MATLAB Mathematics - SERC - Index of

Sparse Matrix Operations
Performance Limitations
This section describes some limitations of the sparse matrix storage format and
their impact on matrix creation, manipulation, and operations.
Creating Sparse Matrices
The best way to create a sparse matrix is to use the sparse function. If you do
not have prior knowledge of the nonzero indices or their values, it is much more
efficient to create the vectors containing these values and then create the
sparse matrix.
Preallocating the memory for a sparse matrix and filling it in an elementwise
manner causes a significant amount of overhead in indexing into the sparse
array:
S1 = spalloc(1000,1000,100000);
tic;
for n = 1:100000
i = ceil(1000*rand(1,1));
j = ceil(1000*rand(1,1));
S1(i,j) = rand(1,1);
end
toc
Elapsed time is 26.281000 seconds.
Whereas constructing the vectors of indices and values eliminates the need to
index into the sparse array, and thus is significantly faster:
i = ceil(1000*rand(100000,1));
j = ceil(1000*rand(100000,1));
v = zeros(size(i));
for n = 1:100000
v(n) = rand(1,1);
end
tic;
S2 = sparse(i,j,v,1000,1000);
toc
Elapsed time is 0.078000 seconds.
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