
ZGEESX(l) ) ZGEESX(l)
NAME
ZGEESX  compute for an NbyN complex nonsymmetric matrix A, the eigenvalues, the Schur
form T, and, optionally, the matrix of Schur vectors Z
SYNOPSIS
SUBROUTINE ZGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W, VS, LDVS, RCONDE,
RCONDV, WORK, LWORK, RWORK, BWORK, INFO )
CHARACTER JOBVS, SENSE, SORT
INTEGER INFO, LDA, LDVS, LWORK, N, SDIM
DOUBLE PRECISION RCONDE, RCONDV
LOGICAL BWORK( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )
LOGICAL SELECT
EXTERNAL SELECT
PURPOSE
ZGEESX computes for an NbyN 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; computes a reciprocal condition
number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal
condition number for the right invariant subspace corresponding to the selected eigenval
ues (RCONDV). The leading columns of Z form an orthonormal basis for this invariant sub
space.
For further explanation of the reciprocal condition numbers RCONDE and RCONDV, see Section
4.10 of the LAPACK Users' Guide (where these quantities are called s and sep respec
tively).
A complex matrix is in Schur form if it is upper triangular.
ARGUMENTS
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*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. An eigenvalue W(j) is selected if SELECT(W(j))
is true.
SENSE (input) CHARACTER*1
Determines which reciprocal condition numbers are computed. = 'N': None are com
puted;
= 'E': Computed for average of selected eigenvalues only;
= 'V': Computed for selected right invariant subspace only;
= 'B': Computed for both. If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the NbyN matrix A. On exit, A is overwritten by its Schur form T.
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*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 (output) 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 (input) INTEGER
The leading dimension of the array VS. LDVS >= 1, and if JOBVS = 'V', LDVS >= N.
RCONDE (output) DOUBLE PRECISION
If SENSE = 'E' or 'B', RCONDE contains the reciprocal condition number for the
average of the selected eigenvalues. Not referenced if SENSE = 'N' or 'V'.
RCONDV (output) DOUBLE PRECISION
If SENSE = 'V' or 'B', RCONDV contains the reciprocal condition number for the
selected right invariant subspace. Not referenced if SENSE = 'N' or 'E'.
WORK (workspace/output) COMPLEX*16 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). Also, if SENSE = 'E' or
'V' or 'B', LWORK >= 2*SDIM*(NSDIM), where SDIM is the number of selected eigen
values computed by this routine. Note that 2*SDIM*(NSDIM) <= N*N/2. For good
performance, LWORK must generally be larger.
RWORK (workspace) DOUBLE PRECISION 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 ith argument had an illegal value.
> 0: if INFO = i, and i is
<= N: the QR algorithm failed to compute all the
eigenvalues; elements 1:ILO1 and i+1:N of W contain those eigenvalues which have
converged; if JOBVS = 'V', VS contains the transformation 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 illcon
ditioned); = N+2: after reordering, roundoff changed values of some complex eigen
values 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 ZGEESX(l) 
