C++ for Scientists - Technische Universität Dresden

5.4. META-TUNING: WRITE YOUR OWN COMPILER OPTIMIZATION 161
};
T data[Rows][Cols];
The bracket operator returns a pointer for the sake of simplicity but a good implementation
should return a proxy that allows for checking the column index. The multiplication with a
vector is realized by means of an expression template for not copying the result vector.
Then the vector assigment needs a specialization for the expression template 17
template
class fsize vector
{
template
self& operator=( const mat vec et& that )
{
typedef mat vec et et;
fsize mat vec mult()(that.A, that.v, ∗this);
return ∗this;
}
};
The functor fsize mat vec mult must now compute the matrix vector product on the three arguments.
The general implementation of the functor reads:
template
struct fsize mat vec mult
{
template
void operator()(const Matrix& A, const VecIn& v in, VecOut& v out)
{
fsize mat vec mult()(A, v in, v out);
v out[Rows]+= A[Rows][Cols] ∗ v in[Cols];
}
};
Again, the functor is only templatized on the sizes and the container types are deduced. The
operator assumes that all smaller column indices are already handled and we can increment
v out[Rows] by A[Rows][Cols] ∗ v in[Cols]. In particular, we assume that the first operation on
v out[Rows] initializes it. Thus we need a (partial) specialization for Cols = 0:
template
struct fsize mat vec mult
{
template
void operator()(const Matrix& A, const VecIn& v in, VecOut& v out)
{
fsize mat vec mult()(A, v in, v out);
v out[Rows]= A[Rows][0] ∗ v in[0];
}
};
The careful reader noticed the substitution of += by =. We also notice that we have to call the
computation for the preceeding row with all columns and inductively for all smaller rows. The
17 A better solution would be implementing all assignments with a functor and specialize the functor because
partial template specialization of functions does not always work as expected.