GNU Octave Beginner's Guide

Table of Contents

GNU Octave

Credits

About the Author

About the Reviewers

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Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Time for action – heading

What just happened?

Pop quiz – heading

Have a go hero – heading

Reader feedback

Customer support

Downloading the example code

Errata

Piracy

Questions

1. Introducing GNU Octave

So what is GNU Octave?

Applications

Limitations of Octave

Octave and MATLAB

The Octave community

Installing Octave

Windows

GNU/Linux

Building Octave from the source under GNU/Linux

Time for action – building Octave from source

What just happened?

Checking your installation with peaks

Time for action – testing with peaks

What just happened?

Customizing Octave

Time for action – creating an Octave home directory under Windows

What just happened?

Creating your first .octaverc file

Time for action – editing the .octaverc file

What just happened?

More on .octaverc

Installing additional packages

Time for action – installing additional packages

What just happened?

Uninstalling a package

Getting help

The behaviour of the Octave command prompt

Summary

2. Interacting with Octave: Variables and Operators

Simple numerical variables

Accessing and changing array elements

More examples

Time for action – manipulating arrays

What just happened?

Complex variables

Text variables

Higher-dimensional arrays

Pop Quiz – working with arrays

Structures and cell arrays

Structures

Time for action – instantiating a structure

What just happened?

Accessing structure fields

Cell arrays

Time for action – instantiating a cell array

What just happened?

Have a go hero – working with structures

Getting information

Time for action – using whos

What just happened?

Size, rows, columns, and length

Identifying the variable type

Deleting variables from the workspace

Pop Quiz – understanding arrays

A few things that make life easier

Basic arithmetic

Addition and subtraction

Time for action – doing addition and subtraction operations

What just happened?

Matrix multiplication

Time for action – doing multiplication operations

What just happened?

Element-by-element, power, and transpose operations

Operators for structures and cell arrays

Solving linear equation systems: left and right division

Time for action – doing left and right division

What just happened?

Basic arithmetic for complex variables

Summary of arithmetic operators

Pop Quiz – understanding simple operations

Have a go hero – doing the dot product

Comparison operators and precedence rules

Precedence rules

Time for action – working with precedence rules

What just happened?

Pop Quiz – understanding precedence rules

A few hints

Summary

3. Working with Octave:Functions and Plotting

Octave functions

Mathematical functions

Time for action – using the cos function

What just happened?

Polynomials in Octave

More complicated mathematical functions

Time for action – putting together mathematical functions

What just happened?

Helper functions

Generating random numbers

min and max

Sorting arrays

find, any, and all

floor, ceil, round, and fix

Time for action – trying out floor, ceil, round, and fix

What just happened?

sum and prod

Absolute values

Complex input arguments

Operator functions

Linear algebra

Time for action – using Octave for advanced linear algebra

What just happened?

Polynomials

Pop Quiz – using simple mathematical functions

Have a go hero – understanding the find function

Two-dimensional plotting

Time for action – making your first plot

What just happened?

plot and set

Time for action – changing the figure properties

What just happened?

Adding lines and text to your plot

Plot styles and colors

Title and legends

Ticks

Grids

fplot

Clear the figure window

Moving on

Time for action – having multiple graphs in the same figure

What just happened?

Multiple figure windows

Subplots

Time for action – making an inset

What just happened?

Saving your plot

Pop Quiz – understanding the plotting options

Have a go hero – making inserts

Three-dimensional plotting

Surface plot

Time for action – making a surface plot

What just happened?

view and colormap

Contour plots

Three-dimensional parametric plots

Time for action – plotting parametric curves

What just happened?

Have a go hero – revisiting peaks

Summary

4. Rationalizing: Octave Scripts

Writing and executing your first script

Time for action – making your first script

What just happened?

Improving your script: input and disp

Time for action – interacting with the user

What just happened?

Flush please

Comments

Very long commands

Workspace

For GNU/Linux and MacOS X users

Pop Quiz – understanding disp and input

Have a go hero – using scripts for plotting

Statements

Prime numbers

Decision making – the if statement

Interlude: Boolean operators

Element-wise Boolean operators

Short-circuit Boolean operators

Using Boolean operators with an if statement

Nested statements

The switch statement

Loops

The for statement

The while and do statements

Incremental operators

Nested loops

Putting it all together

Exception handling

Pop Quiz – understanding statements and Boolean operators

Added flexibility – C style input and output functions

printf

Pop Quiz – printing with printf

Saving your work

Loading your work

Functional forms

Have a go hero – investigating the prime gab

Summary

5. Extensions: Write Your Own Octave Functions

Your first Octave function

Time for action – programming the minmax function

What just happened?

Scripts versus functions

Defining functions at the command prompt

Writing a function help text

Checking the function call

The usage, warning, and error functions

nargin and nargout

Pop Quiz – understanding functions

Have a go hero – converting scripts into functions

Writing and applying user-supplied functions

Using fsolve

Providing the Jacobian

Using lsode – dynamical analysis of the Sel'kov model

Time for action – using lsode for numerical integration

What just happened?

Inline functions

Pop Quiz – implementing mathematical functions as Octave functions

Have a go hero – bifurcation in the Sel'kov model

More advanced function programming: Monte Carlo integration

The feval function

Validating the user-supplied function

Using quad and trapz for numerical integration

Vectorized programming

Time for action – vectorizing the Monte Carlo integrator

What just happened?

Simple debugging

Multiple function file

Pop Quiz – understanding vectorization

Have a go hero – using the debugger

Summary

6. Making Your Own Package: A Poisson Equation Solver

The Poisson equation – two examples of heat conduction

One-dimensional heat conduction

Two-dimensional heat conduction

The Poisson equation

The Dirichlet boundary condition

Pop Quiz – identifying the Poisson equation

Finite differencing

From finite difference to a linear equation system

Interlude: Sparse matrices

Time for action – instantiating a sparse matrix

What just happened?

Memory usage

Implementation and package functions

The coefficient matrix for one dimension

The coefficient matrix for two dimensions

The conversion function

Testing the functions

The coefficient matrices

Time for action – using imagesc

What just happened?

Comparison with analytical solution

Time for action – comparing with analytical solution

What just happened?

Two dimensions

Time for action – solving a two-dimensional Laplace equation

What just happened?

More examples

Wrapping everything into one function

Have a go hero – optimizing the usage of the sparse function

The pois-solv package

Organizing files into the package directory

The DESCRIPTION file

The COPYING file

The INDEX file

Building the package

Limitations and possible extensions to the package

Summary

7. More Examples: Data Analysis

Loading data files

Simple descriptive statistics

Histogram and moments

Sample moments

Comparing data sets

The correlation coefficient

The student t-test

Function fitting

Polynomial fitting

Time for action – using polyfit

What just happened?

Goodness of the fit

Time for action – calculating the correlation coefficient

What just happened?

Residual plot

Non-polynomial fits

Transforms

General least squares fitting

Time for action – using leasqr

What just happened?

Have a go hero – calculating the deviation of the Monte Carlo integrator

Fourier analysis

The Fourier transform

Time for action – using the fft function

What just happened?

Fourier analysis of currency exchange rate

Time for action – analysing the exchange rate

What just happened?

Inverse Fourier transform and data smoothing

The Butterworth filter

Time for action – applying a low pass filter

What just happened?

Have a go hero – implementing your own Fourier transform function

Summary

8. Need for Speed: Optimization and Dynamically Linked Functions

A few optimization techniques

tic, toc

Time for action – using tic and toc

What just happened?

Vectorization

Initialization of variables

Looping row-wise versus looping column-wise

Have a go hero – revision of cmat_1d

Dynamically linked functions

The DEFUN_DLD function macro

Time for action – writing a Hello World program

What just happened?

Managing input arguments and outputs

Time for action – checking user inputs and outputs

What just happened?

Retrieving the inputs

Class types

Functions as input argument

Optimization with oct-files

Time for action – revisiting the Sel'kov model

What just happened

Have a go hero – implementing the Euler integrator

Summary

A. Pop Quiz Answers

Chapter 2: Interacting with Octave: Variables and Operators

Working with arrays

Understanding arrays

Understanding simple operations

Understanding precedence rules

Chapter 3: Working with Octave: Functions and Plotting

Using simple mathematical functions

Understanding the plotting options

Chapter 4: Rationalizing: Octave Scripts

Understanding disp and input

Understanding statements and Boolean operators

Printing with printf

Chapter 5: Extensions: Write Your Own Octave Functions

Understanding functions

Implementing mathematical functions as Octave functions

Understanding vectorization

Chapter 6: Making Your Own Package: A Poisson Equation Solver

Identifying the Poisson equation

Index

GNU Octave

Beginner's Guide

GNU Octave

Beginner's Guide

Copyright © 2011 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, 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: June 2011

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ISBN 978-1-849513-32-6

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Cover Image by John Quick (<[email protected]>)

Credits

Author

Jesper Schmidt Hansen

Reviewers

Piotr Gawron

Kenneth Geisshirt

Jordi Gutiérrez Hermoso

Acquisition Editor

Usha Iyer

Development Editor

Roger D'souza

Technical Editor

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Project Coordinator

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Proofreaders

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Indexers

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Graphics

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Production Coordinator

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Cover Work

Kruthika Bangera

About the Author

Jesper Schmidt Hansen holds a Ph.D. in soft material science and is currently doing research in the field of nanofluidics and dynamics at Roskilde University, Denmark. He has been using GNU Octave on a daily basis for many years, both as a student and later as a researcher. The applications have varied from solving partial and ordinary differential equations, simple data plotting, data generation for other applications, dynamical system investigations, and advanced data analysis.

Firstly, I wish to thank the reviewers. They have been a great help and their many (at times overwhelmingly many) comments and hints have improved the manuscript considerably.

I have received encouragement and good ideas from everyone at the Department of Science, Systems and Models, Roskilde University. Especially, I want to thank Professor Jeppe Dyre from the Danish National Research Foundation centre Glass and Time for giving me the opportunity to finish the book in the last phase of the writing.

Also, I have found Octave's official mailing list very useful. Unlike many other user groups, there is a very constructive and helpful atmosphere here. I thank everyone who has submitted questions and all those that have replied.

I now realize that having a one year old child, a full time job, as well as writing a book is not really an ideal cocktail. I must thank Signe Anthon for her tremendous support and patience during the writing of this book. When I signed the contract with Packt Publishing, I was happy finally to be able to make a contribution to the open source community—Signe's contribution is just as big as mine!

About the Reviewers

Piotr Gawron is a researcher in the field of quantum information processing. His main research topics are quantum programming languages, quantum game theory, and numerical and geometrical methods in quantum information. He works in the Quantum Computer Systems Group of the Institute of Theoretical and Applied Informatics of the Polish Academy of Sciences in Gliwice, Poland. Apart from research in theoretical aspects of computer science, he has gained practical experience in FPGA development and real-time image processing for applications in UAVs working closely with the industry. He is administrator of www.quantiki.org , a portal for the quantum information community. He is a user and strong supporter of free software. He likes hard science-fiction literature, live-action role-playing, and French rock music.

Kenneth Geisshirt is a chemist by education and a geek by nature. He has been programming for more than 25 years—the last 6 years as a subcontractor. In 1990, Kenneth first met free software, and in 1992 turned to Linux as his primary operating system (officially Linux user no. 573 at the Linux Counter). He has written books about Linux, PAM, and JavaScript—and many articles on open source software for computer magazines. Moreover, Kenneth has been a technical reviewer of books on Linux network administration, the Vim editor, and JavaScript testing.

Jordi Gutiérrez Hermoso studied mathematics in Canada and Mexico, both pure and applied respectively. He has been programming since the age of seven, when he started to learn about computers while writing silly programs in BASIC. He has been a Debian user since 2001, his first and still preferred GNU/Linux distribution, to which he now occasionally contributes with GNU Octave packaging. Since 2005, he has been an enthusiastic Octave user and started getting more involved with its development in 2010. As of 2011, he resides in Mexico and works in BlueMessaging, where he's responsible for natural language processing and artificial intelligence. An Emacs user at heart, Jordi feels at home in a GNU environment and will gladly share .emacs configurations with anyone who asks.

I would like to thank my close friends and family for helping me get through difficult times and for celebrating the good ones with me. John W. Eaton, Octave's creator, deserves much recognition for starting and leading the project on which this book is based.

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Preface

Using a range of very different examples, this beginner's guide will take you through the most important aspects of GNU Octave. The book starts by introducing how you work with mathematical objects like vectors and matrices, demonstrating how to perform simple arithmetic operations on these objects and explaining how to use some of the simple functionality that comes with GNU Octave, including plotting. It then goes on to show you how to extend and implement new functionality into GNU Octave, how to make a toolbox package to solve your specific problem, and how to use GNU Octave for complicated data analysis. Finally, it demonstrates how to optimize your code and link GNU Octave with C++ code enabling you to solve even the most computational demanding tasks. After reading GNU Octave Beginner's Guide, you will be able to use and tailor GNU Octave to solve most numerical problems and perform complicated data analysis with ease.

What this book covers

Chapter 1, Introducing GNU Octave briefly introduces you to GNU Octave. It explains how you can install GNU Octave and test your installation. This first chapter also discusses how to customize the appearance and the behavior of GNU Octave as well as how you install additional packages.

Chapter 2, Interacting with Octave: Variables and Operators shows you how to interact with GNU Octave through the interactive environment. Learn to instantiate objects of different types, control their values, and perform simple operations on and between them.

Chapter 3, Working with Octave: Functions and Plotting explains GNU Octave functions and shows several examples of the very useful functionalities that come with GNU Octave. In this chapter, you will see how you can perform two- and three-dimensional plotting, control the graph appearance, how to have multiple plots in the same figure window, and much more.

Chapter 4, Rationalizing: Octave Scripts looks at how you can rationalize your work using scripts. It will teach you how to control the programming flow in your script and how to perform loops using different statements. At the end of the chapter, you are shown how you can save your work and load it back into GNU Octave's workspace.

Chapter 5, Extensions: Write Your Own Octave Functions takes a closer look at functions and teaches how you can write your own GNU Octave functions. You will learn how to control and validate user input to the function. The important concept of vectorization is discussed and an example of this is given in the last part of the chapter.

Chapter 6, Making Your Own Package: A Poisson Equation Solver teaches you how to make your own GNU Octave package from a collection of related functions. The package will be able to solve one- and two-dimensional Poisson equations and is therefore relevant for many problems encountered in science and engineering. In this chapter, you will also learn how to work with sparse matrices in GNU Octave.

Chapter 7, More Examples: Data Analysis shows you examples of how GNU Octave can be used for data analysis. These examples range from simple statistics, through data fitting, to Fourier analysis and data smoothing.

Chapter 8, Need for Speed: Optimization and Dynamically Linked Functions discusses how you can optimize your code. This includes vectorization, partial looping, pre-instantiation of variables, and dynamically linked functions. The main part of the chapter shows how to use GNU Octave's C++ library and how to link this to the GNU Octave interactive environment. Special attention is paid to explaining when and when not to consider using dynamically linked functions.

What you need for this book

If you use Windows, you basically only need to have a full version of GNU Octave installed on your computer. For GNU/Linux, you may need a plotting program like gnuplot, a Fortran and C/C++ compiler like gcc, and the GNU make utility; fortunately these are standard packages on almost all GNU/Linux distributions. In Chapter 1, it will be shown how you install GNU Octave under Windows and GNU/Linux.

Who this book is for

This book is intended for anyone interested in scientific computing and data analysis. The reader should have a good knowledge of mathematics and also a basic understanding of programming will be useful, although it is not a prerequisite.

Conventions

In this book, you will find several headings appearing frequently.

To give clear instructions of how to complete a procedure or task, we use:

Time for action – heading

Action 1

Action 2

Action 3

Instructions often need some extra explanation so that they make sense, so they are followed with:

What just happened?

This heading explains the working of tasks or instructions that you have just completed.

You will also find some other learning aids in the book, including:

Pop quiz – heading

These are short multiple-choice questions intended to help you test your own understanding.

Have a go hero – heading

These set practical challenges and give you ideas for experimenting with what you have learned.

You will also find a number of styles of text that distinguish between different kinds of information. Here are some examples of these styles, and an explanation of their meaning.

Code words in text are shown as follows: For example, the inverse of sine is called asin and the inverse hyperbolic of sine is asinh.

A block of code is set as follows:

# flush the output stream

fflush(stdout);

# Get the number of rows and columns from the user

nr = input(Enter the number of rows in the matrix: );

nc = input(Enter the number of columns in the matrix: );

Any command-line input or output is written as follows:

octave:35> projectile = struct(mass, 10.1, velocity, [1 0 0], type, Cannonball);

New terms and important words are shown in bold. Words that you see on the screen, in menus or dialog boxes for example, appear in the text like this: Now go to the Octave-Forge web page, find the msh package, and click on Details (to the right of the package name).

Specific commands entered in Octave are referred to using the relevant command numbers:

octave:5 > A = [1 2 3; 4 5 6]

A =   1  2  3   4  5  6

Note

Warnings or important notes appear in a box like this.

Tip

Tips and tricks appear like this.

Reader feedback

Feedback from our readers is always welcome. Let us know what you think about this book—what you liked or may have disliked. Reader feedback is important for us to develop titles that you really get the most out of.

To send us general feedback, simply send an e-mail to <[email protected]>, and mention the book title via the subject of your message.

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