CGEEV(3)              LAPACK driver routine (version 3.1)             CGEEV(3)



NAME
       CGEEV  -  for  an N-by-N complex nonsymmetric matrix A, the eigenvalues
       and, optionally, the left and/or right eigenvectors

SYNOPSIS
       SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK,
                         LWORK, RWORK, INFO )

           CHARACTER     JOBVL, JOBVR

           INTEGER       INFO, LDA, LDVL, LDVR, LWORK, N

           REAL          RWORK( * )

           COMPLEX       A(  LDA,  *  ), VL( LDVL, * ), VR( LDVR, * ), W( * ),
                         WORK( * )

PURPOSE
       CGEEV computes for an N-by-N complex nonsymmetric matrix A, the  eigen-
       values and, optionally, the left and/or right eigenvectors.

       The right eigenvector v(j) of A satisfies
                        A * v(j) = lambda(j) * v(j)
       where lambda(j) is its eigenvalue.
       The left eigenvector u(j) of A satisfies
                     u(j)**H * A = lambda(j) * u(j)**H
       where u(j)**H denotes the conjugate transpose of u(j).

       The  computed  eigenvectors are normalized to have Euclidean norm equal
       to 1 and largest component real.


ARGUMENTS
       JOBVL   (input) CHARACTER*1
               = 'N': left eigenvectors of A are not computed;
               = 'V': left eigenvectors of are computed.

       JOBVR   (input) CHARACTER*1
               = 'N': right eigenvectors of A are not computed;
               = 'V': right eigenvectors of A are computed.

       N       (input) INTEGER
               The order of the matrix A. N >= 0.

       A       (input/output) COMPLEX array, dimension (LDA,N)
               On entry, the N-by-N matrix A.  On exit, A has  been  overwrit-
               ten.

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

       W       (output) COMPLEX array, dimension (N)
               W contains the computed eigenvalues.

       VL      (output) COMPLEX array, dimension (LDVL,N)
               If JOBVL = 'V', the left eigenvectors u(j) are stored one after
               another in the columns of VL, in the same order as their eigen-
               values.  If JOBVL = 'N', VL is not referenced.  u(j) = VL(:,j),
               the j-th column of VL.

       LDVL    (input) INTEGER
               The leading dimension of the array VL.  LDVL >= 1; if  JOBVL  =
               'V', LDVL >= N.

       VR      (output) COMPLEX array, dimension (LDVR,N)
               If  JOBVR  =  'V',  the  right eigenvectors v(j) are stored one
               after another in the columns of VR, in the same order as  their
               eigenvalues.   If  JOBVR  =  'N', VR is not referenced.  v(j) =
               VR(:,j), the j-th column of VR.

       LDVR    (input) INTEGER
               The leading dimension of the array VR.  LDVR >= 1; if  JOBVR  =
               'V', LDVR >= N.

       WORK    (workspace/output) COMPLEX 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(1,2*N).  For
               good performance, LWORK must generally be larger.

               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   (workspace) REAL array, dimension (2*N)

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value.
               >  0:   if INFO = i, the QR algorithm failed to compute all the
               eigenvalues, and no eigenvectors have been  computed;  elements
               and i+1:N of W contain eigenvalues which have converged.



 LAPACK driver routine (version 3.N1o)vember 2006                        CGEEV(3)