!>
!> This routine is deprecated and has been replaced by routine SGGEV.
!>
!> SGEGV computes the eigenvalues and, optionally, the left and/or right
!> eigenvectors of a real matrix pair (A,B).
!> Given two square matrices A and B,
!> the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
!> eigenvalues lambda and corresponding (non-zero) eigenvectors x such
!> that
!>
!>    A*x = lambda*B*x.
!>
!> An alternate form is to find the eigenvalues mu and corresponding
!> eigenvectors y such that
!>
!>    mu*A*y = B*y.
!>
!> These two forms are equivalent with mu = 1/lambda and x = y if
!> neither lambda nor mu is zero.  In order to deal with the case that
!> lambda or mu is zero or small, two values alpha and beta are returned
!> for each eigenvalue, such that lambda = alpha/beta and
!> mu = beta/alpha.
!>
!> The vectors x and y in the above equations are right eigenvectors of
!> the matrix pair (A,B).  Vectors u and v satisfying
!>
!>    u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B
!>
!> are left eigenvectors of (A,B).
!>
!> Note: this routine performs  on A and B
!> 

JOBVL

!>          JOBVL is CHARACTER*1
!>          = 'N':  do not compute the left generalized eigenvectors;
!>          = 'V':  compute the left generalized eigenvectors (returned
!>                  in VL).
!> 

JOBVR

!>          JOBVR is CHARACTER*1
!>          = 'N':  do not compute the right generalized eigenvectors;
!>          = 'V':  compute the right generalized eigenvectors (returned
!>                  in VR).
!> 

N

!>          N is INTEGER
!>          The order of the matrices A, B, VL, and VR.  N >= 0.
!> 

A

!>          A is REAL array, dimension (LDA, N)
!>          On entry, the matrix A.
!>          If JOBVL = 'V' or JOBVR = 'V', then on exit A
!>          contains the real Schur form of A from the generalized Schur
!>          factorization of the pair (A,B) after balancing.
!>          If no eigenvectors were computed, then only the diagonal
!>          blocks from the Schur form will be correct.  See SGGHRD and
!>          SHGEQZ for details.
!> 

LDA

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

B

!>          B is REAL array, dimension (LDB, N)
!>          On entry, the matrix B.
!>          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
!>          upper triangular matrix obtained from B in the generalized
!>          Schur factorization of the pair (A,B) after balancing.
!>          If no eigenvectors were computed, then only those elements of
!>          B corresponding to the diagonal blocks from the Schur form of
!>          A will be correct.  See SGGHRD and SHGEQZ for details.
!> 

LDB

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

ALPHAR

!>          ALPHAR is REAL array, dimension (N)
!>          The real parts of each scalar alpha defining an eigenvalue of
!>          GNEP.
!> 

ALPHAI

!>          ALPHAI is 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

!>          BETA is 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.
!> 

VL

!>          VL is REAL array, dimension (LDVL,N)
!>          If JOBVL = 'V', the left eigenvectors u(j) are stored
!>          in the columns of VL, in the same order as their eigenvalues.
!>          If the j-th eigenvalue is real, then u(j) = VL(:,j).
!>          If the j-th and (j+1)-st eigenvalues form a complex conjugate
!>          pair, then
!>             u(j) = VL(:,j) + i*VL(:,j+1)
!>          and
!>            u(j+1) = VL(:,j) - i*VL(:,j+1).
!>
!>          Each eigenvector is scaled so that its largest component has
!>          abs(real part) + abs(imag. part) = 1, except for eigenvectors
!>          corresponding to an eigenvalue with alpha = beta = 0, which
!>          are set to zero.
!>          Not referenced if JOBVL = 'N'.
!> 

LDVL

!>          LDVL is INTEGER
!>          The leading dimension of the matrix VL. LDVL >= 1, and
!>          if JOBVL = 'V', LDVL >= N.
!> 

VR

!>          VR is REAL array, dimension (LDVR,N)
!>          If JOBVR = 'V', the right eigenvectors x(j) are stored
!>          in the columns of VR, in the same order as their eigenvalues.
!>          If the j-th eigenvalue is real, then x(j) = VR(:,j).
!>          If the j-th and (j+1)-st eigenvalues form a complex conjugate
!>          pair, then
!>            x(j) = VR(:,j) + i*VR(:,j+1)
!>          and
!>            x(j+1) = VR(:,j) - i*VR(:,j+1).
!>
!>          Each eigenvector is scaled so that its largest component has
!>          abs(real part) + abs(imag. part) = 1, except for eigenvalues
!>          corresponding to an eigenvalue with alpha = beta = 0, which
!>          are set to zero.
!>          Not referenced if JOBVR = 'N'.
!> 

LDVR

!>          LDVR is INTEGER
!>          The leading dimension of the matrix VR. LDVR >= 1, and
!>          if JOBVR = 'V', LDVR >= N.
!> 

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.  LWORK >= max(1,8*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 + MAX( 6*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

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          = 1,...,N:
!>                The QZ iteration failed.  No eigenvectors have been
!>                calculated, 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 STGEVC
!>                =N+8: error return from SGGBAK (computing VL)
!>                =N+9: error return from SGGBAK (computing VR)
!>                =N+10: error return from SLASCL (various calls)
!> 

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!>
!>  Balancing
!>  ---------
!>
!>  This driver calls SGGBAL to both permute and scale rows and columns
!>  of A and B.  The permutations PL and PR are chosen so that PL*A*PR
!>  and PL*B*R will be upper triangular except for the diagonal blocks
!>  A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
!>  possible.  The diagonal scaling matrices DL and DR are chosen so
!>  that the pair  DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
!>  one (except for the elements that start out zero.)
!>
!>  After the eigenvalues and eigenvectors of the balanced matrices
!>  have been computed, SGGBAK transforms the eigenvectors back to what
!>  they would have been (in perfect arithmetic) if they had not been
!>  balanced.
!>
!>  Contents of A and B on Exit
!>  -------- -- - --- - -- ----
!>
!>  If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or
!>  both), then on exit the arrays A and B will contain the real Schur
!>  form[*] of the  versions of A and B.  If no eigenvectors
!>  are computed, then only the diagonal blocks will be correct.
!>
!>  [*] See SHGEQZ, SGEGS, or read the book ,
!>      by Golub & van Loan, pub. by Johns Hopkins U. Press.
!>