dgegs man page on Scientific

```DGEGS(1)	      LAPACK driver routine (version 3.2)	      DGEGS(1)

NAME
DGEGS - routine i deprecated and has been replaced by routine DGGES

SYNOPSIS
SUBROUTINE DGEGS( JOBVSL,  JOBVSR,  N,  A, LDA, B, LDB, ALPHAR, ALPHAI,
BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, INFO )

CHARACTER	 JOBVSL, JOBVSR

INTEGER	 INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N

DOUBLE	 PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( *	),  B(
LDB,  *  ), BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, *
), WORK( * )

PURPOSE
This routine is deprecated and has  been	 replaced  by  routine	DGGES.
DGEGS  computes the eigenvalues, real Schur form, and, optionally, left
and or/right Schur vectors of a real  matrix  pair  (A,B).   Given  two
square  matrices	 A and B, the generalized real Schur factorization has
the form
A = Q*S*Z**T,	B = Q*T*Z**T
where Q and Z are orthogonal matrices, T is upper triangular, and S  is
an  upper  quasi-triangular  matrix  with  1-by-1  and  2-by-2 diagonal
blocks, the 2-by-2 blocks corresponding to complex conjugate  pairs  of
eigenvalues  of (A,B).  The columns of Q are the left Schur vectors and
the columns of Z are the right Schur vectors.
If only the eigenvalues of (A,B) are needed, the driver	routine	 DGEGV
should be used instead.	See DGEGV for a description of the eigenvalues
of the generalized nonsymmetric eigenvalue problem (GNEP).

ARGUMENTS
JOBVSL  (input) CHARACTER*1
= 'N':  do not compute the left Schur vectors;
= 'V':  compute the left Schur vectors (returned in VSL).

JOBVSR  (input) CHARACTER*1
= 'N':  do not compute the right Schur vectors;
= 'V':  compute the right Schur vectors (returned in VSR).

N       (input) INTEGER
The order of the matrices A, B, VSL, and VSR.  N >= 0.

A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
On entry, the matrix A.	On exit,  the  upper  quasi-triangular
matrix S from the generalized real Schur factorization.

LDA     (input) INTEGER
The leading dimension of A.  LDA >= max(1,N).

B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
On entry, the matrix B.	On exit, the upper triangular matrix T
from the generalized real Schur factorization.

LDB     (input) INTEGER
The leading dimension of B.  LDB >= max(1,N).

ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
The real parts of each scalar alpha defining an	eigenvalue  of
GNEP.

ALPHAI  (output) DOUBLE PRECISION array, dimension (N)
The imaginary parts of each scalar alpha defining an eigenvalue
of GNEP.	 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) = -ALPHAI(j).

BETA    (output) DOUBLE PRECISION array, dimension (N)
The  scalars  beta  that	 define	 the  eigenvalues   of	 GNEP.
Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and beta
= BETA(j) represent the j-th  eigenvalue	 of  the  matrix  pair
(A,B),  in  one	of  the	 forms	lambda	=  alpha/beta  or mu =
beta/alpha.  Since either  lambda  or  mu  may  overflow,  they
should not, in general, be computed.

VSL     (output) DOUBLE PRECISION array, dimension (LDVSL,N)
If  JOBVSL = 'V', the matrix of left Schur vectors Q.  Not ref‐
erenced if JOBVSL = 'N'.

LDVSL   (input) INTEGER
The leading dimension of the matrix VSL. LDVSL >=1, and if JOB‐
VSL = 'V', LDVSL >= N.

VSR     (output) DOUBLE PRECISION array, dimension (LDVSR,N)
If JOBVSR = 'V', the matrix of right Schur vectors Z.  Not ref‐
erenced if JOBVSR = 'N'.

LDVSR   (input) INTEGER
The leading dimension of the matrix VSR. LDVSR  >=  1,  and  if
JOBVSR = 'V', LDVSR >= N.

WORK	  (workspace/output)   DOUBLE	PRECISION   array,   dimension
(MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK.	  LWORK	 >=  max(1,4*N).   For
good  performance,  LWORK must generally be larger.  To compute
the optimal value of LWORK, call ILAENV to get blocksizes  (for
DGEQRF,	DORMQR,	 and DORGQR.)  Then compute: NB	 -- MAX of the
blocksizes for DGEQRF, DORMQR, and DORGQR The optimal LWORK  is
2*N  +  N*(NB+1).   If  LWORK  =	 -1, then a workspace query is
assumed; the routine only calculates the optimal	 size  of  the
WORK  array,  returns this value as the first entry of the WORK
array, and no error message  related  to	 LWORK	is  issued  by
XERBLA.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.
=  1,...,N:  The	 QZ  iteration failed.	(A,B) are not in Schur
form, but ALPHAR(j), ALPHAI(j), and BETA(j) should  be  correct
for  j=INFO+1,...,N.  > N:  errors that usually indicate LAPACK
problems:
=N+1: error return from DGGBAL
=N+2: error return from DGEQRF
=N+3: error return from DORMQR
=N+4: error return from DORGQR
=N+5: error return from DGGHRD
=N+6: error return from DHGEQZ (other  than  failed  iteration)
=N+7: error return from DGGBAK (computing VSL)
=N+8: error return from DGGBAK (computing VSR)
=N+9: error return from DLASCL (various places)

LAPACK driver routine (version 3November 2008			      DGEGS(1)
```
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