MATLAB Mathematics - SERC - Index of

6 Sparse Matrices
This matrix requires storage for nzmax floating-point numbers and nzmax+n+1
integers. At 8 bytes per floating-point number and 4 bytes per integer, the total
number of bytes required to store a sparse matrix is
8*nzmax + 4*(nzmax+n+1)
Note that the storage requirement depends upon nzmax and the number of
columns, n. The memory required to store a sparse matrix containing a large
number of rows but having few columns is much less that the memory required
to store the transpose of this matrix:
S1 = spalloc(2^20,2,1);
S2 = spalloc(2,2^20,1);
whos
Name Size Bytes Class
S1 1048576x2 24 double array (sparse)
S2 2x1048576 4194320 double array (sparse)
Grand total is 2 elements using 4194344 bytes
Sparse matrices with complex elements are also possible. In this case,
MATLAB uses a fourth array with nnz floating-point elements to store the
imaginary parts of the nonzero elements. An element is considered nonzero if
either its real or imaginary part is nonzero.
General Storage Information
The whos command provides high-level information about matrix storage,
including size and storage class. For example, this whos listing shows
information about sparse and full versions of the same matrix.
M_full = magic(1100);
M_full(M_full > 50) = 0;
M_sparse = sparse(M_full);
% Create 1100-by-1100 matrix.
% Set elements >50 to zero.
% Create sparse matrix of same.
6-6