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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.

**Further Comments**
None

**Example**
**Program Text**

None

**Program Data**
None

**Program Results**
None

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