C++ for Scientists - Technische Universität Dresden

4.8. FUNCTORS 119
std::cout ≪ ”Seventh derivative of sin 1 at x=3 is ”
≪ make nth derivative(sin 1, 0.00001)(3.0) ≪ ’\n’;
In the cases above the type of the functor was obvious because we wrote the class ourselves. The
type is less obvious if the type is constructed from an expression, for instance by a λ-function.
Support for λ-functions will be introduced with C ++0x. 25 Emulation is available since some
years with Boost.Lambda [?]. For instance, we can generate a functor object that computes
with the following short expression:
(3.5 ∗ 1 + 4.0) ∗ 1 ∗ 1;
p(x) = 3.5x 3 + 4x 2 = (3.5x + 4)x 2
This expression can be used with our derivative function:
make nth derivative((3.5 ∗ 1 + 4.0) ∗ 1 ∗ 1, 0.0001)
to generate a functor computing (approximating) 21x + 8.
With the lambda expressions, we do not even know the type of our functor but we can compute
its derivative. The type is in fact so long 26 that it is much easier to implement our own functor
when we were obliged to spell the type out.
The following listing illustrates how to approximate p ′′ (2):
#include
// .. our definitions of derivatives
int main()
{
using boost::lambda:: 1;
std::cout ≪ ”Second derivative of 3.5∗xˆ3+4∗xˆ2 at x=2 is ”
≪ make nth derivative((3.5 ∗ 1 + 4.0) ∗ 1 ∗ 1, 0.0001)(2) ≪ ’\n’;
return 0;
}
Unfortunately, we cannot keep the results of our computations if we do not know their types
with current standard C ++. In C ++0x, we will be able to let the compiler deduce the type:
auto p= (3.5 ∗ 1 + 4.0) ∗ 1 ∗ 1; // With C++0x
auto p2= make nth derivative(p, 0.0001);
Once defined, we can reuse p and p2 as often as we want. Of course, calculating the derivatives
of polynomials can be done better than with differential quotients. We will discuss this in
Section 8.2.
25 TODO: Try in g++ 4.3 and 4.4?
26 boost::lambda::lambda functor