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.
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 section Input and Output) simply tells
Octave to print the string "\a". The special character `\a'
stands for the alert character (ASCII 7). See section 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 section 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 (is_vector (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 (is_vector (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 (is_vector (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 holds the number of command line arguments that
were passed to Octave.
silent_functions is nonzero, internal output
from a function is suppressed. Otherwise, the results of expressions
within a function body that are not terminated with a semicolon will
have their values printed. The default value is 0.
For example, if the function
function f () 2 + 2 endfunction
is executed, Octave will either print `ans = 4' or nothing
depending on the value of silent_functions.
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
provided that the built-in variable define_all_return_values is
nonzero and the value of default_return_value is `[]'.
See section Summary of Built-in Variables.
f ()
will result in nargout being set to 0 inside the function
f and
[s, t] = f ()
will result in nargout being set to 2 inside the function
f.
At the top level, nargout is undefined.
define_all_return_values is nonzero. The default value is
[].
define_all_return_values is nonzero, Octave
will substitute the value specified by default_return_value for
any return values that remain undefined when a function returns. The
default value is 0.
This is useful for checking to see that the number of arguments supplied to a function is within an acceptable range.
Octave has a real mechanism for handling functions that take an unspecified number of arguments, so it is not necessary to place an upper bound on the number of optional arguments that a function can accept.
Here is an example of a function that uses the new syntax to print a header followed by an unspecified number of values:
function foo (heading, ...)
disp (heading);
va_start ();
## Pre-decrement to skip `heading' arg.
while (--nargin)
disp (va_arg ());
endwhile
endfunction
The ellipsis that marks the variable argument list may only appear once and must be the last element in the list of arguments.
va_start if you do not plan to cycle through the
arguments more than once. This function may only be called inside
functions that have been declared to accept a variable number of input
arguments.
va_arg()
when there are no more arguments available.
Sometimes it is useful to be able to pass all unnamed arguments to another function. The keyword all_va_args makes this very easy to do. For example,
function f (...)
while (nargin--)
disp (va_arg ())
endwhile
endfunction
function g (...)
f ("begin", all_va_args, "end")
endfunction
g (1, 2, 3)
-| begin
-| 1
-| 2
-| 3
-| end
va_start. It can only be used within functions
that take a variable number of arguments. It is an error to use it in
other contexts.
Octave also has a real mechanism for handling functions that return an unspecified number of values, so it is no longer necessary to place an upper bound on the number of outputs that a function can produce.
Here is an example of a function that uses a variable-length return list to produce n values:
function [...] = f (n, x)
for i = 1:n
vr_val (i * x);
endfor
endfunction
[dos, quatro] = f (2, 2)
=> dos = 2
=> quatro = 4
As with variable argument lists, the ellipsis that marks the variable return list may only appear once and must be the last element in the list of returned values.
vr_val has been called, there is no way to go back to the
beginning of the list and rewrite any of the return values. This
function may only be called within functions that have been declared to
return an unspecified number of output arguments (by using the special
ellipsis notation described above).
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.
return inside a function or
script, it returns control to be 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 is true, and a
function is defined without explicitly specifying a return value, the
function will return the value of the last expression. Otherwise, no
value will be returned. The default value is 0.
For example, the function
function f () 2 + 2; endfunction
will either return nothing, if the value of
return_last_computed_value is 0, or 4, if the value of
return_last_computed_value is nonzero.
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.(4) 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 section 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.
LOADPATH
overrides the environment variable OCTAVE_PATH. See section Installing Octave.
LOADPATH is now handled in the same way as TeX handles
TEXINPUTS. If the path starts with `:', the standard path
is prepended to the value of LOADPATH. If it ends with `:'
the standard path is appended to the value of LOADPATH.
In addition, if any path element ends in `//', that directory and
all subdirectories it contains are searched recursively for function
files. This can result in a slight delay as Octave caches the lists of
files found in the LOADPATH the first time Octave searches for a
function. After that, searching is usually much faster because Octave
normally only needs to search its internal cache for files.
To improve performance of recursive directory searching, it is best for each directory that is to be searched recursively to contain either additional subdirectories or function files, but not a mixture of both.
See section Organization of Functions Distributed with Octave for a description of the function file directories that are distributed with Octave.
stat each time it looks up functions defined in function files.
If ignore_function_time_stamp to "system", Octave will not
automatically recompile function files in subdirectories of
`octave-home/lib/version' if they have changed since
they were last compiled, but will recompile other function files in the
LOADPATH if they change. If set to "all", Octave will not
recompile any function files unless their definitions are removed with
clear. For any other value of ignore_function_time_stamp,
Octave will always check to see if functions defined in function files
need to recompiled. The default value of ignore_function_time_stamp is
"system".
warn_function_name_clash is nonzero, a warning is
issued when Octave finds that the name of a function defined in a
function file differs from the name of the file. (If the names
disagree, the name declared inside the file is ignored.) If the value
is 0, the warning is omitted. The default value is 1.
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.
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 section 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 to in order to
avoid the warning from gcc about an unused function parameter.
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 column vector from the input arguments. 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
ColumnVector dx (3);
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 section Ordinary Differential Equations in about 1.4 second 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 dynamically linked functions when the files that define them are more recent than the last time that the function was loaded. Two variables are available to control how Octave behaves when dynamically linked functions are cleared or reloaded.
auto_unload_dot_oct_files is nonzero, Octave will
automatically unload any `.oct' files when there are no longer any
functions in the symbol table that reference them.
warn_reload_forces_clear, Octave will warn you when this happens,
and print a list of the additional functions that it is forced to clear.
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.
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.
flipud, rot90,
and triu, as well as other basic functions, like
is_matrix, nargchk, etc.
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