DGEGS man page on Scientific

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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       DGEGS - routine i deprecated and has been replaced by routine DGGES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       This routine is deprecated and has  been	 replaced  by  routine	DGGES.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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