ZGEEV(3)       LAPACK routine of NEC Numeric Library Collection       ZGEEV(3)



NAME
       ZGEEV

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



PURPOSE
            ZGEEV 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)
                     JOBVL is CHARACTER*1
                     = 'N': left eigenvectors of A are not computed;
                     = 'V': left eigenvectors of are computed.

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

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

           A         (input/output)
                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the N-by-N matrix A.
                     On exit, A has been overwritten.

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

           W         (output)
                     W is COMPLEX*16 array, dimension (N)
                     W contains the computed eigenvalues.

           VL        (output)
                     VL is COMPLEX*16 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)
                     LDVL is INTEGER
                     The leading dimension of the array VL.  LDVL >= 1; if
                     JOBVL = 'V', LDVL >= N.

           VR        (output)
                     VR is COMPLEX*16 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)
                     LDVR is INTEGER
                     The leading dimension of the array VR.  LDVR >= 1; if
                     JOBVR = 'V', LDVR >= N.

           WORK      (output)
                     WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     LWORK is 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     (output)
                     RWORK is DOUBLE PRECISION array, dimension (2*N)

           INFO      (output)
                     INFO is 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 routine                  31 October 2017                       ZGEEV(3)