 
  
  
  
  
 
An expert driver is provided to compute all the eigenvalues and (optionally) the eigenvectors of the following types of problems:
 
 

where A and B are symmetric or Hermitian and B is positive definite.
For all these problems the eigenvalues   are
real.
When A and B are symmetric, the matrices Z
of computed eigenvectors  satisfy
 are
real.
When A and B are symmetric, the matrices Z
of computed eigenvectors  satisfy 
 (problem types 1 and 3) or
 (problem types 1 and 3) or  (problem type 2), where
 
(problem type 2), where  is a diagonal matrix with the eigenvalues
on the diagonal. Z also satisfies
 is a diagonal matrix with the eigenvalues
on the diagonal. Z also satisfies
 (problem types 1 and 2) or
 (problem types 1 and 2) or  (problem type 3).
When A and B are Hermitian, the matrices Z
of computed eigenvectors  satisfy
 (problem type 3).
When A and B are Hermitian, the matrices Z
of computed eigenvectors  satisfy 
 (problem types 1 and 3) or
 (problem types 1 and 3) or  (problem type 2), where
 
(problem type 2), where  is a diagonal matrix with the eigenvalues
on the diagonal. Z also satisfies
 is a diagonal matrix with the eigenvalues
on the diagonal. Z also satisfies
 (problem types 1 and 2) or
 (problem types 1 and 2) or  (problem type 3).
 (problem type 3).
The routine is listed in table 3.5.
  
Table 3.5: Driver routine for the generalized symmetric definite eigenvalue problems