C++ for Scientists - Technische Universität Dresden

112 CHAPTER 4. GENERIC PROGRAMMING
Note that the function finite difference takes an arbitrary function (from double to double) as
argument.
Now suppose we want to compute the second order derivative. It would make sense to call
finite difference with finite difference as argument. Unfortunately this is not possible since we have
three arguments in this function and the first argument of finite difference only accepts a function
with a single argument.
For this reason, we can use ‘functors’. Functors — not to confuse with functors from category
theory — are either functions or objects of classes providing operator(). This means that
‘functors’ are things which can be called liked functions but are not necessarily functions.
Using objects of a class providing operator() has the additional advantage that it can use an
internal state in terms of member variables. 21
For our example, the functor could be implemented as follows:
struct sin plus cos
{
double operator() (double x) const
{
return sin(x) + cos(x) ;
}
};
but we could also consider a functor with an parameter like this:
class para sin plus cos
{
public:
para sin plus cos(double parameter) : parameter(parameter) {}
double operator() (double x) const
{
return sin(parameter ∗ x) + cos(x) ;
}
private:
double parameter;
} ;
How can we use the functor in a function? We want to be able to pass objects of both sin plus cos
and para sin plus cos to our finite difference function. There are two possible solutions: inheritance
and generic programming, which we now discuss.
4.8.1 Functors via inheritance
TODO: Better as counter-example in OO chapter. We haven’t introduced virtual functions
yet.
Let us first rewrite our function finite difference using an abstract base class.
21 TODO: Do we want the following sentences?: Functors can encapsulate C and C ++ function pointers
employing the concepts templates and polymorphism. All the functions must have the same return-type and
calling parameters.