#### 34.3.1 Defining Indexing And Indexed Assignment

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

Built-in Function: subsref (val, idx)

Perform the subscripted element selection operation according to the subscript specified by idx.

The subscript idx is expected to be a structure array with fields ‘type’ and ‘subs’. Valid values for ‘type’ are ‘"()"’, ‘"{}"’, and ‘"."’. The ‘subs’ field may be either ‘":"’ or a cell array of index values.

The following example shows how to extract the first two columns of a matrix

```val = magic (3)
⇒ val = [ 8   1   6
3   5   7
4   9   2 ]
idx.type = "()";
idx.subs = {":", 1:2};
subsref (val, idx)
⇒ [ 8   1
3   5
4   9 ]
```

Note that this is the same as writing `val(:,1:2)`.

If idx is an empty structure array with fields ‘type’ and ‘subs’, return val.

For example we might decide that indexing with `"()"` evaluates the polynomial and indexing with `"{}"` returns the n-th coefficient (of n-th power). In this case the `subsref` method of our polynomial class might look like

```function b = subsref (a, s)
if (isempty (s))
error ("polynomial: missing index");
endif
switch (s(1).type)
case "()"
ind = s(1).subs;
if (numel (ind) != 1)
error ("polynomial: need exactly one index");
else
b = polyval (fliplr (a.poly), ind{1});
endif
case "{}"
ind = s(1).subs;
if (numel (ind) != 1)
error ("polynomial: need exactly one index");
else
if (isnumeric (ind{1}))
b = a.poly(ind{1}+1);
else
b = a.poly(ind{1});
endif
endif
case "."
fld = s.subs;
if (strcmp (fld, "poly"))
b = a.poly;
else
error ("@polynomial/subsref: invalid property \"%s\"", fld);
endif
otherwise
error ("invalid subscript type");
endswitch
if (numel (s) > 1)
b = subsref (b, s(2:end));
endif
endfunction
```
```
```

The equivalent functionality for subscripted assignments uses the `subsasgn` method.

Built-in Function: subsasgn (val, idx, rhs)

Perform the subscripted assignment operation according to the subscript specified by idx.

The subscript idx is expected to be a structure array with fields ‘type’ and ‘subs’. Valid values for ‘type’ are ‘"()"’, ‘"{}"’, and ‘"."’. The ‘subs’ field may be either ‘":"’ or a cell array of index values.

The following example shows how to set the two first columns of a 3-by-3 matrix to zero.

```val = magic (3);
idx.type = "()";
idx.subs = {":", 1:2};
subsasgn (val, idx, 0)
⇒  [ 0   0   6
0   0   7
0   0   2 ]
```

Note that this is the same as writing `val(:,1:2) = 0`.

If idx is an empty structure array with fields ‘type’ and ‘subs’, return rhs.

Built-in Function: val = optimize_subsasgn_calls ()
Built-in Function: old_val = optimize_subsasgn_calls (new_val)
Built-in Function: optimize_subsasgn_calls (new_val, "local")

Query or set the internal flag for subsasgn method call optimizations.

If true, Octave will attempt to eliminate the redundant copying when calling the subsasgn method of a user-defined class.

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.

Note that the `subsref` and `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 `subsref` or `subsasgn`.

If you wish to use the `end` keyword in subscripted expressions of an object, then the user needs to define the `end` method for the class. For example, the `end` method for our polynomial class might look like

```function r = end (obj, index_pos, num_indices)

if (num_indices != 1)
error ("polynomial object may only have one index")
endif

r = length (obj.poly) - 1;

endfunction
```
```
```

which is a fairly generic `end` method that has a behavior similar to the `end` keyword for Octave Array classes. It can then be used as follows:

```p = polynomial ([1,2,3,4]);
p(end-1)
⇒ 3
```

Objects can also be used as the index in a subscripted expression themselves and this is controlled with the `subsindex` function.

Function File: idx = subsindex (a)

Convert an object to an index vector.

When a is a class object defined with a class constructor, then `subsindex` is the overloading method that allows the conversion of this class object to a valid indexing vector. It is important to note that `subsindex` must return a zero-based real integer vector of the class `"double"`. For example, if the class constructor

```function b = myclass (a)
b = class (struct ("a", a), "myclass");
endfunction
```

then the `subsindex` function

```function idx = subsindex (a)
idx = double (a.a) - 1.0;
endfunction
```

can then be used as follows

```a = myclass (1:4);
b = 1:10;
b(a)
⇒ 1  2  3  4
```

Finally, objects can equally be used like ranges, using the `colon` method
This function is equivalent to the operator syntax `base : limit` or `base : increment : limit`.