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 nnz = sm.nelem ();
returns the number of nonzero elements (like the interpreter function
nnz
). 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, 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. In this case,
the number of rows multiplied by the number of columns is more than two hundred
times the maximum value that can be represented by an unsigned 32-bit int. The
use of numel
should, therefore, be avoided unless it is known that it
will not overflow.
Extreme care is also required when using the elem
method or the
()
operator which perform essentially 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) << "\n";
is a great way of turning a sparse matrix into a dense one, and a very slow way at that since it reallocates the sparse object for each zero element in the matrix.
A simple 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; This is not a costly operation. The example above, re-written to prevent sparse-to-dense conversion, is
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) << "\n";
Finally, because the sparse types aren’t represented by a contiguous block of
memory, the fortran_vec
method of 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,
it is up to the user to respect the sparse matrix compressed column format or
the matrix will become corrupted.