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.

JOBVL

          JOBVL is CHARACTER*1


          = 'N': left eigenvectors of A are not computed;


          = 'V': left eigenvectors of are computed.

JOBVR

          JOBVR is CHARACTER*1


          = 'N': right eigenvectors of A are not computed;


          = 'V': right eigenvectors of A are computed.

N

          N is INTEGER


          The order of the matrix A. N >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)


          On entry, the N-by-N matrix A.


          On exit, A has been overwritten.

LDA

          LDA is INTEGER


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

W

          W is COMPLEX*16 array, dimension (N)


          W contains the computed eigenvalues.

VL

          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

          LDVL is INTEGER


          The leading dimension of the array VL.  LDVL >= 1; if


          JOBVL = 'V', LDVL >= N.

VR

          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

          LDVR is INTEGER


          The leading dimension of the array VR.  LDVR >= 1; if


          JOBVR = 'V', LDVR >= N.

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          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

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

INFO

          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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011