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NAME

       cgegv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cgegv (JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, WORK,
           LWORK, RWORK, INFO)
            CGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors
           for GE matrices

Function/Subroutine Documentation

   subroutine cgegv (characterJOBVL, characterJOBVR, integerN, complex, dimension( lda, * )A,
       integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( * )ALPHA,
       complex, dimension( * )BETA, complex, dimension( ldvl, * )VL, integerLDVL, complex,
       dimension( ldvr, * )VR, integerLDVR, complex, dimension( * )WORK, integerLWORK, real,
       dimension( * )RWORK, integerINFO)
        CGEEVX 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            This routine is deprecated and has been replaced by routine CGGEV.

            CGEGV computes the eigenvalues and, optionally, the left and/or right
            eigenvectors of a complex 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 "full balancing" on A and B

       Parameters:
           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 COMPLEX array, dimension (LDA, N)
                     On entry, the matrix A.
                     If JOBVL = 'V' or JOBVR = 'V', then on exit A
                     contains the 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 elements
                     of the Schur form will be correct.  See CGGHRD and CHGEQZ
                     for details.

           LDA

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

           B

                     B is COMPLEX 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 the diagonal
                     elements of B will be correct.  See CGGHRD and CHGEQZ for
                     details.

           LDB

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

           ALPHA

                     ALPHA is COMPLEX array, dimension (N)
                     The complex scalars alpha that define the eigenvalues of
                     GNEP.

           BETA

                     BETA is COMPLEX array, dimension (N)
                     The complex scalars beta that define the eigenvalues of GNEP.

                     Together, the quantities alpha = ALPHA(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 COMPLEX 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.
                     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 COMPLEX 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.
                     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 JOBVR = 'N'.

           LDVR

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

           WORK

                     WORK is COMPLEX 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(1,2*N).
                     For good performance, LWORK must generally be larger.
                     To compute the optimal value of LWORK, call ILAENV to get
                     blocksizes (for CGEQRF, CUNMQR, and CUNGQR.)  Then compute:
                     NB  -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR;
                     The optimal LWORK is  MAX( 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.

           RWORK

                     RWORK is REAL array, dimension (8*N)

           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 ALPHA(j) and BETA(j) should be
                           correct for j=INFO+1,...,N.
                     > N:  errors that usually indicate LAPACK problems:
                           =N+1: error return from CGGBAL
                           =N+2: error return from CGEQRF
                           =N+3: error return from CUNMQR
                           =N+4: error return from CUNGQR
                           =N+5: error return from CGGHRD
                           =N+6: error return from CHGEQZ (other than failed
                                                          iteration)
                           =N+7: error return from CTGEVC
                           =N+8: error return from CGGBAK (computing VL)
                           =N+9: error return from CGGBAK (computing VR)
                           =N+10: error return from CLASCL (various calls)

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Further Details:

             Balancing
             ---------

             This driver calls CGGBAL 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, CGGBAK 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 complex Schur
             form[*] of the "balanced" versions of A and B.  If no eigenvectors
             are computed, then only the diagonal blocks will be correct.

             [*] In other words, upper triangular form.

       Definition at line 282 of file cgegv.f.

Author

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