The number of elements in a sparse matrix is considered to be the number of nonzero elements rather than the product of the dimensions. Therefore
SparseMatrix sm; … int nel = sm.nelem ();
returns the number of nonzero elements. If the user really requires the
number of elements in the matrix, including the nonzero elements, they
should use numel rather than nelem. Note that for very
large matrices, where the product of the two dimensions is larger than
the representation of an unsigned int, then numel can overflow.
An example is speye (1e6) which will create a matrix with a million
rows and columns, but only a million nonzero elements. Therefore the
number of rows by the number of columns in this case is more than two
hundred times the maximum value that can be represented by an unsigned int.
The use of numel should therefore be avoided unless it is known
that it will not overflow.
Extreme care must be take with the elem method and the "()" operator,
which perform basically the same function. The reason is that if a
sparse object is non-const, then Octave will assume that a
request for a zero element in a sparse matrix is in fact a request
to create this element so it can be filled. Therefore a piece of
code like
SparseMatrix sm;
…
for (int j = 0; j < nc; j++)
for (int i = 0; i < nr; i++)
std::cerr << " (" << i << "," << j << "): " << sm(i,j) << std::endl;
is a great way of turning the sparse matrix into a dense one, and a very slow way at that since it reallocates the sparse object at each zero element in the matrix.
An easy way of preventing the above from happening is to create a temporary constant version of the sparse matrix. Note that only the container for the sparse matrix will be copied, while the actual representation of the data will be shared between the two versions of the sparse matrix. So this is not a costly operation. For example, the above would become
SparseMatrix sm;
…
const SparseMatrix tmp (sm);
for (int j = 0; j < nc; j++)
for (int i = 0; i < nr; i++)
std::cerr << " (" << i << "," << j << "): " << tmp(i,j) << std::endl;
Finally, as the sparse types aren’t represented by a contiguous
block of memory, the fortran_vec method of the Array<T>
is not available. It is, however, replaced by three separate methods
ridx, cidx and data, that access the raw compressed
column format that Octave sparse matrices are stored in. These methods can be
used in a manner similar to elem to allow the matrix to be accessed or
filled. However, in that case it is up to the user to respect the sparse
matrix compressed column format.