Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  for  an  N-by-N complex nonsymmetric matrix A, the eigenvalues and,
       optionally, the left and/or right eigenvectors

SYNOPSIS

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

           CHARACTER     JOBVL, JOBVR

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

           DOUBLE        PRECISION RWORK( * )

           COMPLEX*16    A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), W( * ), WORK( * )

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

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

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

        WORK    (workspace/output) COMPLEX*16 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) DOUBLE PRECISION 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 3.2)        April 2011                             ZGEEV(3lapack)