Octave: A Free, High-Level Language for Mathematics

For numerical computing, high level languages offer advantages over more traditional languages, such as FORTRAN or C. Built-in graphics capabilities, automatic variable typing and flexible data structures combine to provide an environment in which it is easy to develop your ideas without having to fight with the language. That's not to say that FORTRAN and C are of no use, just that sometimes you want to make life a bit easier.

Matlab is a one such language. It is available on many platforms (including Linux) and provides powerful facilities for manipulating matrices, as well as other numerical functions. Unfortunately, Matlab is commercial software and wasn't available for Linux until recently (in the last twelve months or so). However, there are other, freely-available alternatives, and Octave is one such alternative.

Superficially, Octave looks very much like Matlab, and the description in its LSM entry reads “GNU Matlab—A numerical matrix mathematics program.” To begin, type octave at the shell prompt, and Octave greets you with its own prompt. Now we can start doing math.

As you might expect, entering and manipulating matrices is one of Octave's strengths. (In order to differentiate Octave commands from the output, the prompt octave:number of the command precedes the commands in the examples below.) We can enter a matrix with the command:

octave:1 a=[1 2 ; 3 4]

Octave then reports the result of the command, namely:

a =
        1  2
        3  4

octave:2 a'
      ans =
        1  3
        2  4

octave:3 b=[1 0; 3 2]
b =
  1  0
  3  2

octave:4 a*b
ans =
   7   4
  15   8

octave:5 a.*b
ans =
  1  0
  9  8

octave:6 a(1,1)
ans=1

octave:7 a(:,1)
ans =
  1
  3

octave:8 a(1,:)
ans =
  1  2

octave:9 eig(a)
ans =
   5.37228
  -0.37228

octave:10 [v,d]=eig(a)
v =
   0.41597  -0.82456
   0.90938   0.56577
d =
   5.37228   0.00000
   0.00000  -0.37228

Octave provides many other matrix routines, which are detailed in the manual and in the on-line help system.

Octave also lets the user define his own functions via the function keyword. A function definition looks like this:

function [output values] = name (input values)
   sequence of commands
endfunction

The input and output values are optional, so it is possible to write a function that takes no arguments and returns no values, such as

octave:11 function hello
   printf("hello\n")
endfunction

octave:12 hello
   hello

octave:13 function add(x,y)
   x+y
endfunction
octave:14 add(1,2)
   ans = 3

octave:15 function sum=add(x,y)
   sum=x+y;
endfunction

octave:16 fred=add(1,2)
   fred=3

octave:17 function [sum,diff]=sumdiff(x,y)
   sum=x+y;
   diff=x-y;
endfunction

octave:18 ns,d]=sumdiff(1,2)
   s = 3
   d = -1

Octave also provides a full programming language, with flow control and looping constructs, as well as extensive input-output facilities. It is possible to write quite sophisticated programs in Octave, and development time is considerably shorter than you would expect using FORTRAN or C.