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zgees.f(3) LAPACK zgees.f(3)

zgees.f -


subroutine zgees (JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, LDVS, WORK, LWORK, RWORK, BWORK, INFO)
 
ZGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices

ZGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices
Purpose:
 ZGEES 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.
Parameters:
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*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.
          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*16 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*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; if
          JOBVS = 'V', LDVS >= 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 (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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 197 of file zgees.f.

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