zgees.f(3)

NAME
zgees.f

SYNOPSIS

  Functions/Subroutines
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

Function/Subroutine Documentation

  subroutine zgees (character JOBVS, character SORT, external SELECT, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer SDIM, complex*16, dimension( * ) W, complex*16, dimension( ldvs, * ) VS, integer LDVS, complex*16, dimension( * ) WORK, integer LWORK, double precision, dimension( * ) RWORK, logical, dimension( * ) BWORK, integer INFO)

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.

Definition at line 195 of file zgees.f.

Author

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