ZGEESX 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;


 computes a reciprocal condition number for the average of the


 selected eigenvalues (RCONDE); and computes a reciprocal condition


 number for the right invariant subspace corresponding to the


 selected eigenvalues (RCONDV).  The leading columns of Z form an


 orthonormal basis for this invariant subspace.


 For further explanation of the reciprocal condition numbers RCONDE


 and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where


 these quantities are called s and sep respectively).


 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 procedure) LOGICAL FUNCTION of one COMPLEX*16 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.


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

SENSE

          SENSE is CHARACTER*1


          Determines which reciprocal condition numbers are computed.


          = 'N': None are computed;


          = 'E': Computed for average of selected eigenvalues only;


          = 'V': Computed for selected right invariant subspace only;


          = 'B': Computed for both.


          If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.

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 is 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*16 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*16 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, and if


          JOBVS = 'V', LDVS >= N.

RCONDE

          RCONDE is DOUBLE PRECISION


          If SENSE = 'E' or 'B', RCONDE contains the reciprocal


          condition number for the average of the selected eigenvalues.


          Not referenced if SENSE = 'N' or 'V'.

RCONDV

          RCONDV is DOUBLE PRECISION


          If SENSE = 'V' or 'B', RCONDV contains the reciprocal


          condition number for the selected right invariant subspace.


          Not referenced if SENSE = 'N' or 'E'.

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).


          Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM),


          where SDIM is the number of selected eigenvalues computed by


          this routine.  Note that 2*SDIM*(N-SDIM) <= N*N/2. Note also


          that an error is only returned if LWORK < max(1,2*N), but if


          SENSE = 'E' or 'V' or 'B' this may not be large enough.


          For good performance, LWORK must generally be larger.


          If LWORK = -1, then a workspace query is assumed; the routine


          only calculates upper bound on the optimal size of the


          array WORK, 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 (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 transformation 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.

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