The SPARSE function converts an 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 are as follows:

x

specifies an numerical matrix. Typically, x contains many zeros and only nonzeros, where is much smaller than .

type

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

"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 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"}];