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Arguments

A
(input/output) REAL or COMPLEX square array, shape .
On entry, the matrix .
On exit, has been destroyed.

B
(input/output) REAL or COMPLEX square array, shape with (B,1) (A,1).
On entry, the matrix .
On exit, has been destroyed.

alpha
(output) REAL or COMPLEX array, shape with (alpha) (A,1).
The values of . ::= ALPHAR(:), ALPHAI(:) ALPHA(:),
where
ALPHAR(:), ALPHAI(:) are of REAL type (for the real and imaginary parts) and ALPHA(:) is of COMPLEX type.

BETA
(output) REAL or COMPLEX array, shape with (BETA) (A,1).
The values of .
Note: The generalized eigenvalues of the pair are the scalars . These quotients may easily over- or underflow, and may even be zero. Thus, the user should avoid computing them naively.
Note: If A and B are real then complex eigenvalues occur in complex conjugate pairs. Each pair is stored consecutively. Thus a complex conjugate pair is given by where VL
Optional (output) REAL or COMPLEX square array, shape with (VL,1) (A,1).
The left generalized eigenvectors are stored in the columns of VL in the order of their eigenvalues. Each eigenvector is scaled so the largest component has , except that for eigenvalues with , a zero vector is returned as the corresponding eigenvector.
Note: If and are real then complex eigenvectors, like their eigenvalues, occur in complex conjugate pairs. The real and imaginary parts of the first eigenvector of the pair are stored in VL and VL . Thus a complex conjugate pair is given by VR
Optional (output) REAL or COMPLEX square array, shape with (VR,1) (A,1).
The right generalized eigenvectors are stored in the columns of VR in the order of their eigenvalues. Each eigenvector is scaled so the largest component has , except that for eigenvalues with , a zero vector is returned as the corresponding eigenvector.
Note: If and are real then complex eigenvectors, like their eigenvalues, occur in complex conjugate pairs. The real and imaginary parts of the first eigenvector of the pair are stored in VR and VR . Thus a complex conjugate pair is given by INFO
Optional (output) INTEGER. If INFO is not present and an error occurs, then the program is terminated with an error message.
References:  and [17,9,20].     Next: Examples Up: Generalized Nonsymmetric Eigenvalue Problems Previous: Purpose   Contents   Index
Susan Blackford 2001-08-19