SPARSE Function :: SAS/IML(R) 13.1 User's Guide

SPARSE Function

SPARSE (x <, type> ) ;

The SPARSE function converts an $n\times p$ matrix that contains many zeros into a matrix stored in a sparse format which suitable for use with the ITSOLVER call or the SOLVELIN call.

The arguments to the SPARSE function are as follows:

x

specifies an $n\times p$ numerical matrix. Typically, x contains many zeros and only $k$ nonzeros, where $k$ is much smaller than $np$ .

type

specifies whether the x matrix is symmetric. The following values are valid:

“symmetric”: specifies that only the lower triangular nonzero values of the x matrix are used.
“unsymmetric”: specifies that all nonzero values of the x matrix are used. This is the default value.

The type argument is not case-sensitive. The first three characters are used to determine the value. For example, “SYM” and “symmetric” specify the same option.

The matrix returned by the SPARSE function is a $k \times 3$ matrix that contains the folling values:

The first column contains the nonzero values of the x matrix.
The second column contains the row numbers for each value.
The third column contains the column numbers for each value.

For example, the following statements compute a sparse representation of a dense matrix with many zeros:

x = {3   1.1  0   0  ,
     1.1 4    0   3.2,
     0   1   10   0  ,
     0   3.2  0   3  };
a = sparse(x, "sym");
print a[colname={"Value" "Row" "Col"}];

Figure 24.378: Sparse Data Representation

a
Value	Row	Col
3	1	1
1.1	2	1
4	2	2
1	3	2
10	3	3
3.2	4	2
3	4	4