CGEEV (3lapack)

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.