C++ for Scientists - Technische Universität Dresden

130 CHAPTER 4. GENERIC PROGRAMMING
Create a meta function to check whether a type is a pointer. Write a function evaluate that
returns the same value as its argument, except when the argument is a pointer, in which case
you return the value pointed to by the pointer. Hint: look at http://www.boost.org/libs/
utility/enable_if.html for enable if c.
4.11.7 Meta-list
Revisit exercise ??.
Make a list of types. Make meta functions insert, append, delete and size.
4.11.8 Iterator of a vector
Revisit exercise ??. Add methods begin() and end() for returning a begin and end iterator. Add
the types iterator and const iterator to the class. Note that pointers are iterators.
Use the STL functions sort and lower bound.
4.11.9 Iterator of a list
Revisit exercise ??.
Make a generic list type.
Add methods begin() and end() for returning a begin and end const iterator. Add the type
const iterator to the class. Note that pointers cannot be used as iterators.
4.11.10 Trapezoid rule
A simple method for computing the integral of a function is the trapezoid rule. Suppose we
want to integrate the function f over the interval [a, b]. We split the interval in n small intervals
[xi, xi+1] of the same length h = (b − a)/n and approximate f by a piecewise linear function.
The integral is then approximated by the sum of the integrals of the piecewise linear function.
This gives us the formula :
I = h
2
f(a) + h
2
n−1 �
f(b) + h
j=1
f(a + jh) (4.1)
In this exercise, we develop a function for the trapezoid rule, with a functor argument. We
develop software using inheritance and using generic programming. Then we use the function
for integrating the following functions:
• f = exp(−3x) for x ∈ [0, 4]. Try the following arguments of trapezoid:
double exp3( double x ) {
return std::exp( 3.0 ∗ x ) ;
}
struct exp3 {