GNU Octave Beginner's Guide: Become a proficient Octave user by learning this high-level scientific numerical tool from the ground up

As mentioned previously, Octave can be used to solve many different scientific problems. For example, a Copenhagen-based commercial software and consulting company specializes in optimization problems, especially for packing containers on large cargo ships. This can be formulated in terms of linear programming which involves solving large linear equation systems and to this end, the company uses Octave. Pittsburgh supercomputing center also used Octave to study social security number vulnerability. Here Octave ran on a massive parallel computer named Pople with 768 cores and 1.5 TB memory and enabled researches to carry out sophisticated analysis of different strategies before trying out new ones.

In the research community, Octave is used for data analysis, image processing, econometrics, advanced statistical analysis, and much more. We shall see quite a few examples of this throughout the book.

Octave is mainly designed to perform numerical computations and is not meant to be a general purpose programming language such as C or C++. As it is always the case, you should choose your programming language depending on the problem you wish to solve. Nevertheless, Octave has a lot of functionality that can help you with, for example, reading from and writing to files, and you can even use a package named sockets for accessing a network directly.

The fact that Octave uses an interpreter means that Octave first has to convert the instructions into machine readable code before executing it. This has its advantages as well as drawbacks. The main advantage is that the instructions are easy to implement and change, without having to go through the edit, compile, and run phase and gives the programmer or user a very high degree of control. The major drawback is that the program executes relatively slowly compared to pre-compiled programs written in languages such as C or Fortran. Octave is therefore perhaps not the first choice if you want to do extremely large scale parallelized computations, such as state-of-art weather forecasting.

However, as you will experience later in the book, Octave will enable you solve very advanced and computationally demanding problems with only a few instructions or commands and with satisfactory speed. The last chapter of this book teaches you some optimization techniques and how you can use C++ together with Octave to speed things up considerably in some situations.

Octave is not designed to do analytical (or symbolic) mathematics. For example, it is not the best choice if you wish to find the derivative of a function, say f (x) = x2. Here software packages such as Maxima and Sage can be very helpful. It should be mentioned that there exists a package (a package is also referred to as a toolbox) for Octave which can do some basic analytical mathematics.

It is in place to mention MATLAB. Often Octave is referred to as a MATLAB-clone (MATLAB is a product from MathWorksTM). In my opinion, this is wrong! Rather, Octave seeks to be compatible with MATLAB. However, be aware, in some cases you cannot simply execute your Octave programs with MATLAB and vice-versa. Throughout the book, it will be pointed out where compatibility problems can occur, but we shall stick with Octave and make no special effort to be compatible with MATLAB.

The newest version of Octave can be found on the web page http://www.octave.org. Here you will also find the official manual, a Wiki page with tricks and tips, latest news, a bit of history, and other exciting stuff. From this web page, you can join Octave's mailing lists (the help-list is especially relevant), which only require a valid email address. The user community is very active and helpful, and even the developers will answer "simple" user questions. You can also learn quite a lot from browsing through the older thread archives.

There also exists an Usenet discussion group http://groups.google.com/group/comp.soft-sys.octave/topics?lnk. Unfortunately, this group seems quite inactive, so it could take a while for help to arrive.

There exist a very large number of additional packages that do not come with the standard Octave distribution. Many of these can be downloaded from the Octave-Forge http://octave.sourceforge.net. Here you will find specially designed packages for imaging processing, econometrics, information theory, analytical mathematics, and so on. After reading this book and solving the problems at the end of each chapter, you will be able to write your own Octave package. You can then share your work with others, and the entire Octave community can benefit from your efforts. Someone might even extend and improve what you started!

Installing Octave on Windows is straightforward. The steps are as follows:

Notice that Octave's interactive environment (the Octave prompt) may be launched when the installer exits. To close this, simply type:

octave:1> exit

or press the Ctrl key and the D key at the same time. We shall write this combination as Ctrl + D. By the way, Ctrl + D is a UNIX end-of-file indicator and is often used as a shortcut for quitting programs in UNIX-type systems like GNU/Linux.

Alternatively, you can run Octave under Windows through Cygwin, which is similar to the GNU/Linux environment in Windows. I will not go through the installation of Cygwin here, but you may simply refer to the Cygwin web page http://www.cygwin.com.

On many GNU/Linux distributions, Octave is a part of the standard software. Therefore, before installing Octave, check if it already exists on your computer. To do so, open a terminal, and type the following in the terminal shell:

$ octave

If Octave is installed (properly), you should now see Octave's command prompt. Now just exit by typing the following:

octave:1> exit

Alternatively, you may use CTRL + D, that is, press the control key and the D key at the same time.

If Octave is not installed, you can often use the distribution's package management system. For example, for Ubuntu, you can use the Synaptic Package Manager, which is a graphical tool to install and remove software on the computer. Please refer the following screenshot. In case of Fedora and CentOS, you can use YUM.

As you can see, we just performed the standard UNIX installation procedure: configure, make, make install. If you do not have root privileges, you cannot install Octave on the computer. However, you can still launch Octave from the bin/ sub-directory in the installation directory.

Again, the preceding installation will only install Octave and not the plotting program. You will need to have this installed separately for Octave to work properly.

The figure to the left shows a graph of a mathematical function, which is a scalar function of two variables y and x given by:

(1.1)

The function value (range) is evaluated in Octave by the command peaks, which is the nick name for the function f. The graph is then plotted using the Octave function surf. As a default, Octave calculates the range of f using 50 x and y values in the interval [ 3; 3]. As you might have guessed already, the contourf Octave function plots the contours of f. Later we will learn how to label the axis, add text to the figures, and much more.

Did you notice the phrase "Octave function" previously? An Octave function is not necessarily a mathematical function as Equation (1.1), but can perform many different types of operations and have many different functionalities. Do not worry about this for now. We will discuss Octave functions later in the book.

Notice that the interpreter keeps track of the number of commands that have been entered and shows this at the prompt.

The first three Octave commands should be clear: we changed the directory to C:\Documents and Settings\ and created the directory GNU Octave. After this, we opened the global configuration file and added two commands. The next time Octave starts it will then execute these commands. The first instructed the interpreter to set the home directory to C:\Document and Settings\GNU Octave\, and the second made it enter that directory.

Having created the Octave home directory under Windows, we can customize Octave under GNU/Linux and Windows the same way.

PS1(">> ") sets the primary prompt string in Octave to the string given. You can set it to anything you may like. To extend the preceding example given previously, PS1("\\#>> ") will keep the command counter before the>> string. You can test which prompt string is your favorite directly from the command prompt, that is, without editing .octaverc. Try, for example, to use \\d and Hello give a command, \\u. In this book, we will stick with the default prompt string, which is \\s:\\#>.

The command edit mode "async" will ensure that when the edit command is given, you can use the Octave prompt without having to close the editor first. This is not default in GNU/Linux.

Finally, note that under Windows, the behavior will be global because we instructed Octave to look for this particular .octaverc file every time Octave is started. Under GNU/Linux, the .octaverc is saved in the user's home directory and will therefore only affect that particular user.

The default editor can be set in .octaverc. This can be done by adding the following line into your .octaverc file

edit editor name of the editor

where name of the editor is the editor. You may prefer a notepad if you use Windows, or gedit in GNU/Linux. Again, before adding this change to your .octaverc file, you should test whether it works directly from the Octave prompt.

Later in the book, we will write script and function files. Octave will have to be instructed where to look for these files in order to read them. Octave uses a path hierarchy when searching for files, and it is important to learn how to instruct Octave to look for the files in certain directories. I recommend that you create a new directory in your home directory (Octave home directory in Windows) named octave. You can then place your Octave files in this directory and let the interpreter search for them here.

Let us first create the directory. It is easiest simply to enter Octave and type the following:

octave1:> cd ~/
octave2:> mkdir octave

It should be clear what these commands do. Now type this:

octave3:> edit .octaverc

Add the following line into the .octaverc file:

addpath("~/octave");

Save the file, exit the editor, and restart Octave, or use source(".octaverc"). At the Octave prompt, type the following:

octave1:> path

You should now see that the path ~/octave/ is added to the search path. Under Windows, this path will be added for all users. The path list can be long, so you may need to scroll down (using the arrow key) to see the whole list. When you reach the end of the list, you can hit the Q key to return to Octave's command prompt.

The important points have already been explained in detail. Note that you need to install splines before msh because of the dependencies.

You may find it a bit strange that you must first load the package into Octave in order to use it. The package can load automatically if you install it with the auto option. For example, command 3 can be replaced with the following:

octave:3> pkg install auto msh-version-number.tar.gz

Some packages will automatically load even though you do not explicitly instruct it to do so when you install it. You can force packages not to load using noauto.

octave:3> pkg install noauto msh-version-number.tar.gz

Unistalling a package is just as easy:

octave:8> pkg uninstall msh

Note that you will get an error message if you try to uninstall splines before msh because msh depends on splines.