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@c FIXME
@c For now can't include "@" character in the path name, and so name
@c the example directory without the "@"!!

@node Object Oriented Programming
@chapter Object Oriented Programming

Octave has the ability to create user-defined classes---including the
capabilities of operator and function overloading.  Classes can protect
internal properties so that they may not be altered accidentally which
facilitates data encapsulation.  In addition, rules can be created to address
the issue of class precedence in mixed class operations.

This chapter discusses the means of constructing a user class, how to query and
set the properties of a class, and how to overload operators and functions.
Throughout this chapter real code examples are given using a class designed
for polynomials.

@menu
* Creating a Class::
* Class Methods::
* Indexing Objects::
* Overloading Objects::
* Inheritance and Aggregation::
* classdef Classes::
@end menu

@node Creating a Class
@section Creating a Class

This chapter illustrates user-defined classes and object oriented programming
through a custom class designed for polynomials.  This class was chosen for
its simplicity which does not distract unnecessarily from the discussion of
the programming features of Octave.  Even so, a bit of background on the goals
of the polynomial class is necessary before the syntax and techniques of Octave
object oriented programming are introduced.

The polynomial class is used to represent polynomials of the form
@tex
$$
a_0 + a_1 x + a_2 x^2 + \ldots a_n x^n
$$
@end tex
@ifnottex

@example
a0 + a1 * x + a2 * x^2 + @dots{} + an * x^n
@end example

@end ifnottex
@noindent
where
@tex
$a_0$, $a_1$, etc. are elements of $\Re$.
@end tex
@ifnottex
a0, a1, etc.@: are real scalars.
@end ifnottex
Thus the polynomial can be represented by a vector

@example
a = [a0, a1, a2, @dots{}, an];
@end example

@opindex @@ class methods
This is a sufficient specification to begin writing the constructor for the
polynomial class.  All object oriented classes in Octave must be located in a
directory that is the name of the class prepended with the @samp{@@} symbol.
For example, the polynomial class will have all of its methods defined in the
@file{@@polynomial} directory.

The constructor for the class must be the name of the class itself; in this
example the constructor resides in the file @file{@@polynomial/polynomial.m}.
Ideally, even when the constructor is called with no arguments it should return
a valid object.  A constructor for the polynomial class might look like

@example
@EXAMPLEFILE(@polynomial/polynomial.m)
@end example

Note that the return value of the constructor must be the output of the
@code{class} function.  The first argument to the @code{class} function is a
structure and the second is the name of the class itself.  An example of
calling the class constructor to create an instance is

@example
p = polynomial ([1, 0, 1]);
@end example

Methods are defined by m-files in the class directory and can have embedded
documentation the same as any other m-file.  The help for the constructor can
be obtained by using the constructor name alone, that is, for the polynomial
constructor @code{help polynomial} will return the help string.  Help can be
restricted to a particular class by using the class directory name followed
by the method.  For example, @code{help @@polynomial/polynomial} is another
way of displaying the help string for the polynomial constructor.  This second
means is the only way to obtain help for the overloaded methods and functions
of a class.

The same specification mechanism can be used wherever Octave expects a function
name.  For example @code{type @@polynomial/disp} will print the code of the
@code{disp} method of the polynomial class to the screen, and
@code{dbstop @@polynomial/disp} will set a breakpoint at the first executable
line of the @code{disp} method of the polynomial class.

To check whether a variable belongs to a user class, the @code{isobject} and
@code{isa} functions can be used.  For example:

@example
@group
p = polynomial ([1, 0, 1]);
isobject (p)
  @result{} 1
isa (p, "polynomial")
  @result{} 1
@end group
@end example

@DOCSTRING(isobject)

@noindent
The available methods of a class can be displayed with the @code{methods}
function.

@DOCSTRING(methods)

@noindent
To inquire whether a particular method exists for a user class, the
@code{ismethod} function can be used.

@DOCSTRING(ismethod)

@noindent
For a polynomial class it makes sense to have a method to compute its roots.

@example
@group
@EXAMPLEFILE(@polynomial/roots.m)
@end group
@end example

We can check for the existence of the @code{roots}-method by calling:

@example
@group
p = polynomial ([1, 0, 1]);
ismethod (p, "roots")
  @result{} 1
@end group
@end example

@node Class Methods
@section Class Methods

There are a number of basic class methods that can (and should) be defined to
allow the contents of the classes to be queried and set.  The most basic of
these is the @code{disp} method.  The @code{disp} method is used by Octave
whenever a class should be displayed on the screen.  Usually this is the result
of an Octave expression that doesn't end with a semicolon.  If this method is
not defined, then Octave won't print anything when displaying the contents of a
class which can be confusing.

@noindent
An example of a @code{disp} method for the polynomial class might be

@example
@EXAMPLEFILE(@polynomial/disp.m)
@end example

To be consistent with the Octave graphic handle classes, a class should also
define the @code{get} and @code{set} methods.  The @code{get} method accepts
one or two arguments.  The first argument is an object of the appropriate
class.  If no second argument is given then the method should return a
structure with all the properties of the class.  If the optional second
argument is given it should be a property name and the specified property
should be retrieved.

@example
@EXAMPLEFILE(@polynomial/get.m)
@end example

@noindent
Similarly, the first argument to the @code{set} method should be an object and
any additional arguments should be property/value pairs.

@example
@EXAMPLEFILE(@polynomial/set.m)
@end example

@noindent
Note that Octave does not implement pass by reference; Therefore, to modify an
object requires an assignment statement using the return value from the
@code{set} method.

@example
p = set (p, "poly", [1, 0, 0, 0, 1]);
@end example

@noindent
The @code{set} method makes use of the @code{subsasgn} method of the class, and
therefore this method must also be defined.  The @code{subsasgn} method is
discussed more thoroughly in the next section (@pxref{Indexing Objects}).

Finally, user classes can be considered to be a special type of a structure,
and they can be saved to a file in the same manner as a structure.  For
example:

@example
@group
p = polynomial ([1, 0, 1]);
save userclass.mat p
clear p
load userclass.mat
@end group
@end example

@noindent
All of the file formats supported by @code{save} and @code{load} are supported.
In certain circumstances a user class might contain a field that it doesn't
make sense to save, or a field that needs to be initialized before it is saved.
This can be done with the @code{saveobj} method of the class.

@DOCSTRING(saveobj)

@noindent
@code{saveobj} is called just prior to saving the class to a file.  Similarly,
the @code{loadobj} method is called just after a class is loaded from a file,
and can be used to ensure that any removed fields are reinserted into the user
object.

@DOCSTRING(loadobj)

@node Indexing Objects
@section Indexing Objects

@menu
* Defining Indexing And Indexed Assignment::
* Indexed Assignment Optimization::
@end menu

@node Defining Indexing And Indexed Assignment
@subsection Defining Indexing And Indexed Assignment

Objects can be indexed with parentheses or braces, either like
@code{@var{obj}(@var{idx})} or like @code{@var{obj}@{@var{idx}@}}, or even
like @code{@var{obj}(@var{idx}).@var{field}}.  However, it is up to the
programmer to decide what this indexing actually means.  In the case of the
polynomial class @code{@var{p}(@var{n})} might mean either the coefficient of
the @var{n}-th power of the polynomial, or it might be the evaluation of the
polynomial at @var{n}.  The meaning of this subscripted referencing is
determined by the @code{subsref} method.

@DOCSTRING(subsref)

For example, this class uses the convention that indexing with @qcode{"()"}
evaluates the polynomial and indexing with @qcode{"@{@}"} returns the
@var{n}-th coefficient (of the @var{n}-th power).  The code for the
@code{subsref} method looks like

@example
@EXAMPLEFILE(@polynomial/subsref.m)
@end example

The equivalent functionality for subscripted assignments uses the
@code{subsasgn} method.

@DOCSTRING(subsasgn)

@DOCSTRING(optimize_subsasgn_calls)

Note that the @code{subsref} and @code{subsasgn} methods always receive the
whole index chain, while they usually handle only the first element.  It is the
responsibility of these methods to handle the rest of the chain (if needed),
usually by forwarding it again to @code{subsref} or @code{subsasgn}.

If you wish to use the @code{end} keyword in subscripted expressions of an
object, then there must be an @code{end} method defined.  For example, the
@code{end} method for the polynomial class might look like

@example
@group
@EXAMPLEFILE(@polynomial/end.m)
@end group
@end example

@noindent
which is a fairly generic @code{end} method that has a behavior similar to the
@code{end} keyword for Octave Array classes.  An example using the polynomial
class is then

@example
@group
p = polynomial ([1,2,3,4]);
p@{end-1@}
  @result{} 3
@end group
@end example

Objects can also be used themselves as the index in a subscripted expression
and this is controlled by the @code{subsindex} function.

@DOCSTRING(subsindex)

Finally, objects can be used like ranges by providing a @code{colon} method.

@DOCSTRING(colon)

@node Indexed Assignment Optimization
@subsection Indexed Assignment Optimization

Octave's ubiquitous lazily-copied pass-by-value semantics implies a problem for
performance of user-defined @code{subsasgn} methods.  Imagine the following
call to @code{subsasgn}

@example
@group
ss = substruct ("()", @{1@});
x = subsasgn (x, ss, 1);
@end group
@end example

@noindent
where the corresponding method looking like this:

@example
@group
function x = subsasgn (x, ss, val)
  @dots{}
  x.myfield (ss.subs@{1@}) = val;
endfunction
@end group
@end example

The problem is that on entry to the @code{subsasgn} method, @code{x} is still
referenced from the caller's scope, which means that the method will first need
to unshare (copy) @code{x} and @code{x.myfield} before performing the
assignment.  Upon completing the call, unless an error occurs, the result is
immediately assigned to @code{x} in the caller's scope, so that the previous
value of @code{x.myfield} is forgotten.  Hence, the Octave language implies a
copy of N elements (N being the size of @code{x.myfield}), where modifying just
a single element would actually suffice.  In other words, a constant-time
operation is degraded to linear-time one.  This may be a real problem for user
classes that intrinsically store large arrays.

To partially solve the problem Octave uses a special optimization for
user-defined @code{subsasgn} methods coded as m-files.  When the method gets
called as a result of the built-in assignment syntax (not a direct
@code{subsasgn} call as shown above), i.e., @w{@code{x(1) = 1}},  @b{AND} if
the @code{subsasgn} method is declared with identical input and output
arguments, as in the example above, then Octave will ignore the copy of
@code{x} inside the caller's scope; therefore, any changes made to @code{x}
during the method execution will directly affect the caller's copy as well.
This allows, for instance, defining a polynomial class where modifying a single
element takes constant time.

It is important to understand the implications that this optimization brings.
Since no extra copy of @code{x} will exist in the caller's scope, it is
@emph{solely} the callee's responsibility to not leave @code{x} in an invalid
state if an error occurs during the execution.  Also, if the method partially
changes @code{x} and then errors out, the changes @emph{will} affect @code{x}
in the caller's scope.  Deleting or completely replacing @code{x} inside
subsasgn will not do anything, however, only indexed assignments matter.

Since this optimization may change the way code works (especially if badly
written), a function @code{optimize_subsasgn_calls} is provided to
control it.  This feature is enabled by default.  Another way to avoid
the optimization is to declare subsasgn methods with different output
and input arguments like this:

@example
@group
function y = subsasgn (x, ss, val)
  @dots{}
endfunction
@end group
@end example

@node Overloading Objects
@section Overloading Objects

@menu
* Function Overloading::
* Operator Overloading::
* Precedence of Objects::
@end menu

@node Function Overloading
@subsection Function Overloading

Any Octave function can be overloaded, and this allows an object-specific
version of a function to be called as needed.  A pertinent example for the
polynomial class might be to overload the @code{polyval} function.

@example
@group
@EXAMPLEFILE(@polynomial/polyval.m)
@end group
@end example

This function just hands off the work to the normal Octave @code{polyval}
function.  Another interesting example of an overloaded function for the
polynomial class is the @code{plot} function.

@example
@group
@EXAMPLEFILE(@polynomial/plot.m)
@end group
@end example

@noindent
which allows polynomials to be plotted in the domain near the region of the
roots of the polynomial.

Functions that are of particular interest for overloading are the class
conversion functions such as @code{double}.  Overloading these functions allows
the @code{cast} function to work with a user class.  It can also aid in the
use of a class object with methods and functions from other classes since the
object can be transformed to the requisite input form for the new function.
An example @code{double} function for the polynomial class might look like

@example
@group
@EXAMPLEFILE(@polynomial/double.m)
@end group
@end example

@node Operator Overloading
@subsection Operator Overloading
@cindex addition
@cindex and operator
@cindex arithmetic operators
@cindex boolean expressions
@cindex boolean operators
@cindex comparison expressions
@cindex complex-conjugate transpose
@cindex division
@cindex equality operator
@cindex equality, tests for
@cindex exponentiation
@cindex expressions, boolean
@cindex expressions, comparison
@cindex expressions, logical
@cindex greater than operator
@cindex Hermitian operator
@cindex less than operator
@cindex logical expressions
@cindex logical operators
@cindex matrix multiplication
@cindex multiplication
@cindex negation
@cindex not operator
@cindex operators, arithmetic
@cindex operators, boolean
@cindex operators, logical
@cindex operators, relational
@cindex or operator
@cindex quotient
@cindex relational operators
@cindex subtraction
@cindex tests for equality
@cindex transpose
@cindex transpose, complex-conjugate
@cindex unary minus

@c Need at least one plaintext sentence here between the @node and @float
@c table below or the two will overlap due to a bug in Texinfo.
@c This is not our fault; this *is* a ridiculous kluge.
The following table shows, for each built-in numerical operation, the
corresponding function name to use when providing an overloaded method for a
user class.

@float Table,tab:overload_ops
@opindex +
@opindex -
@opindex .*
@opindex *
@opindex ./
@opindex /
@opindex .\
@opindex \
@opindex .^
@opindex ^
@opindex <
@opindex <=
@opindex >
@opindex >=
@opindex ==
@opindex !=
@opindex ~=
@opindex &
@opindex |
@opindex !
@opindex @code{'}
@opindex @code{.'}
@opindex :
@opindex <

@multitable {@code{a(s@math{_1},@dots{},s@math{_n}) = b}} {@code{subsasgn (a, s, b)}} {Complex conjugate transpose}
@headitem Operation @tab Method @tab Description
@item @code{a + b} @tab @code{plus (a, b)} @tab Binary addition
@item @code{a - b} @tab @code{minus (a, b)} @tab Binary subtraction
@item @code{+a} @tab @code{uplus (a)} @tab Unary addition
@item @code{-a} @tab @code{uminus (a)} @tab Unary subtraction
@item @code{a .* b} @tab @code{times (a, b)} @tab Element-wise multiplication
@item @code{a * b} @tab @code{mtimes (a, b)} @tab Matrix multiplication
@item @code{a ./ b} @tab @code{rdivide (a, b)} @tab Element-wise right division
@item @code{a / b} @tab @code{mrdivide (a, b)} @tab Matrix right division
@item @code{a .\ b} @tab @code{ldivide (a, b)} @tab Element-wise left division
@item @code{a \ b} @tab @code{mldivide (a, b)} @tab Matrix left division
@item @code{a .^ b} @tab @code{power (a, b)} @tab Element-wise power
@item @code{a ^ b} @tab @code{mpower (a, b)} @tab Matrix power
@item @code{a < b} @tab @code{lt (a, b)} @tab Less than
@item @code{a <= b} @tab @code{le (a, b)} @tab Less than or equal to
@item @code{a > b} @tab @code{gt (a, b)} @tab Greater than
@item @code{a >= b} @tab @code{ge (a, b)} @tab Greater than or equal to
@item @code{a == b} @tab @code{eq (a, b)} @tab Equal to
@item @code{a != b} @tab @code{ne (a, b)} @tab Not equal to
@item @code{a & b} @tab @code{and (a, b)} @tab Logical and
@item @code{a | b} @tab @code{or (a, b)} @tab Logical or
@item @code{!a} @tab @code{not (a)} @tab Logical not
@item @code{a'} @tab @code{ctranspose (a)} @tab Complex conjugate transpose
@item @code{a.'} @tab @code{transpose (a)} @tab Transpose
@item @code{a:b} @tab @code{colon (a, b)} @tab Two element range
@item @code{a:b:c} @tab @code{colon (a, b, c)} @tab Three element range
@item @code{[a, b]} @tab @code{horzcat (a, b)} @tab Horizontal concatenation
@item @code{[a; b]} @tab @code{vertcat (a, b)} @tab Vertical concatenation
@item @code{a(s@math{_1},@dots{},s@math{_n})} @tab @code{subsref (a, s)} @tab Subscripted reference
@item @code{a(s@math{_1},@dots{},s@math{_n}) = b} @tab @code{subsasgn (a, s, b)} @tab Subscripted assignment
@item @code{b(a)} @tab @code{subsindex (a)} @tab Convert object to index
@item @code{disp} @tab @code{disp (a)} @tab Object display
@end multitable
@caption{Available overloaded operators and their corresponding class method}
@end float

An example @code{mtimes} method for the polynomial class might look like

@example
@group
@EXAMPLEFILE(@polynomial/mtimes.m)
@end group
@end example

@node Precedence of Objects
@subsection Precedence of Objects

Many functions and operators take two or more arguments and the situation can
easily arise where these functions are called with objects of different
classes.  It is therefore necessary to determine the precedence of which method
from which class to call when there are mixed objects given to a function or
operator.  To do this the @code{superiorto} and @code{inferiorto} functions can
be used

@DOCSTRING(superiorto)

@DOCSTRING(inferiorto)

With the polynomial class, consider the case

@example
2 * polynomial ([1, 0, 1]);
@end example

@noindent
that mixes an object of the class @qcode{"double"} with an object of the class
@qcode{"polynomial"}.  In this case the return type should be
@qcode{"polynomial"} and so the @code{superiorto} function is used in the class
constructor.  In particular the polynomial class constructor would be modified
to

@example
@EXAMPLEFILE(@polynomial/polynomial_superiorto.m)
@end example

Note that user classes @emph{always} have higher precedence than built-in
Octave types.  Thus, marking the polynomial class higher than the
@qcode{"double"} class is not actually necessary.

When confronted with two objects of equal precedence, Octave will use the
method of the object that appears first in the list of arguments.

@node Inheritance and Aggregation
@section Inheritance and Aggregation

Using classes to build new classes is supported by Octave through the use of
both inheritance and aggregation.

Class inheritance is provided by Octave using the @code{class} function in the
class constructor.  As in the case of the polynomial class, the Octave
programmer will create a structure that contains the data fields required by
the class, and then call the @code{class} function to indicate that an object
is to be created from the structure.  Creating a child of an existing object is
done by creating an object of the parent class and providing that object as the
third argument of the class function.

This is most easily demonstrated by example.  Suppose the programmer needs a
FIR filter, i.e., a filter with a numerator polynomial but a denominator of 1.
In traditional Octave programming this would be performed as follows.

@example
@group
>> x = [some data vector];
>> n = [some coefficient vector];
>> y = filter (n, 1, x);
@end group
@end example

The equivalent behavior can be implemented as a class @code{@@FIRfilter}.  The
constructor for this class is the file @file{FIRfilter.m} in the class
directory @file{@@FIRfilter}.

@example
@EXAMPLEFILE(@FIRfilter/FIRfilter.m)
@end example

As before, the leading comments provide documentation for the class
constructor.  This constructor is very similar to the polynomial class
constructor, except that a polynomial object is passed as the third argument to
the @code{class} function, telling Octave that the @code{FIRfilter} class will
be derived from the polynomial class.  The FIR filter class itself does not
have any data fields, but it must provide a struct to the @code{class}
function.  Given that the @code{@@polynomial} constructor will add an element
named @var{polynomial} to the object struct, the @code{@@FIRfilter} just
initializes a struct with a dummy field @var{polynomial} which will later be
overwritten.

Note that the sample code always provides for the case in which no arguments
are supplied.  This is important because Octave will call a constructor with
no arguments when loading objects from saved files in order to determine the
inheritance structure.

A class may be a child of more than one class (@pxref{XREFclass,,class}), and
inheritance may be nested.  There is no limitation to the number of parents or
the level of nesting other than memory or other physical issues.

For the @code{FIRfilter} class, more control about the object display is
desired.  Therefore, the @code{display} method rather than the @code{disp}
method is overloaded (@pxref{Class Methods}).  A simple example might be

@example
@group
@EXAMPLEFILE(@FIRfilter/display.m)
@end group
@end example

Note that the @code{FIRfilter}'s display method relies on the @code{disp}
method from the @code{polynomial} class to actually display the filter
coefficients.  Furthermore, note that in the @code{display} method it makes
sense to start the method with the line
@code{@code{printf ("%s =", inputname (1))}} to be consistent with the
rest of Octave which prints the variable name to be displayed followed by the
value.  In general it is not recommended to overload the @code{display}
function.

@DOCSTRING(display)

Once a constructor and display method exist, it is possible to create an
instance of the class.  It is also possible to check the class type and examine
the underlying structure.

@example
@group
octave:1> f = FIRfilter (polynomial ([1 1 1]/3))
f.polynomial = 0.33333 + 0.33333 * X + 0.33333 * X ^ 2
octave:2> class (f)
ans = FIRfilter
octave:3> isa (f, "FIRfilter")
ans =  1
octave:4> isa (f, "polynomial")
ans =  1
octave:5> struct (f)
ans =

  scalar structure containing the fields:

polynomial = 0.33333 + 0.33333 * X + 0.33333 * X ^ 2
@end group
@end example

The only thing remaining to make this class usable is a method for processing
data.  But before that, it is usually desirable to also have a way of changing
the data stored in a class.  Since the fields in the underlying struct are
private by default, it is necessary to provide a mechanism to access the
fields.  The @code{subsref} method may be used for both tasks.

@example
@EXAMPLEFILE(@FIRfilter/subsref.m)
@end example

The @qcode{"()"} case allows us to filter data using the polynomial provided
to the constructor.

@example
@group
octave:2> f = FIRfilter (polynomial ([1 1 1]/3));
octave:3> x = ones (5,1);
octave:4> y = f(x)
y =

   0.33333
   0.66667
   1.00000
   1.00000
   1.00000
@end group
@end example

The @qcode{"."} case allows us to view the contents of the polynomial field.

@example
@group
octave:1> f = FIRfilter (polynomial ([1 1 1]/3));
octave:2> f.polynomial
ans = 0.33333 + 0.33333 * X + 0.33333 * X ^ 2
@end group
@end example

In order to change the contents of the object a @code{subsasgn} method is
needed.  For example, the following code makes the polynomial field publicly
writable

@example
@group
@EXAMPLEFILE(@FIRfilter/subsasgn.m)
@end group
@end example

@noindent
so that

@example
@group
octave:1> f = FIRfilter ();
octave:2> f.polynomial = polynomial ([1 2 3])
f.polynomial = 1 + 2 * X + 3 * X ^ 2
@end group
@end example

Defining the @w{FIRfilter} class as a child of the polynomial class implies
that a @w{FIRfilter} object may be used any place that a polynomial object may
be used.  This is not a normal use of a filter.  It may be a more sensible
design approach to use aggregation rather than inheritance.  In this case, the
polynomial is simply a field in the class structure.  A class constructor for
the aggregation case might be

@example
@EXAMPLEFILE(@FIRfilter/FIRfilter_aggregation.m)
@end example

For this example only the constructor needs changing, and all other class
methods stay the same.

@node classdef Classes
@section @code{classdef} Classes

Since version 4.0, Octave has limited support for @code{classdef} classes.  In
contrast to the aforementioned classes, called @dfn{old style classes} in this
section, @code{classdef} classes can be defined within a single m-file.  Other
innovations of @code{classdef} classes are:

@itemize @bullet
@item
@b{access rights} for properties and methods,

@item
@b{static methods}, i.e., methods that are independent of an object, and

@item
the distinction between @b{value and handle classes}.
@end itemize

Several features have to be added in future versions of Octave to be fully
compatible to @sc{matlab}.  An overview of what is missing can be found at
@url{https://wiki.octave.org/Classdef}.

@menu
* Creating a classdef Class::
* Properties::
* Methods::
* Inheritance::
* Value Classes vs. Handle Classes::
@end menu

@node Creating a classdef Class
@subsection Creating a @code{classdef} Class

A very basic @code{classdef} value class
(@pxref{Value Classes vs. Handle Classes}) is defined by:

@example
@group
classdef some_class
  properties
  endproperties

  methods
  endmethods
endclassdef
@end group
@end example



In contrast to old style classes, the @code{properties}-@code{endproperties}
block as well as the @code{methods}-@code{endmethods} block can be used to
define properties and methods of the class.  Because both blocks are empty,
they can be omitted in this particular case.

For simplicity, a more advanced implementation of a @code{classdef} class is
shown using the @code{polynomial} example again (@pxref{Creating a Class}):

@example
@EXAMPLEFILE(polynomial2.m)
@end example

@noindent
An object of class @code{polynomial2} is created by calling the class
constructor:

@example
@group
>> p = polynomial2 ([1, 0, 1])
@result{} p =

 1 + X ^ 2
@end group
@end example

@node Properties
@subsection Properties

All class properties must be defined within @code{properties} blocks.  The
definition of a default value for a property is optional and can be omitted.
The default initial value for each class property is @code{[]}.

A @code{properties} block can have additional attributes to specify access
rights or to define constants:

@example
@group
classdef some_class
  properties (Access = @var{mode})
    @var{prop1}
  endproperties

  properties (SetAccess = @var{mode}, GetAccess = @var{mode})
    @var{prop2}
  endproperties

  properties (Constant = true)
    @var{prop3} = pi ()
  endproperties

  properties
    @var{prop4} = 1337
  endproperties
endclassdef
@end group
@end example

@noindent
where @var{mode} can be one of:

@table @code
@item public
The properties can be accessed from everywhere.

@item private
The properties can only be accessed from class methods.  Subclasses of that
class cannot access them.

@item protected
The properties can only be accessed from class methods and from subclasses
of that class.
@end table

When creating an object of @code{some_class}, @var{prop1} has the default
value @code{[]} and reading from and writing to @var{prop1} is defined by
a single @var{mode}.  For @var{prop2} the read and write access can be set
differently.  Finally, @var{prop3} is a constant property which can only be
initialized once within the @code{properties} block.

By default, in the example @var{prop4}, properties are not constant and have
public read and write access.

@DOCSTRING(properties)

@node Methods
@subsection Methods

All class methods must be defined within @code{methods} blocks.  An exception
to this rule is described at the end of this subsection.  Those @code{methods}
blocks can have additional attributes specifying the access rights or whether
the methods are static, i.e., methods that can be called without creating an
object of that class.

@example
classdef some_class
  methods
    function obj = some_class ()
      disp ("New instance created.");
    endfunction

    function disp (obj)
      disp ("Here is some_class.");
    endfunction
  endmethods

  methods (Access = @var{mode})
    function r = func (obj, r)
      r = 2 * r;
    endfunction
  endmethods

  methods (Static = true)
    function c = circumference (radius)
      c = 2 * pi () .* radius;
    endfunction
  endmethods
endclassdef
@end example

The constructor of the class is declared in the @code{methods} block and must
have the same name as the class and exactly one output argument which is an
object of its class.

It is also possible to overload built-in or inherited methods, like the
@code{disp} function in the example above to tell Octave how objects of
@code{some_class} should be displayed (@pxref{Class Methods}).

In general, the first argument in a method definition is always the object that
it is called from.  Class methods can either be called by passing the object as
the first argument to that method or by calling the object followed by a dot
("@code{.}") and the method's name with subsequent arguments:

@example
@group
>> obj = some_class ();
New instance created.
>> disp (obj);   # both are
>> obj.disp ();  # equal
@end group
@end example

In @code{some_class}, the method @code{func} is defined within a @code{methods}
block setting the @code{Access} attribute to @var{mode}, which is one of:

@table @code
@item public
The methods can be accessed from everywhere.

@item private
The methods can only be accessed from other class methods.  Subclasses of that
class cannot access them.

@item protected
The methods can only be accessed from other class methods and from subclasses
of that class.
@end table

@noindent
The default access for methods is @code{public}.

Finally, the method @code{circumference} is defined in a static @code{methods}
block and can be used without creating an object of @code{some_class}.  This is
useful for methods, that do not depend on any class properties.  The class name
and the name of the static method, separated by a dot ("@code{.}"), call this
static method.  In contrast to non-static methods, the object is not passed as
first argument even if called using an object of @code{some_class}.

@example
@group
>> some_class.circumference (3)
@result{} ans =  18.850
>> obj = some_class ();
New instance created.
>> obj.circumference (3)
@result{} ans =  18.850
@end group
@end example

Additionally, class methods can be defined as functions in a folder of the same
name as the class prepended with the @samp{@@} symbol
(@pxref{Creating a Class}).  The main @code{classdef} file has to be stored in
this class folder as well.

@node Inheritance
@subsection Inheritance

Classes can inherit from other classes.  In this case all properties and
methods of the superclass are inherited to the subclass, considering their
access rights.  Use this syntax to inherit from @code{superclass}:

@example
@group
classdef subclass < superclass
  @dots{}
endclassdef
@end group
@end example

@node Value Classes vs. Handle Classes
@subsection Value Classes vs. Handle Classes

There are two intrinsically different types of @code{classdef} classes, whose
major difference is the behavior regarding variable assignment.  The first type
are @b{value classes}:

@example
@group
classdef value_class
  properties
    prop1
  endproperties

  methods
    function obj = set_prop1 (obj, val)
      obj.prop1 = val;
    endfunction
  endmethods
endclassdef
@end group
@end example

@noindent
Assigning an object of that class to another variable essentially creates a new
object:

@example
@group
>> a = value_class ();
>> a.prop1 = 1;
>> b = a;
>> b.prop1 = 2;
>> b.prop1
@result{} ans =  2
>> a.prop1
@result{} ans =  1
@end group
@end example

But that also means that you might have to assign the output of a method that
changes properties back to the object manually:

@example
@group
>> a = value_class ();
>> a.prop1 = 1;
>> a.set_prop1 (3);
@result{} ans =

<object value_class>

>> ans.prop1
@result{} ans =  3
>> a.prop1
@result{} ans =  1
@end group
@end example

The second type are @b{handle classes}.  Those classes have to be derived from
the abstract @code{handle} class:

@example
@group
classdef handle_class < handle
  properties
    prop1
  endproperties

  methods
    function set_prop1 (obj, val)
      obj.prop1 = val;
    endfunction
  endmethods
endclassdef
@end group
@end example

In the following example, the variables @code{a} and @code{b} refer to the
very same object of class @code{handle_class}:

@example
@group
>> a = handle_class ();
>> a.prop1 = 1;
>> b = a;
>> b.prop1 = 2;
>> b.prop1
@result{} ans =  2
>> a.prop1
@result{} ans =  2
@end group
@end example

Object properties that are modified by a method of an handle class are changed
persistently:

@example
@group
>> a.set_prop1 (3);
>> a.prop1
@result{} ans =  3
@end group
@end example

