CGEES computes for an N-by-N complex nonsymmetric matrix A, the


 eigenvalues, the Schur form T, and, optionally, the matrix of Schur


 vectors Z.  This gives the Schur factorization A = Z*T*(Z**H).


 Optionally, it also orders the eigenvalues on the diagonal of the


 Schur form so that selected eigenvalues are at the top left.


 The leading columns of Z then form an orthonormal basis for the


 invariant subspace corresponding to the selected eigenvalues.


 A complex matrix is in Schur form if it is upper triangular.

JOBVS

          JOBVS is CHARACTER*1


          = 'N': Schur vectors are not computed;


          = 'V': Schur vectors are computed.

SORT

          SORT is CHARACTER*1


          Specifies whether or not to order the eigenvalues on the


          diagonal of the Schur form.


          = 'N': Eigenvalues are not ordered:


          = 'S': Eigenvalues are ordered (see SELECT).

SELECT

          SELECT is a LOGICAL FUNCTION of one COMPLEX argument


          SELECT must be declared EXTERNAL in the calling subroutine.


          If SORT = 'S', SELECT is used to select eigenvalues to order


          to the top left of the Schur form.


          IF SORT = 'N', SELECT is not referenced.


          The eigenvalue W(j) is selected if SELECT(W(j)) is true.

N

          N is INTEGER


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

A

          A is COMPLEX array, dimension (LDA,N)


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


          On exit, A has been overwritten by its Schur form T.

LDA

          LDA is INTEGER


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

SDIM

          SDIM is INTEGER


          If SORT = 'N', SDIM = 0.


          If SORT = 'S', SDIM = number of eigenvalues for which


                         SELECT is true.

W

          W is COMPLEX array, dimension (N)


          W contains the computed eigenvalues, in the same order that


          they appear on the diagonal of the output Schur form T.

VS

          VS is COMPLEX array, dimension (LDVS,N)


          If JOBVS = 'V', VS contains the unitary matrix Z of Schur


          vectors.


          If JOBVS = 'N', VS is not referenced.

LDVS

          LDVS is INTEGER


          The leading dimension of the array VS.  LDVS >= 1; if


          JOBVS = 'V', LDVS >= N.

WORK

          WORK is COMPLEX 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 REAL array, dimension (N)

BWORK

          BWORK is LOGICAL array, dimension (N)


          Not referenced if SORT = 'N'.

INFO

          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value.


          > 0: if INFO = i, and i is


               <= N:  the QR algorithm failed to compute all the


                      eigenvalues; elements 1:ILO-1 and i+1:N of W


                      contain those eigenvalues which have converged;


                      if JOBVS = 'V', VS contains the matrix which


                      reduces A to its partially converged Schur form.


               = N+1: the eigenvalues could not be reordered because


                      some eigenvalues were too close to separate (the


                      problem is very ill-conditioned);


               = N+2: after reordering, roundoff changed values of


                      some complex eigenvalues so that leading


                      eigenvalues in the Schur form no longer satisfy


                      SELECT = .TRUE..  This could also be caused by


                      underflow due to scaling.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011