Functions and Script Files
**************************

Complicated Octave programs can often be simplified by defining functions.  Functions can be defined directly on the command line during interactive Octave sessions, or in external files, and can be called just like built-in functions.

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.

(nargin)

(silent_functions)

(warn_missing_semicolon)

Multiple Return Values
======================

Unlike many other computer languages, Octave allows you to define functions that return more than one value.  The syntax for defining functions that return multiple values is

     function [RET-LIST] = NAME (ARG-LIST)
       BODY
     endfunction

where NAME, ARG-LIST, and BODY have the same meaning as before, and RET-LIST is a comma-separated list of variable names that will hold the values returned from the function.  The list of return values must have at least one element.  If RET-LIST has only one element, this form of the function statement is equivalent to the form described in the previous section.

Here is an example of a function that returns two values, the maximum element of a vector and the index of its first occurrence in the vector.

     function [max, idx] = vmax (v)
       idx = 1;
       max = v (idx);
       for i = 2:length (v)
         if (v (i) > max)
           max = v (i);
           idx = i;
         endif
       endfor
     endfunction

In this particular case, the two values could have been returned as elements of a single array, but that is not always possible or convenient.  The values to be returned may not have compatible dimensions, and it is often desirable to give the individual return values distinct names.

In addition to setting nargin each time a function is called, Octave also automatically initializes nargout to the number of values that are expected to be returned.  This allows you to write functions that behave differently depending on the number of values that the user of the function has requested.  The implicit assignment to the built-in variable ans does not figure in the count of output arguments, so the value of nargout may be zero.

The svd and lu functions are examples of built-in functions that behave differently depending on the value of nargout.

It is possible to write functions that only set some return values.  For example, calling the function

     function [x, y, z] = f ()
       x = 1;
       z = 2;
     endfunction

as

     [a, b, c] = f ()

produces:

     a = 1

     b = [](0x0)

     c = 2

along with a warning if the value of the built-in variable warn_undefined_return_values is nonzero.

(nargout)

(warn_undefined_return_values)

(nargchk)

Variable-length Argument Lists
==============================

Variable-length Return Lists
============================

Returning From a Function
=========================

The body of a user-defined function can contain a return statement. This statement returns control to the rest of the Octave program.  It looks like this:

     return

Unlike the return statement in C, Octave's return statement cannot be used to return a value from a function.  Instead, you must assign values to the list of return variables that are part of the function statement.  The return statement simply makes it easier to exit a function from a deeply nested loop or conditional statement.

Here is an example of a function that checks to see if any elements of a vector are nonzero.

     function retval = any_nonzero (v)
       retval = 0;
       for i = 1:length (v)
         if (v (i) != 0)
           retval = 1;
           return;
         endif
       endfor
       printf ("no nonzero elements found\n");
     endfunction

Note that this function could not have been written using the break statement to exit the loop once a nonzero value is found without adding extra logic to avoid printing the message if the vector does contain a nonzero element.

 -- Keyword: return
     When Octave encounters the keyword return inside a function or script, it returns control to the caller immediately. At the top level, the return statement is ignored.  A return statement is assumed at the end of every function definition.

(return_last_computed_value)

Function Files
==============

Except for simple one-shot programs, it is not practical to have to define all the functions you need each time you need them.  Instead, you will normally want to save them in a file so that you can easily edit them, and save them for use at a later time.

Octave does not require you to load function definitions from files before using them.  You simply need to put the function definitions in a place where Octave can find them.

When Octave encounters an identifier that is undefined, it first looks for variables or functions that are already compiled and currently listed in its symbol table.  If it fails to find a definition there, it searches the list of directories specified by the built-in variable LOADPATH for files ending in .m that have the same base name as the undefined identifier. (The .m suffix was chosen for compatibility with MATLAB.)  Once Octave finds a file with a name that matches, the contents of the file are read.  If it defines a single function, it is compiled and executed. See Script Files, for more information about how you can define more than one function in a single file.

When Octave defines a function from a function file, it saves the full name of the file it read and the time stamp on the file.  After that, it checks the time stamp on the file every time it needs the function.  If the time stamp indicates that the file has changed since the last time it was read, Octave reads it again.

Checking the time stamp allows you to edit the definition of a function while Octave is running, and automatically use the new function definition without having to restart your Octave session.  Checking the time stamp every time a function is used is rather inefficient, but it has to be done to ensure that the correct function definition is used.

To avoid degrading performance unnecessarily by checking the time stamps on functions that are not likely to change, Octave assumes that function files in the directory tree OCTAVE-HOME/share/octave/VERSION/m will not change, so it doesn't have to check their time stamps every time the functions defined in those files are used.  This is normally a very good assumption and provides a significant improvement in performance for the function files that are distributed with Octave.

If you know that your own function files will not change while you are running Octave, you can improve performance by setting the variable ignore_function_time_stamp to "all", so that Octave will ignore the time stamps for all function files.  Setting it to "system" gives the default behavior.  If you set it to anything else, Octave will check the time stamps on all function files.

(DEFAULT_LOADPATH)

(LOADPATH)

(rehash)

(file_in_loadpath)

(ignore_function_time_stamp)

(warn_function_name_clash)

(warn_future_time_stamp)

Script Files
============

A script file is a file containing (almost) any sequence of Octave commands.  It is read and evaluated just as if you had typed each command at the Octave prompt, and provides a convenient way to perform a sequence of commands that do not logically belong inside a function.

Unlike a function file, a script file must not begin with the keyword function.  If it does, Octave will assume that it is a function file, and that it defines a single function that should be evaluated as soon as it is defined.

A script file also differs from a function file in that the variables named in a script file are not local variables, but are in the same scope as the other variables that are visible on the command line.

Even though a script file may not begin with the function keyword, it is possible to define more than one function in a single script file and load (but not execute) all of them at once.  To do this, the first token in the file (ignoring comments and other white space) must be something other than function.  If you have no other statements to evaluate, you can use a statement that has no effect, like this:

     # Prevent Octave from thinking that this
     # is a function file:

     1;

     # Define function one:

     function one ()
       ...

To have Octave read and compile these functions into an internal form, you need to make sure that the file is in Octave's LOADPATH, then simply type the base name of the file that contains the commands. (Octave uses the same rules to search for script files as it does to search for function files.)

If the first token in a file (ignoring comments) is function, Octave will compile the function and try to execute it, printing a message warning about any non-whitespace characters that appear after the function definition.

Note that Octave does not try to look up the definition of any identifier until it needs to evaluate it.  This means that Octave will compile the following statements if they appear in a script file, or are typed at the command line,

     # not a function file:
     1;
     function foo ()
       do_something ();
     endfunction
     function do_something ()
       do_something_else ();
     endfunction

even though the function do_something is not defined before it is referenced in the function foo.  This is not an error because Octave does not need to resolve all symbols that are referenced by a function until the function is actually evaluated.

Since Octave doesn't look for definitions until they are needed, the following code will always print bar = 3 whether it is typed directly on the command line, read from a script file, or is part of a function body, even if there is a function or script file called bar.m in Octave's LOADPATH.

     eval ("bar = 3");
     bar

Code like this appearing within a function body could fool Octave if definitions were resolved as the function was being compiled.  It would be virtually impossible to make Octave clever enough to evaluate this code in a consistent fashion.  The parser would have to be able to perform the call to eval at compile time, and that would be impossible unless all the references in the string to be evaluated could also be resolved, and requiring that would be too restrictive (the string might come from user input, or depend on things that are not known until the function is evaluated).

Although Octave normally executes commands from script files that have the name FILE.m, you can use the function source to execute commands from any file.

(source)

Dynamically Linked Functions
============================

On some systems, Octave can dynamically load and execute functions written in C++.  Octave can only directly call functions written in C++, but you can also load functions written in other languages by calling them from a simple wrapper function written in C++.

Here is an example of how to write a C++ function that Octave can load, with commentary.  The source for this function is included in the source distributions of Octave, in the file examples/oregonator.cc.  It defines the same set of differential equations that are used in the example problem of Ordinary Differential Equations.  By running that example and this one, we can compare the execution times to see what sort of increase in speed you can expect by using dynamically linked functions.

The function defined in oregonator.cc contains just 8 statements, and is not much different than the code defined in the corresponding M-file (also distributed with Octave in the file examples/oregonator.m).

Here is the complete text of oregonator.cc:

just

     #include <octave/oct.h>

     DEFUN_DLD (oregonator, args, ,
       "The `oregonator'.")
     {
       ColumnVector dx (3);

       ColumnVector x (args(0).vector_value ());

       dx(0) = 77.27 * (x(1) - x(0)*x(1) + x(0)
                        - 8.375e-06*pow (x(0), 2));

       dx(1) = (x(2) - x(0)*x(1) - x(1)) / 77.27;

       dx(2) = 0.161*(x(0) - x(2));

       return octave_value (dx);
     }

The first line of the file,

     #include <octave/oct.h>

includes declarations for all of Octave's internal functions that you will need.  If you need other functions from the standard C++ or C libraries, you can include the necessary headers here.

The next two lines

     DEFUN_DLD (oregonator, args, ,
       "The `oregonator'.")

declares the function.  The macro DEFUN_DLD and the macros that it depends on are defined in the files defun-dld.h, defun.h, and defun-int.h (these files are included in the header file octave/oct.h).

Note that the third parameter to DEFUN_DLD (nargout) is not used, so it is omitted from the list of arguments in order to avoid the warning from gcc about an unused function parameter.

The next line,

     ColumnVector dx (3);

simply declares an object to store the right hand sides of the differential equation, and the statement

     ColumnVector x (args(0).vector_value ());

extracts a vector from the first input argument.  The vector_value method is used so that the user of the function can pass either a row or column vector.  The ColumnVector constructor is needed because the ODE class requires a column vector.  The variable args is passed to functions defined with DEFUN_DLD as an octave_value_list object, which includes methods for getting the length of the list and extracting individual elements.

In this example, we don't check for errors, but that is not difficult. All of the Octave's built-in functions do some form of checking on their arguments, so you can check the source code for those functions for examples of various strategies for verifying that the correct number and types of arguments have been supplied.

The next statements

     dx(0) = 77.27 * (x(1) - x(0)*x(1) + x(0)
                      - 8.375e-06*pow (x(0), 2));

     dx(1) = (x(2) - x(0)*x(1) - x(1)) / 77.27;

     dx(2) = 0.161*(x(0) - x(2));

define the right-hand side of the differential equation.  Finally, we can return dx:

     return octave_value (dx);

The actual return type is octave_value_list, but it is only necessary to convert the return type to an octave_value because there is a default constructor that can automatically create an object of that type from an octave_value object, so we can just use that instead.

To use this file, your version of Octave must support dynamic linking. To find out if it does, type the command octave_config_info ("dld") at the Octave prompt.  Support for dynamic linking is included if this command returns 1.

To compile the example file, type the command mkoctfile oregonator.cc at the shell prompt.  The script mkoctfile should have been installed along with Octave.  Running it will create a file called oregonator.oct that can be loaded by Octave.  To test the oregonator.oct file, start Octave and type the command

     oregonator ([1, 2, 3], 0)

at the Octave prompt.  Octave should respond by printing

     ans =

        77.269353
        -0.012942
        -0.322000

You can now use the oregonator.oct file just as you would the oregonator.m file to solve the set of differential equations.

On a 133 MHz Pentium running Linux, Octave can solve the problem shown in Ordinary Differential Equations, in about 1.4 seconds using the dynamically linked function, compared to about 19 seconds using the M-file.  Similar decreases in execution time can be expected for other functions, particularly those that rely on functions like lsode that require user-supplied functions.

Just as for M-files, Octave will automatically reload a dynamically linked function when the file that defines it is more recent than the last time that the function was loaded.  If more than one function is defined in a single .oct file, reloading the file may force other functions to be cleared and reloaded.  If all the functions loaded from a given .oct file are cleared, Octave will automatically unload the .oct file.

(warn_reload_forces_clear)

(variables_can_hide_functions)

Additional examples for writing dynamically linked functions are available in the files in the src directory of the Octave distribution.  Currently, this includes the files

     balance.cc   fft2.cc      inv.cc       qzval.cc
     chol.cc      filter.cc    log.cc       schur.cc
     colloc.cc    find.cc      lsode.cc     sort.cc
     dassl.cc     fsolve.cc    lu.cc        svd.cc
     det.cc       givens.cc    minmax.cc    syl.cc
     eig.cc       hess.cc      pinv.cc
     expm.cc      ifft.cc      qr.cc
     fft.cc       ifft2.cc     quad.cc

These files use the macro DEFUN_DLD_BUILTIN instead of DEFUN_DLD.  The difference between these two macros is just that DEFUN_DLD_BUILTIN can define a built-in function that is not dynamically loaded if the operating system does not support dynamic linking.  To define your own dynamically linked functions you should use DEFUN_DLD.

There is currently no detailed description of all the functions that you can call in a built-in function.  For the time being, you will have to read the source code for Octave.

Function Handles and Inline
===========================

This is a place holder for the description of function handles and inline functions.

Function Handles
----------------

(functions)

(func2str)

(str2func)

Inline Functions
----------------

(inline)

(argnames)

(formula)

(vectorize)

Organization of Functions Distributed with Octave
=================================================

Many of Octave's standard functions are distributed as function files. They are loosely organized by topic, in subdirectories of OCTAVE-HOME/lib/octave/VERSION/m, to make it easier to find them.

The following is a list of all the function file subdirectories, and the types of functions you will find there.

audio
     Functions for playing and recording sounds.

control
     Functions for design and simulation of automatic control systems.

elfun
     Elementary functions.

general
     Miscellaneous matrix manipulations, like flipud, rot90, and triu, as well as other basic functions, like ismatrix, nargchk, etc.

image
     Image processing tools.  These functions require the X Window System.

io
     Input-ouput functions.

linear-algebra
     Functions for linear algebra.

miscellaneous
     Functions that don't really belong anywhere else.

plot
     A set of functions that implement the MATLAB-like plotting functions.

polynomial
     Functions for manipulating polynomials.

set
     Functions for creating and manipulating sets of unique values.

signal
     Functions for signal processing applications.

specfun
     Special functions.

special-matrix
     Functions that create special matrix forms.

startup
     Octave's system-wide startup file.

statistics
     Statistical functions.

strings
     Miscellaneous string-handling functions.

time
     Functions related to time keeping.