GNU Octave Beginners Guide电子书

GNU Octave

Table of Contents

GNU Octave

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

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