C++ for Scientists - Technische Universität Dresden

4.10. CURSORS AND PROPERTY MAPS 127
Its implementation is almost the same as nz cursor and with some refactoring one could certainly
combine it in one implementation that serves both cursors as base class. For the sake of
simplicity we refrain from it here. The two main differences to nz cursor are
• The lack of operator∗ because the cursor is not intended to be dereferred; and
• The functions begin and end to provide the inter loop traversal.
The according functions to provide a right-open interval of row cursors are straight forward:
template
row cursor row begin(const Matrix& A)
{
return row cursor(0, A);
}
template
row cursor row end(const Matrix& A)
{
return row cursor(A.num rows(), A);
}
We can now write begin and end functions that take a row cursor (instead of a matrix) as
argument and give the right-open interval of the rows non-zeros:
template
nz cursor nz begin(const row cursor& c)
{
return c.begin();
}
template
nz cursor nz end(const row cursor& c)
{
return c.end();
}
For the inner loop we can reuse nz cursor and only need to determine the right intervals within
each row. This is performed with the begin and end function from row cursor which in turn uses
begin row from the matrix. That is why the row cursor needs a matrix reference.
A two-dimensional traversal is realized as follows:
for (row cursor< coo matrix > c= row begin(A), end= row end(A); c != end; ++c) {
std::cout ≪ ”−−−−−\n”;
for (nz cursor ic= nz begin(c), iend= nz end(c); ic != iend; ++ic)
std::cout ≪ ”A[” ≪ row(∗ic) ≪ ”][” ≪ col(∗ic) ≪ ”] = ” ≪ value(∗ic) ≪ ”\n”;
}
std::cout ≪ ”−−−−−\n”;
The outer loop iterates over all rows of the matrix and the inner loop over all non-zeros in this
row.
Résumé The technique is more complicated and less readable than accessing entries with
operator[] and needs some familiarization. However, it allows for