Introduction to Octave

GNU Octave is a really neat prototyping language for machine learning tasks. It is dynamically typed.

Installation

Octave is in the package repositories, so it can be installed with

$ sudo apt-get install octave gnuplot-x11 octave-epstk

and started with

$ octave

Configuration

Create a file ~/.octaverc in your home folder. Write

PS1('>>');
setenv("GNUTERM","x11");

in it to get a nicer prompt and make sure that plots will work.

The Language

Vectors and Matrices

Octave has a lot of neat matrix manipulation features. You can create a matrix \(A = \begin{pmatrix} 1 & 2\\ 3 & 4\end{pmatrix}\) with

>> A = [1 2; 3 4];

When you want to transpose a vector / a matrix, you simply add an apostrophe:

>> A = [1 2; 3 4];
>> A'
ans =

   1   3
   2   4

You can multiply two matrices with A*B or use the dot product with A .* B.

The identity matrix \(I \in \mathbb{R}^{n \times n}\) can be created with

>> I = eye(n);

You can get a part of the matrix by slicing:

>> I = eye(n);
>> I(:, 1:2);

But be careful: Vectors and matrices are 1-indexed, not 0-indexed as you might expect!

You can get the size of a matrix with the function size which returns a matrix:

>> a = [1 2 3; 4 5 6];
>> size(a)
ans =

   2   3

If you simply want the "length", you can directly access the first element:

>> size(a)(1)
ans =  2

Sequences

The sequence 0 1 2 3 4 5 can be created with [0:5].

The sequence 0.2 0.3 0.4 0.5 can be created with [0.2:0.1:0.5]. In general: [<start>:<step>:<end>] where <start> and <end> are included.

You can also very simply apply functions to each element:

>> t = [0.2:0.1:0.5];
>> sin(t)
ans =

   0.19867   0.29552   0.38942   0.47943

The output can be suppressed with ;.

Plotting

I have never seen a language where plotting is so easy:

>> x = [0:0.01:pi];
>> y = sin(x);
>> plot(x, y);

You can add labels and a legend to it, too:

>> xlabel = "x";
>> ylabel = "value";
>> legend('sin', 'cos')
>> title("sin and cos")

And finally, you can store the image:

print -dpng 'my_plot.png'

Control statements

for

for i=1:10;
    printf("%i: %i\n", i, i^2)
end

while

i=1;
while i <= 10,
    printf("%i: %i\n", i, i^2)
end;

if

if 2 == 1+1,
    printf("True\n");
elseif 3 == 2+1,
    printf("Else true");
else
    printf("else");
end;

Functions

Functions have to be saved in a file called [filename].m. One other special thing about functions is that you define the variable with the output at the beginning:

function y = fibonacci(n)
    if n < 2,
        y = 1;
    else
        y = fibonacci(n-1) + fibonacci(n-2);
    end;

You can also return multiple values like this:

function [succ, pred] = succ_and_pred(n)
    succ = n+1;
    pred = n-1;