Page 500 - Applied Numerical Methods Using MATLAB

APPENDIX H

SPARSE MATRICES

A matrix is said to be sparse if it has a large portion of zero elements. MATLAB
has some built-in functions/routines that enable us to exploit the sparsity of a
matrix for computational efficiency.
The MATLAB routine sparse() can be used to convert a (regular) matrix
into a sparse form by squeezing out any zero elements and to generate a sparse
matrix having the elements of a vector given together with the row/column index
vectors. On the other hand, the MATLAB routine full() can be used to convert
a matrix of sparse form into a regular one.
>>row_index = [11234]; col_index = [12234]; elements = [1 2 3 4 5];
>>m =4;n=4;As= sparse(row_index,col_index,elements,m,n)
As = (1,1) 1
(1,2) 2
(2,2) 3
(3,3) 4
(4,4) 5
>>Af = full(As)
Af = 1 2 0 0
0 3 0 0
0 0 4 0
0 0 0 5
We can use the MATLAB routine sprandn(m,n,nzd) to generate an m × n
sparse matrix having the given non-zero density nzd. Let us see how efficient
the operations can be on the matrices in sparse forms.

>>As = sprandn(10,10,0.2); %a sparse matrix and
>>Af = full(As); its full version


Applied Numerical Methods Using MATLAB , by Yang, Cao, Chung, and Morris
Copyright  2005 John Wiley & Sons, I nc., ISBN 0-471-69833-4

489