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- A
- (
*input/output*) **REAL** or **COMPLEX**
square array, shape .

On entry, the matrix .

On exit, the matrix .

- B
- (
*input/output*) **REAL** or **COMPLEX**
square array, shape with
.

On entry, the matrix .

On exit, the matrix .

*alpha*
- (
*output*) **REAL** or **COMPLEX** array,
shape with
.

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
.

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

- VSL
*Optional* (*output*) **REAL** or
**COMPLEX** square array, shape with
(**VSL**,1) (**A**,1).

The left Schur vectors.

- VSR
*Optional* (*output*) **REAL** or
**COMPLEX** square array, shape with
(**VSR**,1) (**A**,1).

The right Schur vectors.

- SELECT
*Optional* (*input*) **LOGICAL FUNCTION**
- LOGICAL FUNCTION SELECT(
*alpha*, BETA )

*type*(*wp*), INTENT(IN) ::
*alpha*, BETA

where

*type* ::= REAL COMPLEX

*wp* ::= KIND(1.0) KIND(1.0D0)

*alpha* ::= ALPHAR, ALPHAI ALPHA

Note: Select must be present if **SDIM**, **RCONDE** and **RCONDF**
are desired.

- SDIM
*Optional* (*output*) **INTEGER**.

The number of eigenvalues (after sorting) for which **SELECT** .**TRUE**.
(If and are real, complex conjugate pairs for which **SELECT** .**TRUE**. for either eigenvalue count as 2).

- RCONDE
*Optional* (*output*) **REAL** array, shape
with (**RCONDE**) .

The reciprocal condition numbers for the average of the selected eigenvalues.

- RCONDV
*Optional* (*output*) **REAL** array, shape with
(**RCONDV**) .

The reciprocal condition numbers
for the left and right deflating subspaces
corresponding to the selected eigenvalues.

- 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 [17,9,20,21].

** Next:** Example (from Program LA_GGESX_EXAMPLE)
** Up:** Generalized Nonsymmetric Eigenvalue Problems
** Previous:** Purpose
** Contents**
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Susan Blackford
2001-08-19