Mercurial > octave
view doc/interpreter/func.txi @ 19069:efd5cf93013b
doc: Move validatestrings into function chapter of manual.
* func.txi: Add validatestrings to function chapter dealing with processing function
inputs.
* strings.txi: Remove validatestrings from strings chapter.
* validateattributes.m: Update seealso cross reference list.
* validatestring.m: Update seealso cross reference list.
author | Rik <rik@octave.org> |
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date | Mon, 01 Sep 2014 11:46:46 -0700 |
parents | be8a12acb20a |
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@c Copyright (C) 1996-2013 John W. Eaton @c @c This file is part of Octave. @c @c Octave is free software; you can redistribute it and/or modify it @c under the terms of the GNU General Public License as published by the @c Free Software Foundation; either version 3 of the License, or (at @c your option) any later version. @c @c Octave is distributed in the hope that it will be useful, but WITHOUT @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License @c for more details. @c @c You should have received a copy of the GNU General Public License @c along with Octave; see the file COPYING. If not, see @c <http://www.gnu.org/licenses/>. @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 * Introduction to Function and Script Files:: * 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 Anonymous Functions Inline Functions:: * Commands:: * Organization of Functions:: @end menu @node Introduction to Function and Script Files @section Introduction to Function and Script Files There are seven different things covered in this section. @enumerate @item Typing in a function at the command prompt. @item Storing a group of commands in a file --- called a script file. @item Storing a function in a file---called a function file. @item Subfunctions in function files. @item Multiple functions in one script file. @item Private functions. @item Nested functions. @end enumerate Both function files and script files end with an extension of .m, for @sc{matlab} compatibility. If you want more than one independent functions in a file, it must be a script file (@pxref{Script Files}), and to use these functions you must execute the script file before you can use the functions that are in the script file. @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 @qcode{"\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. @DOCSTRING(nargin) @DOCSTRING(inputname) @DOCSTRING(silent_functions) @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. @xref{Cell Array Objects}. @DOCSTRING(nthargout) 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. @DOCSTRING(nargout) 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{narginchk} and @code{nargoutchk} are available which provide similar error checking. @DOCSTRING(narginchk) @DOCSTRING(nargoutchk) Besides the number of arguments, inputs can be checked for various properties. @code{validatestring} is used for string arguments and @code{validateattributes} for numeric arguments. @DOCSTRING(validatestring) @DOCSTRING(validateattributes) If none of the preceding functions is sufficient there is also the class @code{inputParser} which can perform extremely complex input checking for functions. @DOCSTRING(inputParser) @anchor{XREFvarargin} @anchor{XREFvarargout} @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 @DOCSTRING(parseparams) @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 @DOCSTRING(isargout) @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. @DOCSTRING(deal) @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 @qcode{"system"} to this function resets the default behavior. @c FIXME -- note about time stamps on files in NFS environments? @DOCSTRING(edit) @DOCSTRING(mfilename) @DOCSTRING(ignore_function_time_stamp) @menu * Manipulating the Load Path:: * Subfunctions:: * Private Functions:: * Nested 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. @DOCSTRING(addpath) @DOCSTRING(genpath) @DOCSTRING(rmpath) @DOCSTRING(savepath) @DOCSTRING(path) @DOCSTRING(pathdef) @DOCSTRING(pathsep) @DOCSTRING(rehash) @DOCSTRING(file_in_loadpath) @DOCSTRING(restoredefaultpath) @DOCSTRING(command_line_path) @DOCSTRING(dir_in_loadpath) @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 Nested Functions @subsection Nested Functions Nested functions are similar to subfunctions in that only the main function is visible outside the file. However, they also allow for child functions to access the local variables in their parent function. This shared access mimics using a global variable to share information --- but a global variable which is not visible to the rest of Octave. As a programming strategy, sharing data this way can create code which is difficult to maintain. It is recommended to use subfunctions in place of nested functions when possible. As a simple example, consider a parent function @code{foo}, that calls a nested child function @code{bar}, with a shared variable @var{x}. @example @group function y = foo () x = 10; bar (); y = x; function bar () x = 20; endfunction endfunction foo () @result{} 20 @end group @end example @noindent Notice that there is no special syntax for sharing @var{x}. This can lead to problems with accidental variable sharing between a parent function and its child. While normally variables are inherited, child function parameters and return values are local to the child function. Now consider the function @code{foobar} that uses variables @var{x} and @var{y}. @code{foobar} calls a nested function @code{foo} which takes @var{x} as a parameter and returns @var{y}. @code{foo} then calls @code{bat} which does some computation. @example @group function z = foobar () x = 0; y = 0; z = foo (5); z += x + y; function y = foo (x) y = x + bat (); function z = bat () z = x; endfunction endfunction endfunction foobar () @result{} 10 @end group @end example @noindent It is important to note that the @var{x} and @var{y} in @code{foobar} remain zero, as in @code{foo} they are a return value and parameter respectively. The @var{x} in @code{bat} refers to the @var{x} in @code{foo}. Variable inheritance leads to a problem for @code{eval} and scripts. If a new variable is created in a parent function, it is not clear what should happen in nested child functions. For example, consider a parent function @code{foo} with a nested child function @code{bar}: @example @group function y = foo (to_eval) bar (); eval (to_eval); function bar () eval ("x = 100;"); eval ("y = x;"); endfunction endfunction foo ("x = 5;") @result{} error: can not add variable "x" to a static workspace foo ("y = 10;") @result{} 10 foo ("") @result{} 100 @end group @end example @noindent The parent function @code{foo} is unable to create a new variable @var{x}, but the child function @code{bar} was successful. Furthermore, even in an @code{eval} statement @var{y} in @code{bar} is the same @var{y} as in its parent function @code{foo}. The use of @code{eval} in conjunction with nested functions is best avoided. As with subfunctions, only the first nested function in a file may be called from the outside. Inside a function the rules are more complicated. In general a nested function may call: @enumerate 0 @item Globally visible functions @item Any function that the nested function's parent can call @item Sibling functions (functions that have the same parents) @item Direct children @end enumerate As a complex example consider a parent function @code{ex_top} with two child functions, @code{ex_a} and @code{ex_b}. In addition, @code{ex_a} has two more child functions, @code{ex_aa} and @code{ex_ab}. For example: @example function ex_top () ## Can call: ex_top, ex_a, and ex_b ## Can NOT call: ex_aa and ex_ab function ex_a () ## Call call everything function ex_aa () ## Can call everything endfunction function ex_ab () ## Can call everything endfunction endfunction function ex_b () ## Can call: ex_top, ex_a, and ex_b ## Can NOT call: ex_aa and ex_ab endfunction endfunction @end example @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. @DOCSTRING(builtin) 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. @DOCSTRING(autoload) @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 @group function my_function () mlock (); @dots{} @end group @end example @noindent prevents @code{my_function} from being removed from memory after it is called, 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 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 () mlock (); persistent calls = 0; printf ("'count_calls' has been called %d times\n", ++calls); endfunction 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 @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. @DOCSTRING(mlock) @DOCSTRING(munlock) @DOCSTRING(mislocked) @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 constructs 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 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{XREFautoload,,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 a part of core Octave 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. @DOCSTRING(source) @node Function Handles Anonymous Functions Inline Functions @section Function Handles, Anonymous Functions, Inline Functions @cindex handle, function handles @cindex anonymous functions @cindex inline, inline 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 @DOCSTRING(is_function_handle) @DOCSTRING(functions) @DOCSTRING(func2str) @DOCSTRING(str2func) @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)}. @DOCSTRING(inline) @DOCSTRING(argnames) @DOCSTRING(formula) @DOCSTRING(symvar) @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