## MB03QV

### Compute eigenvalues of an upper quasi-triangular matrix pencil

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

```  To compute the eigenvalues of an upper quasi-triangular matrix
pencil.

```
Specification
```      SUBROUTINE MB03QV( N, S, LDS, T, LDT, ALPHAR, ALPHAI, BETA, INFO )
C     .. Scalar Arguments ..
INTEGER          INFO, LDS, LDT, N
C     .. Array Arguments ..
DOUBLE PRECISION ALPHAI(*), ALPHAR(*), BETA(*), S(LDS,*), T(LDT,*)

```
Arguments

Input/Output Parameters

```  N       (input) INTEGER
The order of the matrices S and T.  N >= 0.

S       (input) DOUBLE PRECISION array, dimension(LDS,N)
The upper quasi-triangular matrix S.

LDS     INTEGER
The leading dimension of the array S.  LDS >= max(1,N).

T       (input) DOUBLE PRECISION array, dimension(LDT,N)
The upper triangular matrix T.

LDT     INTEGER
The leading dimension of the array T.  LDT >= max(1,N).

ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
ALPHAI  (output) DOUBLE PRECISION array, dimension (N)
BETA    (output) DOUBLE PRECISION array, dimension (N)
On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N,
are the generalized eigenvalues.
ALPHAR(j) + ALPHAI(j)*i, and  BETA(j),j=1,...,N, are the
diagonals of the complex Schur form (S,T) that would
result if the 2-by-2 diagonal blocks of the real Schur
form of (A,B) were further reduced to triangular form
using 2-by-2 complex unitary transformations.
If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
positive, then the j-th and (j+1)-st eigenvalues are a
complex conjugate pair, with ALPHAI(j+1) negative.

```
Error Indicator
```  INFO    INTEGER
= 0:  successful exit;
< 0:  if INFO = -i, the i-th argument had an illegal
value.

```
```  None
```
Example

Program Text

```  None
```
Program Data
```  None
```
Program Results
```  None
```