The EIGENVECTOR statement invokes a variant of the Jacobi-Davidson algorithm (Sleijpen and van der Vorst 2000) that finds eigenvectors (and eigenvalues) for symmetric matrices. The matrix is typically defined in the input data set
that is specified in the DATA_MATRIX= option in the PROC OPTGRAPH statement. The matrix can also be input as a graph by using
the DATA_LINKS= option in the PROC OPTGRAPH statement. Internally, the graph is converted into a (sparse) adjacency matrix.
Eigenvectors and eigenvalues are described in the section Eigenvector Problem.
You can specify the following options in the EIGENVECTOR statement:
-
EIGENVALUES=LA | SA
-
specifies the type of eigenvector to calculate. Table 1.30 describes the valid values for this option.
Table 1.30: Values for the EIGENVALUES= Option
Option Value
|
Description
|
LA
|
Calculates the n largest algebraic eigenvalues (and their corresponding eigenvectors), where n is the value of the NEIGEN= option. This is the default.
|
SA
|
Calculates the n smallest algebraic eigenvalues (and their corresponding eigenvectors), where n is the value of the NEIGEN= option.
|
-
LOGLEVEL=number | string
-
controls the amount of information that is displayed in the SAS log. Table 1.31 describes the valid values for this option.
Table 1.31: Values for LOGLEVEL= Option
number
|
string
|
Description
|
0
|
NONE
|
Turns off all algorithm-related messages in the SAS log
|
1
|
BASIC
|
Displays a basic summary of the algorithmic processing
|
2
|
MODERATE
|
Displays a summary of the algorithmic processing
|
3
|
AGGRESSIVE
|
Displays a detailed summary of the algorithmic processing
|
The default is the value that is specified in the LOGLEVEL=
option in the PROC OPTGRAPH statement (or BASIC if that option is not specified).
-
MAXITER=number
-
specifies the maximum number of matrix-vector multiplications used in the Jacobi-Davidson algorithm to calculate eigenvectors.
By default, MAXITER=10,000.
-
NEIGEN=number
-
specifies the number of eigenvalues (and their corresponding eigenvectors) to generate. This value must be less than or equal
to the dimension of the matrix. By default, NEIGEN=1.
-
OUT=SAS-data-set
-
specifies the output data set to contain the eigenvectors (and eigenvalues) found.