Language Reference

GENEIG Call

computes eigenvalues and eigenvectors of a generalized eigenproblem

CALL GENEIG( eigenvalues, eigenvectors, symmetric-matrix1,

           symmetric-matrix2);

The inputs to the GENEIG subroutine are as follows:

eigenvalues

is a returned vector containing the eigenvalues.

eigenvectors

is a returned matrix containing the corresponding eigenvectors.

symmetric-matrix1

is a symmetric numeric matrix.

symmetric-matrix2

is a positive definite symmetric matrix.

The GENEIG subroutine computes eigenvalues and eigenvectors of the generalized eigenproblem. Consider the following statement:

  
    call geneig (m,e,a,b);
 

This statement computes eigenvalues and eigenvectors of the generalized eigenproblem , where and are symmetric and is positive definite. The vector contains the eigenvalues arranged in descending order, and the matrix contains the corresponding eigenvectors in the columns.

The following example is from Wilkinson and Reinsch (1971, p. 311):

  
    a={10   2   3   1   1, 
        2  12   1   2   1, 
        3   1  11   1  -1, 
        1   2   1   9   1, 
        1   1  -1   1  15}; 
  
    b={12   1  -1   2    1, 
        1  14   1  -1    1, 
       -1   1  16  -1    1, 
        2  -1  -1  12   -1, 
        1   1   1  -1   11}; 
  
    call geneig(m,e,a,b);
 

The matrices produced are as follows:

  
               M 
               1.49235 
               1.10928 
               0.94385 
               0.66366 
               0.43278 
  
               E 
              -0.07638   0.14201   0.19171  -0.08292  -0.13459 
               0.01709   0.14242  -0.15899  -0.15314   0.06129 
              -0.06666   0.12099   0.07483   0.11860   0.15790 
               0.08604   0.12553  -0.13746   0.18281  -0.10946 
               0.28943   0.00769   0.08897  -0.00356   0.04147