LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ cgees()

subroutine cgees ( character jobvs,
character sort,
external select,
integer n,
complex, dimension( lda, * ) a,
integer lda,
integer sdim,
complex, dimension( * ) w,
complex, dimension( ldvs, * ) vs,
integer ldvs,
complex, dimension( * ) work,
integer lwork,
real, dimension( * ) rwork,
logical, dimension( * ) bwork,
integer info )

CGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices

Download CGEES + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> 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.
!>
Parameters
[in]JOBVS
!>          JOBVS is CHARACTER*1
!>          = 'N': Schur vectors are not computed;
!>          = 'V': Schur vectors are computed.
!>
[in]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).
!>
[in]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.
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix A. N >= 0.
!>
[in,out]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.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
[out]SDIM
!>          SDIM is INTEGER
!>          If SORT = 'N', SDIM = 0.
!>          If SORT = 'S', SDIM = number of eigenvalues for which
!>                         SELECT is true.
!>
[out]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.
!>
[out]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.
!>
[in]LDVS
!>          LDVS is INTEGER
!>          The leading dimension of the array VS.  LDVS >= 1; if
!>          JOBVS = 'V', LDVS >= N.
!>
[out]WORK
!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
[in]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.
!>
[out]RWORK
!>          RWORK is REAL array, dimension (N)
!>
[out]BWORK
!>          BWORK is LOGICAL array, dimension (N)
!>          Not referenced if SORT = 'N'.
!>
[out]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.