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- 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**: [1] and [17,9,20].

** Next:** Examples
** Up:** Generalized Nonsymmetric Eigenvalue Problems
** Previous:** Purpose
** Contents**
** Index**
Susan Blackford
2001-08-19