NAME

       sgegs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgegs (JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL,
           VSR, LDVSR, WORK, LWORK, INFO)
            SGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors
           for GE matrices

Function/Subroutine Documentation

   subroutine sgegs (characterJOBVSL, characterJOBVSR, integerN, real, dimension( lda, * )A,
       integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( * )ALPHAR, real,
       dimension( * )ALPHAI, real, dimension( * )BETA, real, dimension( ldvsl, * )VSL,
       integerLDVSL, real, dimension( ldvsr, * )VSR, integerLDVSR, real, dimension( * )WORK,
       integerLWORK, integerINFO)
        SGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       GE matrices

       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            This routine is deprecated and has been replaced by routine SGGES.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).

       Parameters:
           JOBVSL

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

           JOBVSR

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

           N

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

           A

                     A is 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

                     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.
                     On exit, the upper triangular matrix T from the generalized
                     real Schur factorization.

           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.

           VSL

                     VSL is REAL array, dimension (LDVSL,N)
                     If JOBVSL = 'V', the matrix of left Schur vectors Q.
                     Not referenced if JOBVSL = 'N'.

           LDVSL

                     LDVSL is INTEGER
                     The leading dimension of the matrix VSL. LDVSL >=1, and
                     if JOBVSL = 'V', LDVSL >= N.

           VSR

                     VSR is REAL array, dimension (LDVSR,N)
                     If JOBVSR = 'V', the matrix of right Schur vectors Z.
                     Not referenced if JOBVSR = 'N'.

           LDVSR

                     LDVSR is INTEGER
                     The leading dimension of the matrix VSR. LDVSR >= 1, and
                     if JOBVSR = 'V', LDVSR >= 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(1,4*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

                     INFO is 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)

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Definition at line 226 of file sgegs.f.

Author

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