13.1 Defining Functions

In its simplest form, the definition of a function named name looks like this:

     function name
       body
     endfunction

A valid function name is like a valid variable name: a sequence of letters, digits and underscores, not starting with a digit. Functions share the same pool of names as variables.

The function body consists of Octave statements. It is the most important part of the definition, because it says what the function should actually do.

For example, here is a function that, when executed, will ring the bell on your terminal (assuming that it is possible to do so):

     function wakeup
       printf ("\a");
     endfunction

The printf statement (see Input and Output) simply tells Octave to print the string "\a". The special character `\a' stands for the alert character (ASCII 7). See Strings.

Once this function is defined, you can ask Octave to evaluate it by typing the name of the function.

Normally, you will want to pass some information to the functions you define. The syntax for passing parameters to a function in Octave is

     function name (arg-list)
       body
     endfunction

where arg-list is a comma-separated list of the function's arguments. When the function is called, the argument names are used to hold the argument values given in the call. The list of arguments may be empty, in which case this form is equivalent to the one shown above.

To print a message along with ringing the bell, you might modify the beep to look like this:

     function wakeup (message)
       printf ("\a%s\n", message);
     endfunction

Calling this function using a statement like this

     wakeup ("Rise and shine!");

will cause Octave to ring your terminal's bell and print the message `Rise and shine!', followed by a newline character (the `\n' in the first argument to the printf statement).

In most cases, you will also want to get some information back from the functions you define. Here is the syntax for writing a function that returns a single value:

     function ret-var = name (arg-list)
       body
     endfunction

The symbol ret-var is the name of the variable that will hold the value to be returned by the function. This variable must be defined before the end of the function body in order for the function to return a value.

Variables used in the body of a function are local to the function. Variables named in arg-list and ret-var are also local to the function. See Global Variables, for information about how to access global variables inside a function.

For example, here is a function that computes the average of the elements of a vector:

     function retval = avg (v)
       retval = sum (v) / length (v);
     endfunction

If we had written avg like this instead,

     function retval = avg (v)
       if (isvector (v))
         retval = sum (v) / length (v);
       endif
     endfunction

and then called the function with a matrix instead of a vector as the argument, Octave would have printed an error message like this:

     error: `retval' undefined near line 1 column 10
     error: evaluating index expression near line 7, column 1

because the body of the if statement was never executed, and retval was never defined. To prevent obscure errors like this, it is a good idea to always make sure that the return variables will always have values, and to produce meaningful error messages when problems are encountered. For example, avg could have been written like this:

     function retval = avg (v)
       retval = 0;
       if (isvector (v))
         retval = sum (v) / length (v);
       else
         error ("avg: expecting vector argument");
       endif
     endfunction

There is still one additional problem with this function. What if it is called without an argument? Without additional error checking, Octave will probably print an error message that won't really help you track down the source of the error. To allow you to catch errors like this, Octave provides each function with an automatic variable called nargin. Each time a function is called, nargin is automatically initialized to the number of arguments that have actually been passed to the function. For example, we might rewrite the avg function like this:

     function retval = avg (v)
       retval = 0;
       if (nargin != 1)
         usage ("avg (vector)");
       endif
       if (isvector (v))
         retval = sum (v) / length (v);
       else
         error ("avg: expecting vector argument");
       endif
     endfunction

Although Octave does not automatically report an error if you call a function with more arguments than expected, doing so probably indicates that something is wrong. Octave also does not automatically report an error if a function is called with too few arguments, but any attempt to use a variable that has not been given a value will result in an error. To avoid such problems and to provide useful messages, we check for both possibilities and issue our own error message.