cgeev(3F)

NAME
     CGEEV - compute 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
     eigenvalues 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 overwritten.

     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
             eigenvalues.  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 (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.

     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.