cgees.f - Man Page




subroutine cgees (jobvs, sort, select, n, a, lda, sdim, w, vs, ldvs, work, lwork, rwork, bwork, info)
CGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices

Function/Subroutine Documentation

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  


 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 is CHARACTER*1
          = 'N': Schur vectors are not computed;
          = 'V': Schur vectors are computed.


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


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


          SDIM is INTEGER
          If SORT = 'N', SDIM = 0.
          If SORT = 'S', SDIM = number of eigenvalues for which
                         SELECT is true.


          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 is COMPLEX array, dimension (LDVS,N)
          If JOBVS = 'V', VS contains the unitary matrix Z of Schur
          If JOBVS = 'N', VS is not referenced.


          LDVS is INTEGER
          The leading dimension of the array VS.  LDVS >= 1; if
          JOBVS = 'V', LDVS >= N.


          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal 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 is REAL array, dimension (N)


          BWORK is LOGICAL array, dimension (N)
          Not referenced if SORT = 'N'.


          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.

Definition at line 195 of file cgees.f.


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Referenced By

The man page cgees(3) is an alias of cgees.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK