The two basic reasons to use sparse matrices are to reduce the memory usage and to not have to do calculations on zero elements. The two are closely related in that the computation time on a sparse matrix operator or function is roughly linear with the number of nonzero elements.
Therefore, there is a certain density of nonzero elements of a matrix where it no longer makes sense to store it as a sparse matrix, but rather as a full matrix. For this reason operators and functions that have a high probability of returning a full matrix will always return one. For example adding a scalar constant to a sparse matrix will almost always make it a full matrix, and so the example,
speye (3) + 0 ⇒ 1 0 0 0 1 0 0 0 1
returns a full matrix as can be seen.
sparse_auto_mutate is true, all sparse functions
test the amount of memory occupied by the sparse matrix to see if the
amount of storage used is larger than the amount used by the full
speye (2) * 1 will return a full matrix as
the memory used is smaller for the full version than the sparse version.
As all of the mixed operators and functions between full and sparse
matrices exist, in general this does not cause any problems. However,
one area where it does cause a problem is where a sparse matrix is
promoted to a full matrix, where subsequent operations would resparsify
the matrix. Such cases are rare, but can be artificially created, for
(fliplr (speye (3)) + speye (3)) - speye (3) gives a full
matrix when it should give a sparse one. In general, where such cases
occur, they impose only a small memory penalty.
There is however one known case where this behavior of Octave’s sparse matrices will cause a problem. That is in the handling of the diag function. Whether diag returns a sparse or full matrix depending on the type of its input arguments. So
a = diag (sparse ([1,2,3]), -1);
should return a sparse matrix. To ensure this actually happens, the sparse function, and other functions based on it like speye, always returns a sparse matrix, even if the memory used will be larger than its full representation.
Query or set the internal variable that controls whether Octave will automatically mutate sparse matrices to full matrices to save memory.
s = speye (3); sparse_auto_mutate (false); s(:, 1) = 1; typeinfo (s) ⇒ sparse matrix sparse_auto_mutate (true); s(1, :) = 1; typeinfo (s) ⇒ matrix
When called from inside a function with the
"local" option, the
variable is changed locally for the function and any subroutines it calls.
The original variable value is restored when exiting the function.
Note that the
sparse_auto_mutate option is incompatible with
MATLAB, and so it is off by default.