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.

Array of Random Numbers

An array of 10 random throws of a six-sided die can be produced as follows.

octave:17> A = floor(6 * rand(10, 1) + 1)

Plotting a Histogram

Histograms can easily be plotted from the array. The second argument [1 2 3 4 5 6] provides the midpoints of the 'bins' for our histogram.

octave:18> hist(A, [1 2 3 4 5 6]);

Plotting Multiple Histograms on Same Graph

 # Plots three histograms of random data from six-sided die                                     
 # Histograms vary in their population
 graphics_toolkit("gnuplot")

 # Generate three random data sets of six-sided die throws
 A = floor(6 * rand(10000, 1) + 1)
 B = floor(6 * rand(100, 1) + 1)
 C = floor(6 * rand(10, 1) + 1)

 # Plot data as histograms
 hold on
 hist(A, [1, 2, 3, 4, 5, 6], "facecolor", "cyan");
 hist(B, [1, 2, 3, 4, 5, 6], "facecolor", "magenta");
 hist(C, [1, 2, 3, 4, 5, 6], "facecolor", "green");
 colormap( summer(64));

 # Use a logarithmic scale
 set(gca, 'yscale', 'log');

 # Add Titles and Legends
 grid on
 title("Histogram Plots: Six-sided Die Simulations");

 xlabel("Six-sided Die Roll")
 ylabel("Frequency of Occurrence (log scale)")

 legend ("10 thousand samples", "100 samples", "10 samples", "location", "northeastoutside");

 # Print to a file
 print -dpng histogram.png

Reading from a Remote URL

We can read the contents of a remote URL using the following command:

octave:17> s = urlread ("https://www.codermerlin.com/users/john-williams/sample.csv");

Reading from a String

We can read the contents of a string using the following command, interpreting each value read as a Double:

octave:18> A = strread(s, "%n");

Appending from a String

We can append the contents of a string to an existing array using the following command:

octave:18> A = [A; strread(s, "%n")];