Computational Advantages of Sparse Matrices
Using sparse matrices to store data that contains a large number
of zero-valued elements can both save a significant amount of memory
and speed up the processing of that data.
an attribute that you can assign to any two-dimensional MATLAB® matrix
that is composed of
sparse attribute allows MATLAB to:
For full matrices, MATLAB stores every matrix element internally. Zero-valued elements require the same amount of storage space as any other matrix element. For sparse matrices, however, MATLAB stores only the nonzero elements and their indices. For large matrices with a high percentage of zero-valued elements, this scheme significantly reduces the amount of memory required for data storage.
whos command provides high-level information
about matrix storage, including size and storage class. For example,
whos listing shows information about sparse
and full versions of the same matrix.
M_full = magic(1100); % Create 1100-by-1100 matrix. M_full(M_full > 50) = 0; % Set elements >50 to zero. M_sparse = sparse(M_full); % Create sparse matrix of same. whos
Name Size Bytes Class Attributes M_full 1100x1100 9680000 double M_sparse 1100x1100 9608 double sparse
Notice that the number of bytes used is fewer in the sparse case, because zero-valued elements are not stored.
Sparse matrices also have significant advantages in terms of
computational efficiency. Unlike operations with full matrices, operations
with sparse matrices do not perform unnecessary low-level arithmetic,
such as zero-adds (
x+0 is always
The resulting efficiencies can lead to dramatic improvements in execution
time for programs working with large amounts of sparse data.