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@node Functions and Scripts
@chapter Functions and Scripts
@cindex defining functions
@cindex user-defined functions
@cindex functions, user-defined
@cindex 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.

@menu
* Defining Functions::          
* Multiple Return Values::      
* Variable-length Argument Lists::  
* Ignoring Arguments::  
* Variable-length Return Lists::  
* Returning from a Function::   
* Default Arguments::   
* Function Files::              
* Script Files::                
* Function Handles Inline Functions and Anonymous Functions::
* Commands::
* Organization of Functions::   
@end menu

@node Defining Functions
@section Defining Functions
@cindex @code{function} statement
@cindex @code{endfunction} statement

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

@example
@group
function @var{name}
  @var{body}
endfunction
@end group
@end example

@noindent
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 @var{body} consists of Octave statements.  It is the
most important part of the definition, because it says what the function
should actually @emph{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):

@example
@group
function wakeup
  printf ("\a");
endfunction
@end group
@end example

The @code{printf} statement (@pxref{Input and Output}) simply tells
Octave to print the string @code{"\a"}.  The special character @samp{\a}
stands for the alert character (ASCII 7).  @xref{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

@example
@group
function @var{name} (@var{arg-list})
  @var{body}
endfunction
@end group
@end example

@noindent
where @var{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
@code{wakeup} to look like this:

@example
@group
function wakeup (message)
  printf ("\a%s\n", message);
endfunction
@end group
@end example

Calling this function using a statement like this

@example
wakeup ("Rise and shine!");
@end example

@noindent
will cause Octave to ring your terminal's bell and print the message
@samp{Rise and shine!}, followed by a newline character (the @samp{\n}
in the first argument to the @code{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:

@example
@group
function @var{ret-var} = @var{name} (@var{arg-list})
  @var{body}
endfunction
@end group
@end example

@noindent
The symbol @var{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 @var{arg-list} and @var{ret-var} are also
local to the function.  @xref{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:

@example
@group
function retval = avg (v)
  retval = sum (v) / length (v);
endfunction
@end group
@end example

If we had written @code{avg} like this instead,

@example
@group
function retval = avg (v)
  if (isvector (v))
    retval = sum (v) / length (v);
  endif
endfunction
@end group
@end example

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

@example
@group
error: value on right hand side of assignment is undefined
@end group
@end example

@noindent
because the body of the @code{if} statement was never executed, and
@code{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, @code{avg} could have been
written like this:

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

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
@code{nargin}.  Each time a function is called, @code{nargin} is
automatically initialized to the number of arguments that have actually
been passed to the function.  For example, we might rewrite the
@code{avg} function like this:

@example
@group
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
@end group
@end example

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.

@c nargin src/ov-usr-fcn.cc
@anchor{doc-nargin}
@deftypefn  {Built-in Function} {} nargin ()
@deftypefnx {Built-in Function} {} nargin (@var{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 @var{fcn_name}, return the
maximum number of arguments the named function can accept, or -1 if the
function accepts a variable number of arguments.
@seealso{@ref{doc-nargout,,nargout}, @ref{doc-varargin,,varargin}, @ref{doc-isargout,,isargout}, @ref{doc-varargout,,varargout}, @ref{doc-nthargout,,nthargout}}
@end deftypefn


@c inputname scripts/miscellaneous/inputname.m
@anchor{doc-inputname}
@deftypefn {Function File} {} inputname (@var{n})
Return the name of the @var{n}-th argument to the calling function.
If the argument is not a simple variable name, return an empty string.
@end deftypefn


@c silent_functions src/pt-eval.cc
@anchor{doc-silent_functions}
@deftypefn  {Built-in Function} {@var{val} =} silent_functions ()
@deftypefnx {Built-in Function} {@var{old_val} =} silent_functions (@var{new_val})
@deftypefnx {Built-in Function} {} silent_functions (@var{new_val}, "local")
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.

When called from inside a function with the "local" option, the variable is
changed locally for the function and any subroutines it calls.  The original
variable value is restored when exiting the function.
@end deftypefn


@node Multiple Return Values
@section 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

@example
@group
function [@var{ret-list}] = @var{name} (@var{arg-list})
  @var{body}
endfunction
@end group
@end example

@noindent
where @var{name}, @var{arg-list}, and @var{body} have the same meaning
as before, and @var{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 @var{ret-list} has
only one element, this form of the @code{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.

@example
@group
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
@end group
@end example

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.

It is possible to use the @code{nthargout} function to obtain only some
of the return values or several at once in a cell array.
@ref{Cell Array Objects}

@c nthargout scripts/general/nthargout.m
@anchor{doc-nthargout}
@deftypefn  {Function File} {} nthargout (@var{n}, @var{func}, @dots{})
@deftypefnx {Function File} {} nthargout (@var{n}, @var{ntot}, @var{func}, @dots{})
Return the @var{n}th output argument of function given by the
function handle or string @var{func}.  Any arguments after @var{func}
are passed to @var{func}.  The total number of arguments to call
@var{func} with can be passed in @var{ntot}; by default @var{ntot}
is @var{n}.  The input @var{n} can also be a vector of indices of the
output, in which case the output will be a cell array of the
requested output arguments.

The intended use @code{nthargout} is to avoid intermediate variables.
For example, when finding the indices of the maximum entry of a
matrix, the following two compositions of nthargout

@example
@group
@var{m} = magic (5);
cell2mat (nthargout ([1, 2], @@ind2sub, size(@var{m}),
                     nthargout (2, @@max, @var{m}(:))))
@result{} 5   3
@end group
@end example

@noindent
are completely equivalent to the following lines:

@example
@group
@var{m} = magic(5);
[~, idx] = max (@var{M}(:));
[i, j] = ind2sub (size (@var{m}), idx);
[i, j]
@result{} 5   3
@end group
@end example

It can also be helpful to have all output arguments in a single cell
in the following manner:

@example
@var{USV} = nthargout ([1:3], @@svd, hilb (5));
@end example

@seealso{@ref{doc-nargin,,nargin}, @ref{doc-nargout,,nargout}, @ref{doc-varargin,,varargin}, @ref{doc-varargout,,varargout}, @ref{doc-isargout,,isargout}}
@end deftypefn


In addition to setting @code{nargin} each time a function is called,
Octave also automatically initializes @code{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 @code{ans} does not figure in the count of output
arguments, so the value of @code{nargout} may be zero.

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

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

@example
@group
function [x, y, z] = f ()
  x = 1;
  z = 2;
endfunction
@end group
@end example

@noindent
as

@example
[a, b, c] = f ()
@end example

@noindent
produces:

@example
@group
a = 1

b = [](0x0)

c = 2
@end group
@end example

@noindent
along with a warning.

@c nargout src/ov-usr-fcn.cc
@anchor{doc-nargout}
@deftypefn  {Built-in Function} {} nargout ()
@deftypefnx {Built-in Function} {} nargout (@var{fcn_name})
Within a function, return the number of values the caller expects to
receive.  If called with the optional argument @var{fcn_name}, return the
maximum number of values the named function can produce, or -1 if the
function can produce a variable number of values.

For example,

@example
f ()
@end example

@noindent
will cause @code{nargout} to return 0 inside the function @code{f} and

@example
[s, t] = f ()
@end example

@noindent
will cause @code{nargout} to return 2 inside the function
@code{f}.

At the top level, @code{nargout} is undefined.
@seealso{@ref{doc-nargin,,nargin}, @ref{doc-varargin,,varargin}, @ref{doc-isargout,,isargout}, @ref{doc-varargout,,varargout}, @ref{doc-nthargout,,nthargout}}
@end deftypefn


It is good practice at the head of a function to verify that it has been called
correctly.  In Octave the following idiom is seen frequently

@example
@group
if (nargin < min_#_inputs || nargin > max_#_inputs)
  print_usage ();
endif
@end group
@end example

@noindent
which stops the function execution and prints a message about the correct
way to call the function whenever the number of inputs is wrong.

For compatibility with @sc{matlab}, @code{nargchk}, @code{narginchk} and
@code{nargoutchk} are available which provide similar error checking.

@c nargchk scripts/general/nargchk.m
@anchor{doc-nargchk}
@deftypefn  {Function File} {@var{msgstr} =} nargchk (@var{minargs}, @var{maxargs}, @var{nargs})
@deftypefnx {Function File} {@var{msgstr} =} nargchk (@var{minargs}, @var{maxargs}, @var{nargs}, "string")
@deftypefnx {Function File} {@var{msgstruct} =} nargchk (@var{minargs}, @var{maxargs}, @var{nargs}, "struct")
Return an appropriate error message string (or structure) if the
number of inputs requested is invalid.

This is useful for checking to see that the number of input arguments
supplied to a function is within an acceptable range.
@seealso{@ref{doc-nargoutchk,,nargoutchk}, @ref{doc-narginchk,,narginchk}, @ref{doc-error,,error}, @ref{doc-nargin,,nargin}, @ref{doc-nargout,,nargout}}
@end deftypefn


@c narginchk scripts/general/narginchk.m
@anchor{doc-narginchk}
@deftypefn {Function File} {} narginchk (@var{minargs}, @var{maxargs})
Check for correct number of arguments or generate an error message if
the number of arguments in the calling function is outside the range
@var{minargs} and @var{maxargs}.  Otherwise, do nothing.

Both @var{minargs} and @var{maxargs} need to be scalar numeric
values.  Zero, Inf and negative values are all allowed, and
@var{minargs} and @var{maxargs} may be equal.

Note that this function evaluates @code{nargin} on the caller.

@seealso{@ref{doc-nargchk,,nargchk}, @ref{doc-nargoutchk,,nargoutchk}, @ref{doc-error,,error}, @ref{doc-nargout,,nargout}, @ref{doc-nargin,,nargin}}
@end deftypefn


@c nargoutchk scripts/general/nargoutchk.m
@anchor{doc-nargoutchk}
@deftypefn  {Function File} {} nargoutchk (@var{minargs}, @var{maxargs})
@deftypefnx {Function File} {@var{msgstr} =} nargoutchk (@var{minargs}, @var{maxargs}, @var{nargs})
@deftypefnx {Function File} {@var{msgstr} =} nargoutchk (@var{minargs}, @var{maxargs}, @var{nargs}, "string")
@deftypefnx {Function File} {@var{msgstruct} =} nargoutchk (@var{minargs}, @var{maxargs}, @var{nargs}, "struct")
Check for correct number of output arguments.

On the first form, returns an error unless the number of arguments in its
caller is between the values of @var{minargs} and @var{maxargs}.  It does
nothing otherwise.  Note that this function evaluates the value of
@code{nargout} on the caller so its value must have not been tampered with.

Both @var{minargs} and @var{maxargs} need to be a numeric scalar.  Zero, Inf
and negative are all valid, and they can have the same value.

For backward compatibility reasons, the other forms return an appropriate
error message string (or structure) if the number of outputs requested is
invalid.

This is useful for checking to see that the number of output
arguments supplied to a function is within an acceptable range.
@seealso{@ref{doc-nargchk,,nargchk}, @ref{doc-narginchk,,narginchk}, @ref{doc-error,,error}, @ref{doc-nargout,,nargout}, @ref{doc-nargin,,nargin}}
@end deftypefn


@anchor{doc-varargin} @anchor{doc-varargout}
@node Variable-length Argument Lists
@section Variable-length Argument Lists
@cindex variable-length argument lists
@cindex @code{varargin}

Sometimes the number of input arguments is not known when the function
is defined.  As an example think of a function that returns the smallest
of all its input arguments.  For example:

@example
@group
a = smallest (1, 2, 3);
b = smallest (1, 2, 3, 4);
@end group
@end example

@noindent
In this example both @code{a} and @code{b} would be 1.  One way to write
the @code{smallest} function is

@example
@group
function val = smallest (arg1, arg2, arg3, arg4, arg5)
  @var{body}
endfunction
@end group
@end example

@noindent
and then use the value of @code{nargin} to determine which of the input
arguments should be considered.  The problem with this approach is
that it can only handle a limited number of input arguments.

If the special parameter name @code{varargin} appears at the end of a
function parameter list it indicates that the function takes a variable
number of input arguments.  Using @code{varargin} the function
looks like this

@example
@group
function val = smallest (varargin)
  @var{body}
endfunction
@end group
@end example

@noindent
In the function body the input arguments can be accessed through the
variable @code{varargin}.  This variable is a cell array containing
all the input arguments.  @xref{Cell Arrays}, for details on working
with cell arrays.  The @code{smallest} function can now be defined
like this

@example
@group
function val = smallest (varargin)
  val = min ([varargin@{:@}]);
endfunction
@end group
@end example

@noindent
This implementation handles any number of input arguments, but it's also
a very simple solution to the problem.

A slightly more complex example of @code{varargin} is a function 
@code{print_arguments} that prints all input arguments.  Such a function
can be defined like this

@example
@group
function print_arguments (varargin)
  for i = 1:length (varargin)
    printf ("Input argument %d: ", i);
    disp (varargin@{i@});
  endfor
endfunction
@end group
@end example

@noindent
This function produces output like this

@example
@group
print_arguments (1, "two", 3);
     @print{} Input argument 1:  1
     @print{} Input argument 2: two
     @print{} Input argument 3:  3
@end group
@end example

@c parseparams scripts/miscellaneous/parseparams.m
@anchor{doc-parseparams}
@deftypefn  {Function File} {[@var{reg}, @var{prop}] =} parseparams (@var{params})
@deftypefnx {Function File} {[@var{reg}, @var{var1}, @dots{}] =} parseparams (@var{params}, @var{name1}, @var{default1}, @dots{})
Return in @var{reg} the cell elements of @var{param} up to the first
string element and in @var{prop} all remaining elements beginning
with the first string element.  For example:

@example
@group
[reg, prop] = parseparams (@{1, 2, "linewidth", 10@})
reg =
@{
  [1,1] = 1
  [1,2] = 2
@}
prop =
@{
  [1,1] = linewidth
  [1,2] = 10
@}
@end group
@end example

The parseparams function may be used to separate 'regular'
arguments and additional arguments given as property/value pairs of
the @var{varargin} cell array.

In the second form of the call, available options are specified directly
with their default values given as name-value pairs.
If @var{params} do not form name-value pairs, or if an option occurs
that does not match any of the available options, an error occurs.
When called from an m-file function, the error is prefixed with the
name of the caller function.
The matching of options is case-insensitive.

@seealso{@ref{doc-varargin,,varargin}}
@end deftypefn


@node Ignoring Arguments
@section Ignoring Arguments

In the formal argument list, it is possible to use the dummy placeholder
@code{~} instead of a name.  This indicates that the corresponding argument
value should be ignored and not stored to any variable.

@example
@group
function val = pick2nd (~, arg2)
  val = arg2;
endfunction
@end group
@end example

The value of @code{nargin} is not affected by using this declaration.

Return arguments can also be ignored using the same syntax.  Functions may
take advantage of ignored outputs to reduce the number of calculations
performed.  To do so, use the @code{isargout} function to query whether the
output argument is wanted.  For example:

@example
@group
function [out1, out2] = long_function (x, y, z)
  if (isargout (1))
    ## Long calculation
    @dots{}
    out1 = result;
  endif
  @dots{}
endfunction
@end group
@end example

@c isargout src/ov-usr-fcn.cc
@anchor{doc-isargout}
@deftypefn {Built-in Function} {} isargout (@var{k})
Within a function, return a logical value indicating whether the argument
@var{k} will be assigned on output to a variable.  If the result is false,
the argument has been ignored during the function call through the use of
the tilde (~) special output argument.  Functions can use @code{isargout} to
avoid performing unnecessary calculations for outputs which are unwanted.

If @var{k} is outside the range @code{1:max(nargout)}, the function returns
false.  @var{k} can also be an array, in which case the function works
element-by-element and a logical array is returned.  At the top level,
@code{isargout} returns an error.
@seealso{@ref{doc-nargout,,nargout}, @ref{doc-nargin,,nargin}, @ref{doc-varargin,,varargin}, @ref{doc-varargout,,varargout}, @ref{doc-nthargout,,nthargout}}
@end deftypefn


@node Variable-length Return Lists
@section Variable-length Return Lists
@cindex variable-length return lists
@cindex @code{varargout}

It is possible to return a variable number of output arguments from a
function using a syntax that's similar to the one used with the
special @code{varargin} parameter name.  To let a function return a
variable number of output arguments the special output parameter name
@code{varargout} is used.  As with @code{varargin}, @code{varargout} is
a cell array that will contain the requested output arguments.

As an example the following function sets the first output argument to
1, the second to 2, and so on.

@example
@group
function varargout = one_to_n ()
  for i = 1:nargout
    varargout@{i@} = i;
  endfor
endfunction
@end group
@end example

@noindent
When called this function returns values like this

@example
@group
[a, b, c] = one_to_n ()
     @result{} a =  1
     @result{} b =  2
     @result{} c =  3
@end group
@end example

If @code{varargin} (@code{varargout}) does not appear as the last
element of the input (output) parameter list, then it is not special,
and is handled the same as any other parameter name.

@c deal scripts/general/deal.m
@anchor{doc-deal}
@deftypefn  {Function File} {[@var{r1}, @var{r2}, @dots{}, @var{rn}] =} deal (@var{a})
@deftypefnx {Function File} {[@var{r1}, @var{r2}, @dots{}, @var{rn}] =} deal (@var{a1}, @var{a2}, @dots{}, @var{an})

Copy the input parameters into the corresponding output parameters.
If only one input parameter is supplied, its value is copied to each
of the outputs.

For example,

@example
[a, b, c] = deal (x, y, z);
@end example

@noindent
is equivalent to

@example
@group
a = x;
b = y;
c = z;
@end group
@end example

@noindent
and

@example
[a, b, c] = deal (x);
@end example

@noindent
is equivalent to

@example
a = b = c = x;
@end example
@end deftypefn


@node Returning from a Function
@section Returning from a Function

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

@example
return
@end example

Unlike the @code{return} statement in C, Octave's @code{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 @code{function} statement.  The @code{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.

@example
@group
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
@end group
@end example

Note that this function could not have been written using the
@code{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.

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

@node Default Arguments
@section Default Arguments
@cindex default arguments

Since Octave supports variable number of input arguments, it is very useful
to assign default values to some input arguments.  When an input argument
is declared in the argument list it is possible to assign a default
value to the argument like this

@example
@group
function @var{name} (@var{arg1} = @var{val1}, @dots{})
  @var{body}
endfunction
@end group
@end example

@noindent
If no value is assigned to @var{arg1} by the user, it will have the
value @var{val1}.

As an example, the following function implements a variant of the classic
``Hello, World'' program.

@example
@group
function hello (who = "World")
  printf ("Hello, %s!\n", who);
endfunction
@end group
@end example

@noindent
When called without an input argument the function prints the following

@example
@group
hello ();
     @print{} Hello, World!
@end group
@end example

@noindent
and when it's called with an input argument it prints the following

@example
@group
hello ("Beautiful World of Free Software");
     @print{} Hello, Beautiful World of Free Software!
@end group
@end example

Sometimes it is useful to explicitly tell Octave to use the default value
of an input argument.  This can be done writing a @samp{:} as the value
of the input argument when calling the function.

@example
@group
hello (:);
     @print{} Hello, World!
@end group
@end example

@node Function Files
@section Function Files
@cindex function file

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 a list of directories (the @dfn{path}) for files ending in
@file{.m} that have the same base name as the undefined
identifier.@footnote{The @samp{.m} suffix was chosen for compatibility
with @sc{matlab}.}  Once Octave finds a file with a name that matches,
the contents of the file are read.  If it defines a @emph{single}
function, it is compiled and executed.  @xref{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.  If the time
stamp on the file changes, Octave may reload the file.  When Octave is
running interactively, time stamp checking normally happens at most once
each time Octave prints the prompt.  Searching for new function
definitions also occurs if the current working directory changes.

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.

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
@file{@var{octave-home}/share/octave/@var{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 calling
@code{ignore_function_time_stamp ("all")}, so that Octave will
ignore the time stamps for all function files.  Passing
@code{"system"} to this function resets the default behavior.

@c FIXME -- note about time stamps on files in NFS environments?

@c edit scripts/miscellaneous/edit.m
@anchor{doc-edit}
@deftypefn  {Command} {} edit @var{name}
@deftypefnx {Command} {} edit @var{field} @var{value}
@deftypefnx {Command} {@var{value} =} edit get @var{field}
Edit the named function, or change editor settings.

If @code{edit} is called with the name of a file or function as
its argument it will be opened in a text editor.

@itemize @bullet
@item
If the function @var{name} is available in a file on your path and
that file is modifiable, then it will be edited in place.  If it
is a system function, then it will first be copied to the directory
@env{HOME} (see further down) and then edited.
If no file is found, then the m-file
variant, ending with ".m", will be considered.  If still no file
is found, then variants with a leading "@@" and then with both a
leading "@@" and trailing ".m" will be considered.

@item
If @var{name} is the name of a function defined in the interpreter but
not in an m-file, then an m-file will be created in @env{HOME}
to contain that function along with its current definition.

@item
If @code{name.cc} is specified, then it will search for @code{name.cc}
in the path and try to modify it, otherwise it will create a new
@file{.cc} file in @env{HOME}.  If @var{name} happens to be an
m-file or interpreter defined function, then the text of that
function will be inserted into the .cc file as a comment.

@item
If @var{name.ext} is on your path then it will be edited, otherwise
the editor will be started with @file{HOME/name.ext} as the
filename.  If @file{name.ext} is not modifiable, it will be copied to
@env{HOME} before editing.

@strong{Warning:} You may need to clear name before the new definition
is available.  If you are editing a .cc file, you will need
to mkoctfile @file{name.cc} before the definition will be available.
@end itemize

If @code{edit} is called with @var{field} and @var{value} variables,
the value of the control field @var{field} will be @var{value}.
If an output argument is requested and the first argument is @code{get}
then @code{edit} will return the value of the control field @var{field}.
If the control field does not exist, edit will return a structure
containing all fields and values.  Thus, @code{edit get all} returns
a complete control structure.
The following control fields are used:

@table @samp
@item editor
This is the editor to use to modify the functions.  By default it uses
Octave's @env{EDITOR} built-in function, which comes from
@code{getenv("EDITOR")} and defaults to @code{emacs}.  Use @code{%s}
In place of the function name.  For example,
@table @samp
@item [EDITOR, " %s"]
Use the editor which Octave uses for @code{edit_history}.

@item "xedit %s &"
pop up simple X11 editor in a separate window

@item "gnudoit -q \"(find-file \\\"%s\\\")\""
Send it to current Emacs; must have @code{(gnuserv-start)} in @file{.emacs}.
@end table

See also field 'mode', which controls how the editor is run by Octave.

On Cygwin, you will need to convert the Cygwin path to a Windows
path if you are using a native Windows editor.  For example:
@c Set example in small font to prevent overfull line in TeX

@smallexample
@exdent '"C:/Program Files/Good Editor/Editor.exe" "$(cygpath -wa %s)"'
@end smallexample

@item home
This is the location of user local m-files.  Be be sure it is in your
path.  The default is @file{~/octave}.

@item author
This is the name to put after the "## Author:" field of new functions.
By default it guesses from the @code{gecos} field of password database.

@item email
This is the e-mail address to list after the name in the author field.
By default it guesses @code{<$LOGNAME@@$HOSTNAME>}, and if @code{$HOSTNAME}
is not defined it uses @code{uname -n}.  You probably want to override this.
Be sure to use @code{<user@@host>} as your format.

@item license
@table @samp
@item gpl
GNU General Public License (default).

@item bsd
BSD-style license without advertising clause.

@item pd
Public domain.

@item "text"
Your own default copyright and license.
@end table

Unless you specify @samp{pd}, edit will prepend the copyright statement
with "Copyright (C) yyyy Function Author".

@item mode
This value determines whether the editor should be started in async mode
(editor is started in the background and Octave continues) or sync mode
(Octave waits until the editor exits).  Set it to "sync" to start the editor
in sync mode.  The default is "async" (see also "system").

@item editinplace
Determines whether files should be edited in place, without regard to
whether they are modifiable or not.  The default is @code{false}.
@end table
@end deftypefn


@c mfilename src/oct-parse.cc
@anchor{doc-mfilename}
@deftypefn  {Built-in Function} {} mfilename ()
@deftypefnx {Built-in Function} {} mfilename ("fullpath")
@deftypefnx {Built-in Function} {} mfilename ("fullpathext")
Return the name of the currently executing file.  At the top-level,
return the empty string.  Given the argument @code{"fullpath"},
include the directory part of the file name, but not the extension.
Given the argument @code{"fullpathext"}, include the directory part
of the file name and the extension.
@end deftypefn


@c ignore_function_time_stamp src/symtab.cc
@anchor{doc-ignore_function_time_stamp}
@deftypefn  {Built-in Function} {@var{val} =} ignore_function_time_stamp ()
@deftypefnx {Built-in Function} {@var{old_val} =} ignore_function_time_stamp (@var{new_val})
Query or set the internal variable that controls whether Octave checks
the time stamp on files each time it looks up functions defined in
function files.  If the internal variable is set to @code{"system"},
Octave will not automatically recompile function files in subdirectories of
@file{@var{octave-home}/lib/@var{version}} if they have changed since
they were last compiled, but will recompile other function files in the
search path if they change.  If set to @code{"all"}, Octave will not
recompile any function files unless their definitions are removed with
@code{clear}.  If set to "none", Octave will always check time stamps
on files to determine whether functions defined in function files
need to recompiled.
@end deftypefn


@menu
* Manipulating the Load Path::
* Subfunctions::
* Private Functions::
* Overloading and Autoloading::
* Function Locking::
* Function Precedence::
@end menu

@node Manipulating the Load Path
@subsection Manipulating the Load Path

When a function is called, Octave searches a list of directories for
a file that contains the function declaration.  This list of directories
is known as the load path.  By default the load path contains
a list of directories distributed with Octave plus the current
working directory.  To see your current load path call the @code{path}
function without any input or output arguments.

It is possible to add or remove directories to or from the load path
using @code{addpath} and @code{rmpath}.  As an example, the following
code adds @samp{~/Octave} to the load path.

@example
addpath("~/Octave")
@end example

@noindent
After this the directory @samp{~/Octave} will be searched for functions.
 
@c addpath src/load-path.cc
@anchor{doc-addpath}
@deftypefn  {Built-in Function} {} addpath (@var{dir1}, @dots{})
@deftypefnx {Built-in Function} {} addpath (@var{dir1}, @dots{}, @var{option})
Add @var{dir1}, @dots{} to the current function search path.  If
@var{option} is "-begin" or 0 (the default), prepend the
directory name to the current path.  If @var{option} is "-end"
or 1, append the directory name to the current path.
Directories added to the path must exist.

In addition to accepting individual directory arguments, lists of
directory names separated by @code{pathsep} are also accepted.  For example:

@example
addpath ("dir1:/dir2:~/dir3");
@end example
@seealso{@ref{doc-path,,path}, @ref{doc-rmpath,,rmpath}, @ref{doc-genpath,,genpath}, @ref{doc-pathdef,,pathdef}, @ref{doc-savepath,,savepath}, @ref{doc-pathsep,,pathsep}}
@end deftypefn


@c genpath src/load-path.cc
@anchor{doc-genpath}
@deftypefn  {Built-in Function} {} genpath (@var{dir})
@deftypefnx {Built-in Function} {} genpath (@var{dir}, @var{skip}, @dots{})
Return a path constructed from @var{dir} and all its subdirectories.
If additional string parameters are given, the resulting path will
exclude directories with those names.
@end deftypefn


@c rmpath src/load-path.cc
@anchor{doc-rmpath}
@deftypefn {Built-in Function} {} rmpath (@var{dir1}, @dots{})
Remove @var{dir1}, @dots{} from the current function search path.

In addition to accepting individual directory arguments, lists of
directory names separated by @code{pathsep} are also accepted.  For example:

@example
rmpath ("dir1:/dir2:~/dir3");
@end example
@seealso{@ref{doc-path,,path}, @ref{doc-addpath,,addpath}, @ref{doc-genpath,,genpath}, @ref{doc-pathdef,,pathdef}, @ref{doc-savepath,,savepath}, @ref{doc-pathsep,,pathsep}}
@end deftypefn


@c savepath scripts/path/savepath.m
@anchor{doc-savepath}
@deftypefn {Function File} {} savepath (@var{file})
Save the portion of the current function search path, that is
not set during Octave's initialization process, to @var{file}.
If @var{file} is omitted, @file{~/.octaverc} is used.  If successful,
@code{savepath} returns 0.
@seealso{@ref{doc-path,,path}, @ref{doc-addpath,,addpath}, @ref{doc-rmpath,,rmpath}, @ref{doc-genpath,,genpath}, @ref{doc-pathdef,,pathdef}, @ref{doc-pathsep,,pathsep}}
@end deftypefn


@c path src/load-path.cc
@anchor{doc-path}
@deftypefn {Built-in Function} {} path (@dots{})
Modify or display Octave's load path.

If @var{nargin} and @var{nargout} are zero, display the elements of
Octave's load path in an easy to read format.

If @var{nargin} is zero and nargout is greater than zero, return the
current load path.

If @var{nargin} is greater than zero, concatenate the arguments,
separating them with @code{pathsep}.  Set the internal search path
to the result and return it.

No checks are made for duplicate elements.
@seealso{@ref{doc-addpath,,addpath}, @ref{doc-rmpath,,rmpath}, @ref{doc-genpath,,genpath}, @ref{doc-pathdef,,pathdef}, @ref{doc-savepath,,savepath}, @ref{doc-pathsep,,pathsep}}
@end deftypefn


@c pathdef scripts/path/pathdef.m
@anchor{doc-pathdef}
@deftypefn {Function File} {@var{val} =} pathdef ()
Return the default path for Octave.
The path information is extracted from one of three sources.
In order of preference, those are;

@enumerate
@item @file{~/.octaverc}

@item @file{<octave-home>/@dots{}/<version>/m/startup/octaverc}

@item Octave's path prior to changes by any octaverc.
@end enumerate
@seealso{@ref{doc-path,,path}, @ref{doc-addpath,,addpath}, @ref{doc-rmpath,,rmpath}, @ref{doc-genpath,,genpath}, @ref{doc-savepath,,savepath}, @ref{doc-pathsep,,pathsep}}
@end deftypefn


@c pathsep src/dirfns.cc
@anchor{doc-pathsep}
@deftypefn  {Built-in Function} {@var{val} =} pathsep ()
@deftypefnx {Built-in Function} {@var{old_val} =} pathsep (@var{new_val})
Query or set the character used to separate directories in a path.
@seealso{@ref{doc-filesep,,filesep}}
@end deftypefn


@c rehash src/load-path.cc
@anchor{doc-rehash}
@deftypefn {Built-in Function} {} rehash ()
Reinitialize Octave's load path directory cache.
@end deftypefn


@c file_in_loadpath src/utils.cc
@anchor{doc-file_in_loadpath}
@deftypefn  {Built-in Function} {} file_in_loadpath (@var{file})
@deftypefnx {Built-in Function} {} file_in_loadpath (@var{file}, "all")

Return the absolute name of @var{file} if it can be found in
the list of directories specified by @code{path}.
If no file is found, return an empty character string.

If the first argument is a cell array of strings, search each
directory of the loadpath for element of the cell array and return
the first that matches.

If the second optional argument @code{"all"} is supplied, return
a cell array containing the list of all files that have the same
name in the path.  If no files are found, return an empty cell array.
@seealso{@ref{doc-file_in_path,,file_in_path}, @ref{doc-path,,path}}
@end deftypefn


@c restoredefaultpath src/load-path.cc
@anchor{doc-restoredefaultpath}
@deftypefn {Built-in Function} {} restoredefaultpath (@dots{})
Restore Octave's path to its initial state at startup.

@seealso{@ref{doc-path,,path}, @ref{doc-addpath,,addpath}, @ref{doc-rmpath,,rmpath}, @ref{doc-genpath,,genpath}, @ref{doc-pathdef,,pathdef}, @ref{doc-savepath,,savepath}, @ref{doc-pathsep,,pathsep}}
@end deftypefn


@c command_line_path src/load-path.cc
@anchor{doc-command_line_path}
@deftypefn {Built-in Function} {} command_line_path (@dots{})
Return the command line path variable.

@seealso{@ref{doc-path,,path}, @ref{doc-addpath,,addpath}, @ref{doc-rmpath,,rmpath}, @ref{doc-genpath,,genpath}, @ref{doc-pathdef,,pathdef}, @ref{doc-savepath,,savepath}, @ref{doc-pathsep,,pathsep}}
@end deftypefn


@c find_dir_in_path src/utils.cc
@anchor{doc-find_dir_in_path}
@deftypefn  {Built-in Function} {} find_dir_in_path (@var{dir})
@deftypefnx {Built-in Function} {} find_dir_in_path (@var{dir}, "all")
Return the full name of the path element matching @var{dir}.  The
match is performed at the end of each path element.  For example, if
@var{dir} is @code{"foo/bar"}, it matches the path element
@code{"/some/dir/foo/bar"}, but not @code{"/some/dir/foo/bar/baz"}
or @code{"/some/dir/allfoo/bar"}.

The second argument is optional.  If it is supplied, return a cell array
containing all name matches rather than just the first.
@end deftypefn


@node Subfunctions
@subsection Subfunctions

A function file may contain secondary functions called
@dfn{subfunctions}.  These secondary functions are only visible to the
other functions in the same function file.  For example, a file
@file{f.m} containing

@example
@group
function f ()
  printf ("in f, calling g\n");
  g ()
endfunction
function g ()
  printf ("in g, calling h\n");
  h ()
endfunction
function h ()
  printf ("in h\n")
endfunction
@end group
@end example

@noindent
defines a main function @code{f} and two subfunctions.  The
subfunctions @code{g} and @code{h} may only be called from the main
function @code{f} or from the other subfunctions, but not from outside
the file @file{f.m}.

@node Private Functions
@subsection Private Functions

In many cases one function needs to access one or more helper
functions.  If the helper function is limited to the scope of a single
function, then subfunctions as discussed above might be used.  However,
if a single helper function is used by more than one function, then
this is no longer possible.  In this case the helper functions might
be placed in a subdirectory, called "private", of the directory in which
the functions needing access to this helper function are found.

As a simple example, consider a function @code{func1}, that calls a helper
function @code{func2} to do much of the work.  For example:

@example
@group
function y = func1 (x)
  y = func2 (x);
endfunction
@end group
@end example

@noindent
Then if the path to @code{func1} is @code{<directory>/func1.m}, and if
@code{func2} is found in the directory @code{<directory>/private/func2.m}, 
then @code{func2} is only available for use of the functions, like 
@code{func1}, that are found in @code{<directory>}.

@node Overloading and Autoloading
@subsection Overloading and Autoloading

Functions can be overloaded to work with different input arguments.  For
example, the operator '+' has been overloaded in Octave to work with single,
double, uint8, int32, and many other arguments.  The preferred way to overload
functions is through classes and object oriented programming 
(@pxref{Function Overloading}).  Occasionally, however, one needs to undo
user overloading and call the default function associated with a specific
type.  The @code{builtin} function exists for this purpose.

@c builtin src/oct-parse.cc
@anchor{doc-builtin}
@deftypefn {Loadable Function} {[@dots{}]} builtin (@var{f}, @dots{})
Call the base function @var{f} even if @var{f} is overloaded to
another function for the given type signature.
@end deftypefn


A single dynamically linked file might define several
functions.  However, as Octave searches for functions based on the
functions filename, Octave needs a manner in which to find each of the
functions in the dynamically linked file.  On operating systems that
support symbolic links, it is possible to create a symbolic link to the
original file for each of the functions which it contains.

However, there is at least one well known operating system that doesn't
support symbolic links.  Making copies of the original file for each of
the functions is undesirable as it increases the
amount of disk space used by Octave.  Instead Octave supplies the
@code{autoload} function, that permits the user to define in which
file a certain function will be found.

@c autoload src/oct-parse.cc
@anchor{doc-autoload}
@deftypefn {Built-in Function} {} autoload (@var{function}, @var{file})
Define @var{function} to autoload from @var{file}.

The second argument, @var{file}, should be an absolute file name or
a file name in the same directory as the function or script from which
the autoload command was run.  @var{file} should not depend on the
Octave load path.

Normally, calls to @code{autoload} appear in PKG_ADD script files that
are evaluated when a directory is added to the Octave's load path.  To
avoid having to hardcode directory names in @var{file}, if @var{file}
is in the same directory as the PKG_ADD script then

@example
autoload ("foo", "bar.oct");
@end example

@noindent
will load the function @code{foo} from the file @code{bar.oct}.  The above
when @code{bar.oct} is not in the same directory or uses like

@example
autoload ("foo", file_in_loadpath ("bar.oct"))
@end example

@noindent
are strongly discouraged, as their behavior might be unpredictable.

With no arguments, return a structure containing the current autoload map.
@seealso{@ref{doc-PKG_ADD,,PKG_ADD}}
@end deftypefn


@node Function Locking
@subsection Function Locking

It is sometime desirable to lock a function into memory with the
@code{mlock} function.  This is typically used for dynamically linked
functions in Oct-files or mex-files that contain some initialization,
and it is desirable that calling @code{clear} does not remove this
initialization.

As an example,

@example
mlock ("my_function");
@end example

@noindent
prevents @code{my_function} from being removed from memory, even if
@code{clear} is called.  It is possible to determine if a function is
locked into memory with the @code{mislocked}, and to unlock a function
with @code{munlock}, which the following illustrates.

@example
@group
mlock ("my_function");
mislocked ("my_function")
@result{} ans = 1
munlock ("my_function");
mislocked ("my_function")
@result{} ans = 0
@end group
@end example

A common use of @code{mlock} is to prevent persistent variables from
being removed from memory, as the following example shows:

@example
@group
function count_calls()
  persistent calls = 0;
  printf ("'count_calls' has been called %d times\n",
          ++calls);
endfunction
mlock ("count_calls");

count_calls ();
@print{} 'count_calls' has been called 1 times

clear count_calls
count_calls ();
@print{} 'count_calls' has been called 2 times
@end group
@end example

@noindent
It is, however, often inconvenient to lock a function from the prompt,
so it is also possible to lock a function from within its body.  This
is simply done by calling @code{mlock} from within the function.

@example
@group
function count_calls ()
  mlock ();
  persistent calls = 0;
  printf ("'count_calls' has been called %d times\n",
          ++calls);
endfunction
@end group
@end example

@code{mlock} might equally be used to prevent changes to a function from having
effect in Octave, though a similar effect can be had with the
@code{ignore_function_time_stamp} function.

@c mlock src/variables.cc
@anchor{doc-mlock}
@deftypefn {Built-in Function} {} mlock ()
Lock the current function into memory so that it can't be cleared.
@seealso{@ref{doc-munlock,,munlock}, @ref{doc-mislocked,,mislocked}, @ref{doc-persistent,,persistent}}
@end deftypefn


@c munlock src/variables.cc
@anchor{doc-munlock}
@deftypefn  {Built-in Function} {} munlock ()
@deftypefnx {Built-in Function} {} munlock (@var{fcn})
Unlock the named function @var{fcn}.  If no function is named
then unlock the current function.
@seealso{@ref{doc-mlock,,mlock}, @ref{doc-mislocked,,mislocked}, @ref{doc-persistent,,persistent}}
@end deftypefn


@c mislocked src/variables.cc
@anchor{doc-mislocked}
@deftypefn  {Built-in Function} {} mislocked ()
@deftypefnx {Built-in Function} {} mislocked (@var{fcn})
Return true if the named function @var{fcn} is locked.  If no function is
named then return true if the current function is locked.
@seealso{@ref{doc-mlock,,mlock}, @ref{doc-munlock,,munlock}, @ref{doc-persistent,,persistent}}
@end deftypefn


@node Function Precedence
@subsection Function Precedence

Given the numerous different ways that Octave can define a function, it
is possible and even likely that multiple versions of a function, might be
defined within a particular scope.  The precedence of which function will be
used within a particular scope is given by

@enumerate 1
@item Subfunction
A subfunction with the required function name in the given scope.

@item Private function
A function defined within a private directory of the directory 
which contains the current function.

@item Class constructor
A function that constuctors a user class as defined in chapter 
@ref{Object Oriented Programming}.

@item Class method
An overloaded function of a class as in chapter
@ref{Object Oriented Programming}.

@item Legacy Dispatch
An overloaded function as defined by @code{dispatch}.

@item Command-line Function
A function that has been defined on the command-line.

@item Autoload function
A function that is marked as autoloaded with @xref{doc-autoload}.

@item A Function on the Path
A function that can be found on the users load-path.  There can also be
Oct-file, mex-file or m-file versions of this function and the precedence
between these versions are in that order.

@item Built-in function
A function that is builtin to Octave itself such as @code{numel},
@code{size}, etc.
@end enumerate

@node Script Files
@section 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 @emph{not} begin with the
keyword @code{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 @code{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 @code{function}.  If you have no
other statements to evaluate, you can use a statement that has no
effect, like this:

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

1;

# Define function one:

function one ()
  @dots{}
@end group
@end example

To have Octave read and compile these functions into an internal form,
you need to make sure that the file is in Octave's load path
(accessible through the @code{path} function), 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 @code{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,

@example
@group
# not a function file:
1;
function foo ()
  do_something ();
endfunction
function do_something ()
  do_something_else ();
endfunction
@end group
@end example

@noindent
even though the function @code{do_something} is not defined before it is
referenced in the function @code{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 @samp{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
@file{bar.m} in Octave's path.

@example
@group
eval ("bar = 3");
bar
@end group
@end example

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 @code{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{@var{file}.m}, you can use the function @code{source} to
execute commands from any file.

@c source src/oct-parse.cc
@anchor{doc-source}
@deftypefn {Built-in Function} {} source (@var{file})
Parse and execute the contents of @var{file}.  This is equivalent to
executing commands from a script file, but without requiring the file to
be named @file{@var{file}.m}.
@end deftypefn


@node Function Handles Inline Functions and Anonymous Functions
@section Function Handles, Inline Functions, and Anonymous Functions
@cindex handle, function handles
@cindex inline, inline functions
@cindex anonymous functions

It can be very convenient store a function in a variable so that it
can be passed to a different function.  For example, a function that
performs numerical minimization needs access to the function that 
should be minimized.

@menu
* Function Handles::
* Anonymous Functions::
* Inline Functions::
@end menu

@node Function Handles
@subsection Function Handles

A function handle is a pointer to another function and is defined with
the syntax

@example
@@@var{function-name}
@end example

@noindent
For example,

@example
f = @@sin;
@end example

@noindent
creates a function handle called @code{f} that refers to the
function @code{sin}.

Function handles are used to call other functions indirectly, or to pass
a function as an argument to another function like @code{quad} or
@code{fsolve}.  For example:

@example
@group
f = @@sin;
quad (f, 0, pi)
    @result{} 2
@end group
@end example

You may use @code{feval} to call a function using function handle, or
simply write the name of the function handle followed by an argument
list.  If there are no arguments, you must use an empty argument list
@samp{()}.  For example:

@example
@group
f = @@sin;
feval (f, pi/4)
    @result{} 0.70711
f (pi/4)
    @result{} 0.70711
@end group
@end example

@c is_function_handle src/ov-fcn-handle.cc
@anchor{doc-is_function_handle}
@deftypefn {Built-in Function} {} is_function_handle (@var{x})
Return true if @var{x} is a function handle.
@seealso{@ref{doc-isa,,isa}, @ref{doc-typeinfo,,typeinfo}, @ref{doc-class,,class}}
@end deftypefn


@c functions src/ov-fcn-handle.cc
@anchor{doc-functions}
@deftypefn {Built-in Function} {} functions (@var{fcn_handle})
Return a struct containing information about the function handle
@var{fcn_handle}.
@end deftypefn


@c func2str src/ov-fcn-handle.cc
@anchor{doc-func2str}
@deftypefn {Built-in Function} {} func2str (@var{fcn_handle})
Return a string containing the name of the function referenced by
the function handle @var{fcn_handle}.
@end deftypefn


@c str2func src/ov-fcn-handle.cc
@anchor{doc-str2func}
@deftypefn  {Built-in Function} {} str2func (@var{fcn_name})
@deftypefnx {Built-in Function} {} str2func (@var{fcn_name}, "global")
Return a function handle constructed from the string @var{fcn_name}.
If the optional "global" argument is passed, locally visible functions
are ignored in the lookup.
@end deftypefn


@node Anonymous Functions
@subsection Anonymous Functions

Anonymous functions are defined using the syntax

@example
@@(@var{argument-list}) @var{expression}
@end example

@noindent
Any variables that are not found in the argument list are inherited from
the enclosing scope.  Anonymous functions are useful for creating simple
unnamed functions from expressions or for wrapping calls to other
functions to adapt them for use by functions like @code{quad}.  For
example,

@example
@group
f = @@(x) x.^2;
quad (f, 0, 10)
    @result{} 333.33
@end group
@end example

@noindent
creates a simple unnamed function from the expression @code{x.^2} and
passes it to @code{quad},

@example
@group
quad (@@(x) sin (x), 0, pi)
    @result{} 2
@end group
@end example

@noindent
wraps another function, and

@example
@group
a = 1;
b = 2;
quad (@@(x) betainc (x, a, b), 0, 0.4)
    @result{} 0.13867
@end group
@end example

@noindent
adapts a function with several parameters to the form required by
@code{quad}.  In this example, the values of @var{a} and @var{b} that
are passed to @code{betainc} are inherited from the current
environment.

@node Inline Functions
@subsection Inline Functions

An inline function is created from a string containing the function
body using the @code{inline} function.  The following code defines the
function @math{f(x) = x^2 + 2}.

@example
f = inline("x^2 + 2");
@end example

@noindent
After this it is possible to evaluate @math{f} at any @math{x} by
writing @code{f(x)}.

@c inline src/ov-fcn-inline.cc
@anchor{doc-inline}
@deftypefn  {Built-in Function} {} inline (@var{str})
@deftypefnx {Built-in Function} {} inline (@var{str}, @var{arg1}, @dots{})
@deftypefnx {Built-in Function} {} inline (@var{str}, @var{n})
Create an inline function from the character string @var{str}.
If called with a single argument, the arguments of the generated
function are extracted from the function itself.  The generated
function arguments will then be in alphabetical order.  It should
be noted that i, and j are ignored as arguments due to the
ambiguity between their use as a variable or their use as an inbuilt
constant.  All arguments followed by a parenthesis are considered
to be functions.

If the second and subsequent arguments are character strings,
they are the names of the arguments of the function.

If the second argument is an integer @var{n}, the arguments are
@code{"x"}, @code{"P1"}, @dots{}, @code{"P@var{N}"}.
@seealso{@ref{doc-argnames,,argnames}, @ref{doc-formula,,formula}, @ref{doc-vectorize,,vectorize}}
@end deftypefn


@c argnames src/ov-fcn-inline.cc
@anchor{doc-argnames}
@deftypefn {Built-in Function} {} argnames (@var{fun})
Return a cell array of character strings containing the names of
the arguments of the inline function @var{fun}.
@seealso{@ref{doc-inline,,inline}, @ref{doc-formula,,formula}, @ref{doc-vectorize,,vectorize}}
@end deftypefn


@c formula src/ov-fcn-inline.cc
@anchor{doc-formula}
@deftypefn {Built-in Function} {} formula (@var{fun})
Return a character string representing the inline function @var{fun}.
Note that @code{char (@var{fun})} is equivalent to
@code{formula (@var{fun})}.
@seealso{@ref{doc-argnames,,argnames}, @ref{doc-inline,,inline}, @ref{doc-vectorize,,vectorize}}
@end deftypefn


@c symvar scripts/miscellaneous/symvar.m
@anchor{doc-symvar}
@deftypefn {Function File} {} symvar (@var{s})
Identify the argument names in the function defined by a string.
Common constant names such as @code{pi}, @code{NaN}, @code{Inf},
@code{eps}, @code{i} or @code{j} are ignored.  The arguments that are
found are returned in a cell array of strings.  If no variables are
found then the returned cell array is empty.
@end deftypefn


@node Commands
@section Commands

Commands are a special class of functions that only accept string
input arguments.  A command can be called as an ordinary function, but
it can also be called without the parentheses.  For example,

@example
my_command hello world
@end example

@noindent
is equivalent to 

@example
my_command("hello", "world")
@end example

@noindent
The general form of a command call is

@example
@var{cmdname} @var{arg1} @var{arg2} @dots{}
@end example

@noindent
which translates directly to

@example
@var{cmdname} ("@var{arg1}", "@var{arg2}", @dots{})
@end example

Any regular function can be used as a command if it accepts string input
arguments.  For example:

@example
@group
toupper lower_case_arg
   @result{} ans = LOWER_CASE_ARG
@end group
@end example

One difficulty of commands occurs when one of the string input arguments
is stored in a variable.  Because Octave can't tell the difference between
a variable name and an ordinary string, it is not possible to pass a
variable as input to a command.  In such a situation a command must be
called as a function.  For example:

@example
@group
strvar = "hello world";
toupper strvar
   @result{} ans = STRVAR
toupper (strvar)
   @result{} ans = HELLO WORLD
@end group
@end example


@node Organization of Functions
@section 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
@file{@var{octave-home}/lib/octave/@var{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.

@table @file
@item audio
Functions for playing and recording sounds.

@item deprecated
Out-of-date functions which will eventually be removed from Octave.

@item elfun
Elementary functions, principally trigonometric.

@item @@ftp
Class functions for the FTP object.

@item general
Miscellaneous matrix manipulations, like @code{flipud}, @code{rot90},
and @code{triu}, as well as other basic functions, like
@code{ismatrix}, @code{nargchk}, etc.

@item geometry
Functions related to Delaunay triangulation.

@item help
Functions for Octave's built-in help system.

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

@item io
Input-output functions.

@item linear-algebra
Functions for linear algebra.

@item miscellaneous
Functions that don't really belong anywhere else.

@item optimization
Functions related to minimization, optimization, and root finding.

@item path
Functions to manage the directory path Octave uses to find functions.

@item pkg
Package manager for installing external packages of functions in Octave.

@item plot
Functions for displaying and printing two- and three-dimensional graphs.

@item polynomial
Functions for manipulating polynomials.

@item prefs
Functions implementing user-defined preferences.

@item set
Functions for creating and manipulating sets of unique values.

@item signal
Functions for signal processing applications.

@item sparse
Functions for handling sparse matrices.

@item specfun
Special functions such as @code{bessel} or @code{factor}.

@item special-matrix
Functions that create special matrix forms such as Hilbert or Vandermonde
matrices.

@item startup
Octave's system-wide startup file.

@item statistics
Statistical functions.

@item strings
Miscellaneous string-handling functions.

@item testfun
Functions for performing unit tests on other functions.

@item time
Functions related to time and date processing.
@end table
