The OPTGRAPH Procedure

EIGENVECTOR Statement

  • EIGENVECTOR < options >;

  • EIGEN < options >;

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.