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### 33.5 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 `class` function in the class constructor. As in the case of the polynomial class, the octave programmer will create a struct that contains the data fields required by the class, and then call the class function to indicate that an object is to be created from the struct. 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 easily demonstrated by example. Suppose the programmer needs an FIR filter, i.e. a filter with a numerator polynomial but a unity denominator polynomial. In traditional octave programming, this would be performed as follows.

         octave:1> x = [some data vector];
         octave:2> n = [some coefficient vector];
         octave:3> y = filter (n, 1, x);

The equivalent class could be implemented in a class directory @FIRfilter that is on the octave path. The constructor is a file FIRfilter.m in the class directory.

         ## -*- texinfo -*-
         ## @deftypefn {Function File} {} FIRfilter ()
         ## @deftypefnx {Function File} {} FIRfilter (@var{p})
         ## Creates an FIR filter with polynomial @var{p} as
         ## coefficient vector.
         ##
         ## @end deftypefn

         function f = FIRfilter (p)

           f.polynomial = [];
           if (nargin == 0)
             p = @polynomial ([1]);
           elseif (nargin == 1)
             if (!isa (p, "polynomial"))
               error ("FIRfilter: expecting polynomial as input argument");
             endif
           else
             print_usage ();
           endif
           f = class (f, "FIRfilter", p);
         endfunction

As before, the leading comments provide command-line documentation for the class constructor. This constructor is very similar to the polynomial class constructor, except that we pass a polynomial object as the third argument to the class function, telling octave that the FIRfilter class will be derived from the polynomial class. Our FIR filter does not have any data fields, but we must provide a struct to the `class` function. The `class` function will add an element named polynomial to the object struct, so we simply add a dummy element named polynomial as the first line of the constructor. This dummy element will be overwritten by the class function.

Note further that all our examples provide for the case in which no arguments are supplied. This is important since octave will call the constructor with no arguments when loading ojects from save files to determine the inheritance structure.

A class may be a child of more than one class (see the documentation for the `class` function), 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.

As before, we need a `display` method. A simple example might be

         function display (f)

           display(f.polynomial);

         endfunction

Note that we have used the polynomial field of the struct to display the filter coefficients.

Once we have the class constructor and display method, we may create an object by calling the class constructor. We may also check the class type and examine the underlying structure.

         octave:1> f=FIRfilter(polynomial([1 1 1]/3))
         f.polynomial = 0.333333 + 0.333333 * X + 0.333333 * 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 =
         {
         polynomial = 0.333333 + 0.333333 * X + 0.333333 * X ^ 2
         }

We only need to define a method to actually process data with our filter and our class is usable. It is also useful to provide a means of changing the data stored in the class. Since the fields in the underlying struct are private by default, we could provide a mechanism to access the fields. The `subsref` method may be used for both.

         function out = subsref (f, x)
           switch x.type
             case "()"
               n = f.polynomial;
               out = filter(n.poly, 1, x.subs{1});
             case "."
               fld = x.subs;
               if (strcmp (fld, "polynomial"))
                 out = f.polynomial;
               else
                 error ("@FIRfilter/subsref: invalid property \"%s\"", fld);
               endif
             otherwise
               error ("@FIRfilter/subsref: invalid subscript type for FIR filter");
           endswitch
         endfunction

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

         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

The "." case allows us to view the contents of the polynomial field.

         octave:1> f=FIRfilter(polynomial([1 1 1]/3));
         octave:2> f.polynomial
         ans = 0.333333 + 0.333333 * X + 0.333333 * X ^ 2

In order to change the contents of the object, we need to define a `subsasgn` method. For example, we may make the polynomial field publicly writeable.

         function out = subsasgn (f, index, val)
           switch (index.type)
             case "."
               fld = index.subs;
               if (strcmp (fld, "polynomial"))
                 out = f;
                 out.polynomial = val;
               else
                 error ("@FIRfilter/subsref: invalid property \"%s\"", fld);
               endif
             otherwise
               error ("FIRfilter/subsagn: Invalid index type")
           endswitch
         endfunction

So that

         octave:6> f=FIRfilter();
         octave:7> f.polynomial = polynomial([1 2 3]);
         f.polynomial = 1 + 2 * X + 3 * X ^ 2

Defining the FIRfilter class as a child of the polynomial class implies that and FIRfilter object may be used any place that a polynomial may be used. This is not a normal use of a filter, so that aggregation may be a more sensible design approach. In this case, the polynomial is simply a field in the class structure. A class constructor for this case might be

         ## -*- texinfo -*-
         ## @deftypefn {Function File} {} FIRfilter ()
         ## @deftypefnx {Function File} {} FIRfilter (@var{p})
         ## Creates an FIR filter with polynomial @var{p} as
         ## coefficient vector.
         ##
         ## @end deftypefn

         function f = FIRfilter (p)

           if (nargin == 0)
             f.polynomial = @polynomial ([1]);
           elseif (nargin == 1)
             if (isa (p, "polynomial"))
               f.polynomial = p;
             else
               error ("FIRfilter: expecting polynomial as input argument");
             endif
           else
             print_usage ();
           endif
           f = class (f, "FIRfilter");
         endfunction

For our example, the remaining class methods remain unchanged.