Octave

Within these castle walls be forged Mavens of Computer Science ...

— Merlin, The Coder

Octave

GNU Octave is software featuring a high-level programming language, primarily intended for numerical computations. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB.

Preparation

In this exercise, you'll be generating graphic files by using Octave. In order to view these files, you'll save them in a special directory called "~www" which must be created in your home directory. The following instructions will instruct you on how to create this directory.

Create a directory to be served by the web server. If the directory already exists, no error will occur.

amrit-gupta@codermerlin:~$ mkdir --parents ~/www

Enter the directory.

amrit-gupta@codermerlin:~$ cd ~/www

Set the permissions so that the files can be accessed by the web server. If permission errors are encountered, re-execute this command.

amrit-gupta@codermerlin:~$ chmod -R a+rX ~/www

Graphing

Octave may be started by typing 'octave' in the shell. It's easiest to perform this in your www directory so the files that you create will be saved there.

liang-xue@codermerlin:~$ cd ~/www

liang-xue@codermerlin:~$ octave

You'll know you're in Octave when you see the Octave prompt.

octave:1> 

In order to enable graphics plotting, execute the following command:

octave:1> graphics_toolkit("gnuplot")

We'll begin with a 3-D example to demonstrate the power of Octave and the ease with which complex graphs can be created.

Examples

3-D Sombrero Plot

octave:2> tx = ty = linspace (-8, 8, 41)';

octave:3> [xx, yy] = meshgrid (tx, ty);

octave:4> r = sqrt (xx .^ 2 + yy .^ 2) + eps;

octave:5> tz = sin (r) ./ r;

octave:6> mesh (tx, ty, tz);

octave:7> xlabel ("tx");

octave:8> ylabel ("ty");

octave:9> zlabel ("tz");

octave:10> title ("3-D Sombrero plot");

We can now print the plot to a file with:

octave:11> print -dpng sombrero.png

It may take a few seconds to produce the file; be patient.

It's necessary to adjust the file's permissions to enable web server access. This may easily be performed from within octave using the following command:

octave:12> system("chmod -R a+rX ~/www")

When the prompt returns, the file may be viewed in a browser. Every user has a personal URL. Your file may be viewed here: You must be logged in to view your personal URL.

Random Numbers

We can produce results similar to those of throwing a six-sided die by using the rand function which returns a random value in the interval (0, 1).

octave:13> rand

Try executing this command several times and observe the results. In order to obtain integer values in the range from 1 to 6 we'll multiply the result of rand by 6, add 1, and then take the floor of this result.

octave:16> floor(6*rand + 1)

Try executing this command several times and observe the results.