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full

Convert sparse matrix to full storage

Description

example

A = full(S) converts sparse matrix S to full storage organization, such that issparse(A) returns logical 0 (false).

Examples

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Change the storage format of a matrix and compare the storage requirements.

Create a random sparse matrix. The display of sparse matrices in MATLAB ® omits all zeros and shows the location and value of nonzero elements.

rng default %for reproducibility
S = sprand(8,8,0.3)
S =
(2,1)       0.0344
(7,1)       0.4456
(8,1)       0.7547
(2,2)       0.4387
(4,3)       0.7655
(7,3)       0.6463
(8,4)       0.2760
(1,6)       0.9502
(5,6)       0.1869
(8,6)       0.6797
(3,7)       0.3816
(4,7)       0.7952
(8,7)       0.6551
(6,8)       0.4898
(7,8)       0.7094

Convert the matrix to full storage. The MATLAB display of the matrix reflects the new storage format.

A = full(S)
A = 8×8

0         0         0         0         0    0.9502         0         0
0.0344    0.4387         0         0         0         0         0         0
0         0         0         0         0         0    0.3816         0
0         0    0.7655         0         0         0    0.7952         0
0         0         0         0         0    0.1869         0         0
0         0         0         0         0         0         0    0.4898
0.4456         0    0.6463         0         0         0         0    0.7094
0.7547         0         0    0.2760         0    0.6797    0.6551         0

Compare the storage requirements of the two formats:

• A uses storage for 64 doubles (8 bytes each), or $64\cdot 8=512$ bytes.

• S uses storage for 15 nonzero elements, as well as 24 integers describing their positions, for a total of $39\cdot 8=312$ bytes.

whos
Name      Size            Bytes  Class     Attributes

A         8x8               512  double
S         8x8               312  double    sparse

Input Arguments

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Sparse matrix to convert, specified as a matrix. If S is already a full matrix, then A is identical to S.

Tips

• If X is an m-by-n matrix with nz nonzero elements, then full(X) requires space to store m*n elements. On the other hand, sparse(X) requires space to store nz elements and (nz+n+1) integers.

The density of a matrix (nnz(X)/numel(X)) determines whether it is more efficient to store the matrix as sparse or full. The exact crossover point depends on the matrix class, as well as the platform. For example, in 32-bit MATLAB®, a double sparse matrix with less than about 2/3 density requires less space than the same matrix in full storage. In 64-bit MATLAB, however, double matrices with fewer than half of their elements nonzero are more efficient to store as sparse matrices.