MATLAB Mathematics - SERC - Index of
MATLAB Mathematics - SERC - Index of MATLAB Mathematics - SERC - Index of
6 Sparse Matrices Manipulating Sparse Matrices Because sparse matrices are stored in a column-major format, accessing the matrix by columns is more efficient than by rows. Compare the time required for adding rows of a matrix 1000 times S = sparse(10000,10000,1); tic; for n = 1:1000 A = S(100,:) + S(200,:); end; toc Elapsed time is 1.208162 seconds. versus the time required for adding columns S = sparse(10000,10000,1); tic; for n = 1:1000 B = S(:,100) + S(:,200); end; toc Elapsed time is 0.088747 seconds. When possible, you can transpose the matrix, perform operations on the columns, and then retranspose the result: S = sparse(10000,10000,1); tic; for n = 1:1000 A = S(100,:)' + S(200,:)'; A = A'; end; toc Elapsed time is 0.597142 seconds. The time required to transpose the matrix is negligible. Note that the sparse matrix memory requirements may prevent you from transposing a sparse matrix having a large number of rows. This might occur even when the number of nonzero values is small. 6-42
Sparse Matrix Operations Using linear indexing to access or assign an element in a large sparse matrix will fail if the linear index exceeds intmax. To access an element whose linear index is greater than intmax, use array indexing: S = spalloc(216^2, 216^2, 2) S(1) = 1 S(end) = 1 S(216^2,216^2) = 1 6-43
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Sparse Matrix Operations<br />
Using linear indexing to access or assign an element in a large sparse matrix<br />
will fail if the linear index exceeds intmax. To access an element whose linear<br />
index is greater than intmax, use array indexing:<br />
S = spalloc(216^2, 216^2, 2)<br />
S(1) = 1<br />
S(end) = 1<br />
S(216^2,216^2) = 1<br />
6-43
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