Language Reference

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

The GENEIG subroutine computes eigenvalues and eigenvectors of a generalized eigenproblem.

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 eigenproblem. If and are symmetric and is positive definite, then the vector and the matrix solve the generalized eigenproblem 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;