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CGEEV(1)	      LAPACK driver routine (version 3.2)	      CGEEV(1)

NAME
       CGEEV  -	 computes for an N-by-N complex nonsymmetric matrix A, the ei‐
       genvalues 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	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 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 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 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 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 (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	calcu‐
	       lates 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) 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.

 LAPACK driver routine (version 3November 2008			      CGEEV(1)
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