C++ for Scientists - Technische Universität Dresden

5.2. PROVIDING TYPE INFORMATION 139
The reader will imagine that implementations in libraries like MTL or GLAS will provide
a larger interface in such classes. this short example is expressive enough to demonstrate the
approach. However, the example is large enough to demonstrate the need of meta-programming
in certain views.
An object of this class can be handled like a matrix so that a template function use it as
argument whereever a matrix is expected. The transposition is achieved by calling operator() in
the referred object with switched indices. For every matrix object we can define a transposed
view that behaves like a matrix
mtl::dense2D A(3, 3);
A= 2, 3, 4,
5, 6, 7,
8, 9, 10;
tst::transposed view At(A);
When we access At(i, j) we will get A(j, i). We even define a non-const access so that we can
even change entries:
At(2, 0)= 4.5;
This operation sets A(0, 2) to 4.5.
The definition of a transposed view object does not leed to particularly concise programs. For
convience we define a function that returns the transposed view.
template
transposed view inline trans(Matrix& A)
{
return transposed view(A);
}
Now we can use the transposed elegantly in our scientific software, for instance in a matrix
vector product:
v= trans(A) ∗ q;
In this case, a temporary view is created and used in the product. Since operator() from the
view is inlined the transposed product will be as fast as with A itself.
Dealing with Const-ness
So far, so good. Problems arise if we build the transposed view of a constant matrix:
const mtl::dense2D B(A);
We still can create the transposed view of B but we cannot access its elements:
std::cout ≪ ”tst::trans(B)(2, 0) = ” ≪ tst::trans(B)(2, 0) ≪ ’\n’; // error
The compiler will tell us that it cannot initialize a ‘float&’ from a ‘const float’. If we look at the
location of the error we will realize that this is line 9 in Listing 5.1. But we did the compiler
used the non-constant version of the operator? In line 10 we defined an operator for constant
objects which returns a constant reference and fits perfectly for this situation.