C++ for Scientists - Technische Universität Dresden

138 CHAPTER 5. META-PROGRAMMING
We can now consider extending this definition to vectors and matrices, e.g., to determine the
return type of a norm. The specialization reads
template
struct Magnitude
{
typedef T type; // not really perfect
};
However, if the value type of the vector is complex, its norm will not. Instead, we need the
magitude type from the values:
template
struct Magnitude
{
typedef typename Magnitude::type type;
};
5.2.2 A const-clean View Example
In this section, we look at an efficient and expressive implementation of a transposed matrix. If
you compute the transposed of a matrix, many software packages return a new matrix object
with the interchanged values. This is a quite expensive operation: it requires memory allocation
and deallocation and often copying a lot of data.
Writing a Simple View Class
A much more efficient approach is implementing a ‘View’ of the existing object. We refer
internally to the viewed object and just adapt its interface. This can be done very nicely for
the transposed of a matrix:
1 template
2 class transposed view
3 {
4 public:
5 typedef typename mtl::Collection::value type value type;
6 typedef typename mtl::Collection::size type size type;
7
8 transposed view(Matrix& A) : ref(A) {}
9
10 value type& operator()(size type r, size type c) { return ref(c, r); }
11 const value type& operator()(size type r, size type c) const { return ref(c, r); }
12
13 private:
14 Matrix& ref;
15 };
Listing 5.1: Simple view implementation
We assume that the matrix class has an operator() taking two arguments for the row and column
index respectively. We further suppose that type traits are defined for value type and size type.
This is all we need to know about the referred matrix, 3 at least in this mini example.
3 TODO: We should define a concept for it.