### 11.1 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 `wakeup` 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.

— Built-in Function: nargin ()
— Built-in Function: nargin (fcn_name)

> Within a function, return the number of arguments passed to the function. At the top level, return the number of command line arguments passed to Octave. If called with the optional argument fcn_name, return the maximum number of arguments the named function can accept, or -1 if the function accepts a variable number of arguments.

> See also: nargout, varargin, varargout.

— Function File: inputname (n)

> Return the text defining n-th input to the function.

— Built-in Function: val = silent_functions ()
— Built-in Function: old_val = silent_functions (new_val)

> Query or set the internal variable that controls whether internal output from a function is suppressed. If this option is disabled, Octave will display the results produced by evaluating expressions within a function body that are not terminated with a semicolon.