octave: Array and Sparse Class Differences
A.1.6.1 Array and Sparse Class Differences
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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.
Info Catalog
octave: Sparse Matrices in Oct-Files
octave: Creating Sparse Matrices in Oct-Files