython Notebook

Symbolic computing using SymPy

The features of SymPy

Why SymPy?

The plotting library

Summary

3. Efficiently Fabricating and Managing Scientific Data

The basic concepts of data

Data storage software and toolkits

Files

Structured files

Unstructured files

Database

Possible operations on data

Scientific data format

Ready-to-use standard datasets

Data generation

Synthetic data generation (fabrication)

Using Python's built-in functions for random number generation

Bookkeeping functions

Functions for integer random number generation

Functions for sequences

Statistical-distribution-based functions

Nondeterministic random number generator

Designing and implementing random number generators based on statistical distributions

A program with simple logic to generate five-digit random numbers

A brief note about large-scale datasets

Summary

4. Scientific Computing APIs for Python

Numerical scientific computing in Python

The NumPy package

The ndarrays data structure

File handling

Some sample NumPy programs

The SciPy package

The optimization package

The interpolation package

Integration and differential equations in SciPy

The stats module

Clustering package and spatial algorithms in SciPy

Image processing in SciPy

Sample SciPy programs

Statistics using SciPy

Optimization in SciPy

Image processing using SciPy

Symbolic computations using SymPy

Computer Algebra System

Features of a general-purpose CAS

A brief idea of SymPy

Core capability

Polynomials

Calculus

Solving equations

Discrete math

Matrices

Geometry

Plotting

Physics

Statistics

Printing

SymPy modules

Simple exemplary programs

Basic symbol manipulation

Expression expansion in SymPy

Simplification of an expression or formula

Simple integrations

APIs and toolkits for data analysis and visualization

Data analysis and manipulation using pandas

Important data structures of pandas

Special features of pandas

Data visualization using matplotlib

Interactive computing in Python using IPython

Sample data analysis and visualization programs

Summary

5. Performing Numerical Computing

The NumPy fundamental objects

The ndarray object

The attributes of an array

Basic operations on arrays

Special operations on arrays (shape change and conversion)

Classes associated with arrays

The matrix sub class

Masked array

The structured/recor array

The universal function object

Attributes

Methods

Various available ufunc

The NumPy mathematical modules

Introduction to SciPy

Mathematical functions in SciPy

Advanced modules/packages

Integration

Signal processing (scipy.signal)

Fourier transforms (scipy.fftpack)

Spatial data structures and algorithms (scipy.spatial)

Optimization (scipy.optimize)

Interpolation (scipy.interpolate)

Linear algebra (scipy.linalg)

Sparse eigenvalue problems with ARPACK

Statistics (scipy.stats)

Multidimensional image processing (scipy.ndimage)

Clustering

Curve fitting

File I/O (scipy.io)

Summary

6. Applying Python for Symbolic Computing

Symbols, expressions, and basic arithmetic

Equation solving

Functions for rational numbers, exponentials, and logarithms

Polynomials

Trigonometry and complex numbers

Linear algebra

Calculus

Vectors

The physics module

Hydrogen wave functions

Matrices and Pauli algebra

The quantum harmonic oscillator in 1-D and 3-D

Second quantization

High-energy Physics

Mechanics

Pretty printing

LaTeX Printing

The cryptography module

Parsing input

The logic module

The geometry module

Symbolic integrals

Polynomial manipulation

Sets

The simplify and collect operations

Summary

7. Data Analysis and Visualization

Matplotlib

The architecture of matplotlib

The scripting layer (pyplot)

The artist layer

The backend layer

Graphics with matplotlib

Output generation

The pandas library

Series

DataFrame

Panel

The common functionality among the data structures

Time series and date functions

Handling missing data

I/O operations

Working on CSV files

Ready-to-eat datasets

The pandas plotting

IPython

The IPython console and system shell

The operating system interface

Nonblocking plotting

Debugging

IPython Notebook

Summary

8. Parallel and Large-scale Scientific Computing

Parallel computing using IPython

The architecture of IPython parallel computing

The components of parallel computing

The IPython engine

The IPython controller

IPython view and interfaces

The IPython client

Example of performing parallel computing

A parallel decorator

IPython's magic functions

Activating specific views

Engines and QtConsole

Advanced features of IPython

Fault-tolerant execution

Dynamic load balancing

Pushing and pulling objects between clients and engines

Database support for storing the requests and results

Using MPI in IPython

Managing dependencies among tasks

Functional dependency

Decorators for functional dependency

Graph dependency

Impossible dependencies

The DAG dependency and the NetworkX library

Using IPython on an Amazon EC2 cluster with StarCluster

A note on security of IPython

Well-known parallel programming styles

Issues in parallel programming

Parallel programming

Concurrent programming

Distributed programming

Multiprocessing in Python

Multithreading in Python

Hadoop-based MapReduce in Python

Spark in Python

Summary

9. Revisiting Real-life Case Studies

Scientific computing applications developed in Python

The one Laptop per Child project used Python for their user interface

ExpEYES – eyes for science

A weather prediction application in Python

An aircraft conceptual designing tool and API in Python

OpenQuake Engine

SMS Siemag AG application for energy efficiency

Automated code generator for analysis of High-energy Physics data

Python for computational chemistry applications

Python for developing a Blind Audio Tactile Mapping System

TAPTools for air traffic control

Energy-efficient lights with an embedded system

Scientific computing libraries developed in Python

A maritime designing API by Tribon

Molecular Modeling Toolkit

Standard Python packages

Summary

10. Best Practices for Scientific Computing

The best practices for designing

The implementation of best practices

The best practices for data management and application deployment

The best practices to achieving high performance

The best practices for data privacy and security

Testing and maintenance best practices

General Python best practices

Summary

Index

Mastering Python Scientific Computing

Mastering Python Scientific Computing

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.

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First published: September 2015

Production reference: 1180915

Published by Packt Publishing Ltd.

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ISBN 978-1-78328-882-3

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Credits

Author

Hemant Kumar Mehta

Reviewers

Austen Groener

Sachin R. Joglekar

Commissioning Editor

Kartikey Pandey

Acquisition Editor

Kevin Colaco

Content Development Editor

Arshiya Umer

Technical Editor

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Indexer

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Graphics

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Cover Work

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About the Author

Hemant Kumar Mehta is a distributed and scientific computing enthusiast. He has more than 13 years of experience of teaching, research, and software development. He received his BSc (in computer science) Hons., master of computer applications degree, and PhD in computer science from Devi Ahilya University, Indore, India in 1998, 2001, and 2011, respectively. He has experience of working in diverse international environments as a software developer in MNCs. He is a post-doctorate fellow at an international university of high reputation.

Hemant has published more than 20 highly cited research papers in reputed national and international conferences and journals sponsored by ACM, IEEE, and Springer. He is the author of Getting Started with Oracle Public Cloud, Packt Publishing. He is also the coauthor of a book named Internet and Web Technology, published by Kaushal Prakashan Mandir, Indore.

He earned his PhD in the field of cloud computing and big data. Hemant is a member of ACM (Special Interest Group on High-performance Computing Education: SIGHPC-Edu), senior member of IEEE (the computer society, STC on cloud computing, and the big data technical committee), and a senior member of IACSIT, IAENG, and MIR Labs.

I am extremely thankful to my PhD supervisors, namely Professor Priyesh Kanungo and the late Professor Manohar Chandwani from Devi Ahilya University. Their words work as continuous guiding lights in my career and life.

I express heartfelt thanks to my dear student and friend, Pawan Pawar, for helping me develop some programs for this book.

I am also thankful to the entire Packt Publishing team and the reviewers for their tremendous support in maintaining the highest quality of work in this book.

Most of all, I thank my family. I am infinitely grateful to my parents. I thank my wife, Priya, and darling sons, Luv and Darsh, for whom this acknowledgement cannot be covered in words.

About the Reviewers

Austen Groener was raised in Southfield, Massachusetts, USA. He completed his BA in physics from Hartwick College and went on to pursue his MS and PhD in physics from Drexel University in Philadelphia, Pennsylvania, USA. He is a reputed astrophysicist, with research interests surrounding the detailed distribution of dark matter within the largest objects in the universe—galaxy clusters. When he is not studying the cosmos, he enjoys spending his free time developing software tools for other astronomers to use. Austen has a newfound interest in web development.

I would like to thank my family and friends for their unwavering support. To my wife, Brittany: you are the love of my life, my best friend, and my inspiration.

Sachin R. Joglekar is a computer science graduate from BITS-Pilani (Goa campus) in India. His areas of interest primarily include machine learning and intelligent systems. He graduated in December 2014. Since then, he has been working as the cofounder of a start-up based in Mumbai. His work involves the design and development of server infrastructure and backend analytics for sensor networks. Sachin has also worked as an open source developer for SymPy, a symbolic computing library written in pure Python. His work at Google Summer of Code 2014 involved developing the vector module for SymPy.

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To my parents and my gurus, Late Prof. Manohar Chandwani and Prof. Priyesh Kanungo

Preface

This book covers the Python APIs and toolkits used to perform scientific computing. It is highly recommended for readers who perform computerized engineering or scientific computations. Scientific computing is an interdisciplinary branch that requires a background in computer science, mathematics, general science (at least any one branch out of physics, chemistry, environmental science, biology, and others), and engineering. Python consists of a large number of packages, APIs, and toolkits for supporting the functionalities required by these diverse scientific and engineering domains.

A large community of users, lots of help and documentation, a large collection of scientific libraries and environments, great performance, and good support make Python a great choice for scientific computing.

What this book covers

Chapter 1, The Landscape of Scientific Computing – and Why Python?, introduces the basic concepts of scientific computing. It also discusses the background of Python, its guiding principle, and why using Python for scientific computing is efficient.

Chapter 2, A Deeper Dive into Scientific Workflows and the Ingredients of Scientific Computing Recipes, discusses the various concepts of mathematical and numerical analysis that are generally required to solve scientific problems. It also covers a brief introduction to the packages, toolkits, and APIs meant for performing scientific computing in the Python language.

Chapter 3, Efficiently Fabricating and Managing Scientific Data, discusses all the aspects about the underlying data of scientific applications, including the basic concepts, various operations, and the formats and software used to store data. It also presents standard datasets and techniques of preparing synthetic data.

Chapter 4, Scientific Computing APIs for Python, covers the basic concepts, features, and selected sample programs of various scientific computing APIs and toolkits, including NumPy, SciPy, and SymPy. A basic introduction to interactive computing, data analysis, and data visualization is also discussed in this chapter using IPython, matplotlib, and pandas.

Chapter 5, Performing Numerical Computing, discusses how to perform numerical computations using the NumPy and SciPy packages of Python. This chapter starts with the basics of numerical computation and covers a number of advanced concepts, such as optimization, interpolation, Fourier transformation, signal processing, linear algebra, statistics, spatial algorithms, image processing, file input/output, and others.

Chapter 6, Applying Python for Symbolic Computing, starts with the fundamentals of the Computerized Algebra System (CAS) and performing symbolic computations using SymPy. It covers a vast range of topics on CAS, from using simple expressions and basic arithmetic to advanced concepts of mathematics and physics.

Chapter 7, Data Analysis and Visualization, presents the concepts and applications of matplotlib and pandas for data analysis and visualization.

Chapter 8, Parallel and Large-scale Scientific Computing, discusses the concepts of high-performance scientific computing using IPython (which is done using MPI), the management of the Amazon EC2 cluster using StarCluster, multiprocessing, multithreading, Hadoop, and Spark.

Chapter 9, Revisiting Real-life Case Studies, illustrates several case studies of scientific computing applications, libraries, and tools developed using the Python language. Some cases studied from various engineering and science domains are presented in this chapter.

Chapter 10, Best Practices for Scientific Computing, discusses the best practices for scientific computing. It consists of the best practices for designing, coding, data management, application deployment, high-performance computing, security, data privacy, maintenance, and support. We also cover the best practices for general Python-based development.

What you need for this book

The example programs given in this book require a computer with Python 2.7.9 or a higher version, and several Python APIs/packages/toolkits. You will also require some Python libraries (namely NumPy, SciPy, SymPy, matplotlib, pandas, IPython), the IPython.parallel package, pyzmq, SSH for security (if necessary), and Hadoop.

Who this book is for

The book is intended for Python programmers willing to get hands-on exposure to scientific computing. The book expects that you have had exposure to various concepts of Python programming.

Conventions

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: The functions of the random module are bound methods of a hidden instance of the random.Random class.

A block of code is set as follows:

import random

print random.random()

print random.uniform(1,9)

print random.randrange(20)

print random.randrange(0, 99, 3)

print random.choice('ABCDEFGHIJKLMNOPQRSTUVWXYZ') # Output 'P'

items = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

random.shuffle(items)

print items

print random.sample([1, 2, 3, 4, 5, 6, 7, 8, 9, 10],  5) 

weighted_choices = [('Three', 3), ('Two', 2), ('One', 1), ('Four', 4)]

population = [val for val, cnt in weighted_choices for i in range(cnt)]

print random.choice(population)

Note

Warnings or important notes appear in a box like this.

Tip

Tips and tricks appear like this.

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Chapter 1. The Landscape of Scientific Computing – and Why Python?

Using computerized mathematical modeling and numerical analysis techniques to analyze and solve problems in the science and engineering domains is called scientific computing. Scientific problems include problems from various branches of science, such as earth science, space science, social science, life science, physical science, and formal science. These branches cover almost all the science domains that exist, from traditional science to modern engineering science, such as computer science. Engineering problems include problems from civil and electrical to (the latest) biomedical engineering.

In this chapter, we will cover the following topics:

Fundamentals of scientific computing

The flow of the scientific computation process

Examples from scientific and engineering domains

The strategy to solve complex problems

Approximation, errors, and related terms

Concepts of error analysis

Computer arithmetic and floating-point numbers

A background of Python

Why choose Python for scientific computing?

Mathematical modeling refers to