CGEES(l) ) CGEES(l)
CGEES - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur
form T, and, optionally, the matrix of Schur vectors Z
SUBROUTINE CGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, LDVS, WORK, LWORK, RWORK,
BWORK, INFO )
CHARACTER JOBVS, SORT
INTEGER INFO, LDA, LDVS, LWORK, N, SDIM
LOGICAL BWORK( * )
REAL RWORK( * )
COMPLEX A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )
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 (input) CHARACTER*1
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.
SORT (input) 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 (input) 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))
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the N-by-N matrix A. On exit, A has been overwritten by its Schur form
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
SDIM (output) INTEGER
If SORT = 'N', SDIM = 0. If SORT = 'S', SDIM = number of eigenvalues for which
SELECT is true.
W (output) 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 (output) COMPLEX array, dimension (LDVS,N)
If JOBVS = 'V', VS contains the unitary matrix Z of Schur vectors. If JOBVS =
'N', VS is not referenced.
LDVS (input) INTEGER
The leading dimension of the array VS. LDVS >= 1; if JOBVS = 'V', LDVS >= N.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) 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 (workspace) REAL array, dimension (N)
BWORK (workspace) LOGICAL array, dimension (N)
Not referenced if SORT = 'N'.
INFO (output) 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.
LAPACK version 3.0 15 June 2000 CGEES(l)