```      SUBROUTINE SGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR,
\$                  ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
\$                  LWORK, INFO )
*
*  -- LAPACK driver routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          JOBVSL, JOBVSR
INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
*     ..
*     .. Array Arguments ..
REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
\$                   B( LDB, * ), BETA( * ), VSL( LDVSL, * ),
\$                   VSR( LDVSR, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  This routine is deprecated and has been replaced by routine SGGES.
*
*  SGEGS 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
*  SGEGV should be used instead.  See SGEGV 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) REAL 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) REAL 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) REAL array, dimension (N)
*          The real parts of each scalar alpha defining an eigenvalue
*          of GNEP.
*
*  ALPHAI  (output) REAL 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) REAL 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) REAL array, dimension (LDVSL,N)
*          If JOBVSL = 'V', the matrix of left Schur vectors Q.
*          Not referenced if JOBVSL = 'N'.
*
*  LDVSL   (input) INTEGER
*          The leading dimension of the matrix VSL. LDVSL >=1, and
*          if JOBVSL = 'V', LDVSL >= N.
*
*  VSR     (output) REAL array, dimension (LDVSR,N)
*          If JOBVSR = 'V', the matrix of right Schur vectors Z.
*          Not referenced if JOBVSR = 'N'.
*
*  LDVSR   (input) INTEGER
*          The leading dimension of the matrix VSR. LDVSR >= 1, and
*          if JOBVSR = 'V', LDVSR >= N.
*
*  WORK    (workspace/output) REAL 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 SGEQRF, SORMQR, and SORGQR.)  Then compute:
*          NB  -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR
*          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 SGGBAL
*                =N+2: error return from SGEQRF
*                =N+3: error return from SORMQR
*                =N+4: error return from SORGQR
*                =N+5: error return from SGGHRD
*                =N+6: error return from SHGEQZ (other than failed
*                                                iteration)
*                =N+7: error return from SGGBAK (computing VSL)
*                =N+8: error return from SGGBAK (computing VSR)
*                =N+9: error return from SLASCL (various places)
*
*  =====================================================================
*
*     .. Parameters ..
REAL               ZERO, ONE
PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
*     ..
*     .. Local Scalars ..
LOGICAL            ILASCL, ILBSCL, ILVSL, ILVSR, LQUERY
INTEGER            ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT,
\$                   ILO, IRIGHT, IROWS, ITAU, IWORK, LOPT, LWKMIN,
\$                   LWKOPT, NB, NB1, NB2, NB3
REAL               ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
\$                   SAFMIN, SMLNUM
*     ..
*     .. External Subroutines ..
EXTERNAL           SGEQRF, SGGBAK, SGGBAL, SGGHRD, SHGEQZ, SLACPY,
\$                   SLASCL, SLASET, SORGQR, SORMQR, XERBLA
*     ..
*     .. External Functions ..
LOGICAL            LSAME
INTEGER            ILAENV
REAL               SLAMCH, SLANGE
EXTERNAL           ILAENV, LSAME, SLAMCH, SLANGE
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          INT, MAX
*     ..
*     .. Executable Statements ..
*
*     Decode the input arguments
*
IF( LSAME( JOBVSL, 'N' ) ) THEN
IJOBVL = 1
ILVSL = .FALSE.
ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
IJOBVL = 2
ILVSL = .TRUE.
ELSE
IJOBVL = -1
ILVSL = .FALSE.
END IF
*
IF( LSAME( JOBVSR, 'N' ) ) THEN
IJOBVR = 1
ILVSR = .FALSE.
ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
IJOBVR = 2
ILVSR = .TRUE.
ELSE
IJOBVR = -1
ILVSR = .FALSE.
END IF
*
*     Test the input arguments
*
LWKMIN = MAX( 4*N, 1 )
LWKOPT = LWKMIN
WORK( 1 ) = LWKOPT
LQUERY = ( LWORK.EQ.-1 )
INFO = 0
IF( IJOBVL.LE.0 ) THEN
INFO = -1
ELSE IF( IJOBVR.LE.0 ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
INFO = -12
ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
INFO = -14
ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
INFO = -16
END IF
*
IF( INFO.EQ.0 ) THEN
NB1 = ILAENV( 1, 'SGEQRF', ' ', N, N, -1, -1 )
NB2 = ILAENV( 1, 'SORMQR', ' ', N, N, N, -1 )
NB3 = ILAENV( 1, 'SORGQR', ' ', N, N, N, -1 )
NB = MAX( NB1, NB2, NB3 )
LOPT = 2*N+N*(NB+1)
WORK( 1 ) = LOPT
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGEGS ', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
*     Get machine constants
*
EPS = SLAMCH( 'E' )*SLAMCH( 'B' )
SAFMIN = SLAMCH( 'S' )
SMLNUM = N*SAFMIN / EPS
BIGNUM = ONE / SMLNUM
*
*     Scale A if max element outside range [SMLNUM,BIGNUM]
*
ANRM = SLANGE( 'M', N, N, A, LDA, WORK )
ILASCL = .FALSE.
IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
ANRMTO = SMLNUM
ILASCL = .TRUE.
ELSE IF( ANRM.GT.BIGNUM ) THEN
ANRMTO = BIGNUM
ILASCL = .TRUE.
END IF
*
IF( ILASCL ) THEN
CALL SLASCL( 'G', -1, -1, ANRM, ANRMTO, N, N, A, LDA, IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 9
RETURN
END IF
END IF
*
*     Scale B if max element outside range [SMLNUM,BIGNUM]
*
BNRM = SLANGE( 'M', N, N, B, LDB, WORK )
ILBSCL = .FALSE.
IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
BNRMTO = SMLNUM
ILBSCL = .TRUE.
ELSE IF( BNRM.GT.BIGNUM ) THEN
BNRMTO = BIGNUM
ILBSCL = .TRUE.
END IF
*
IF( ILBSCL ) THEN
CALL SLASCL( 'G', -1, -1, BNRM, BNRMTO, N, N, B, LDB, IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 9
RETURN
END IF
END IF
*
*     Permute the matrix to make it more nearly triangular
*     Workspace layout:  (2*N words -- "work..." not actually used)
*        left_permutation, right_permutation, work...
*
ILEFT = 1
IRIGHT = N + 1
IWORK = IRIGHT + N
CALL SGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, WORK( ILEFT ),
\$             WORK( IRIGHT ), WORK( IWORK ), IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 1
GO TO 10
END IF
*
*     Reduce B to triangular form, and initialize VSL and/or VSR
*     Workspace layout:  ("work..." must have at least N words)
*        left_permutation, right_permutation, tau, work...
*
IROWS = IHI + 1 - ILO
ICOLS = N + 1 - ILO
ITAU = IWORK
IWORK = ITAU + IROWS
CALL SGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
\$             WORK( IWORK ), LWORK+1-IWORK, IINFO )
IF( IINFO.GE.0 )
\$   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
IF( IINFO.NE.0 ) THEN
INFO = N + 2
GO TO 10
END IF
*
CALL SORMQR( 'L', 'T', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
\$             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ),
\$             LWORK+1-IWORK, IINFO )
IF( IINFO.GE.0 )
\$   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
IF( IINFO.NE.0 ) THEN
INFO = N + 3
GO TO 10
END IF
*
IF( ILVSL ) THEN
CALL SLASET( 'Full', N, N, ZERO, ONE, VSL, LDVSL )
CALL SLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
\$                VSL( ILO+1, ILO ), LDVSL )
CALL SORGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
\$                WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK,
\$                IINFO )
IF( IINFO.GE.0 )
\$      LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
IF( IINFO.NE.0 ) THEN
INFO = N + 4
GO TO 10
END IF
END IF
*
IF( ILVSR )
\$   CALL SLASET( 'Full', N, N, ZERO, ONE, VSR, LDVSR )
*
*     Reduce to generalized Hessenberg form
*
CALL SGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
\$             LDVSL, VSR, LDVSR, IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 5
GO TO 10
END IF
*
*     Perform QZ algorithm, computing Schur vectors if desired
*     Workspace layout:  ("work..." must have at least 1 word)
*        left_permutation, right_permutation, work...
*
IWORK = ITAU
CALL SHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
\$             ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR,
\$             WORK( IWORK ), LWORK+1-IWORK, IINFO )
IF( IINFO.GE.0 )
\$   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
IF( IINFO.NE.0 ) THEN
IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN
INFO = IINFO
ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN
INFO = IINFO - N
ELSE
INFO = N + 6
END IF
GO TO 10
END IF
*
*     Apply permutation to VSL and VSR
*
IF( ILVSL ) THEN
CALL SGGBAK( 'P', 'L', N, ILO, IHI, WORK( ILEFT ),
\$                WORK( IRIGHT ), N, VSL, LDVSL, IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 7
GO TO 10
END IF
END IF
IF( ILVSR ) THEN
CALL SGGBAK( 'P', 'R', N, ILO, IHI, WORK( ILEFT ),
\$                WORK( IRIGHT ), N, VSR, LDVSR, IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 8
GO TO 10
END IF
END IF
*
*     Undo scaling
*
IF( ILASCL ) THEN
CALL SLASCL( 'H', -1, -1, ANRMTO, ANRM, N, N, A, LDA, IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 9
RETURN
END IF
CALL SLASCL( 'G', -1, -1, ANRMTO, ANRM, N, 1, ALPHAR, N,
\$                IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 9
RETURN
END IF
CALL SLASCL( 'G', -1, -1, ANRMTO, ANRM, N, 1, ALPHAI, N,
\$                IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 9
RETURN
END IF
END IF
*
IF( ILBSCL ) THEN
CALL SLASCL( 'U', -1, -1, BNRMTO, BNRM, N, N, B, LDB, IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 9
RETURN
END IF
CALL SLASCL( 'G', -1, -1, BNRMTO, BNRM, N, 1, BETA, N, IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + 9
RETURN
END IF
END IF
*
10 CONTINUE
WORK( 1 ) = LWKOPT
*
RETURN
*
*     End of SGEGS
*
END

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