Language Reference

CALL GENEIG (eval, evecs, sym-matrix1, sym-matrix2) ;

This subroutine is supported by the IML procedure and the iml action.

The GENEIG subroutine computes eigenvalues and eigenvectors of a generalized eigenvalue problem.

The input arguments to the GENEIG subroutine are as follows:

The subroutine returns the following output arguments:

The GENEIG subroutine computes eigenvalues and eigenvectors of the generalized eigenvalue problem. If and are symmetric and is positive definite, then the vector and the matrix solve the generalized eigenvalue problem provided that

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):

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);
print M, E;