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NAME

        ZGEEV - compute for an N-by-N complex nonsymmetric matrix A, the eigen‐
        values 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  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*16 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*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 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*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 (LWORK)
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.
 

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