ZGEESX(l) ) ZGEESX(l)
NAME
ZGEESX - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vec-
tors 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 N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vec-
tors 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 eigenvalues (RCONDV). The lead-
ing columns of Z form an orthonormal basis for this invariant subspace.
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 respectively).
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 computed;
= '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 N-by-N 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*(N-SDIM), where SDIM is
the number of selected eigenvalues computed by this routine. Note that 2*SDIM*(N-SDIM) <= 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 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 trans-
formation which reduces A to its partially converged Schur form. = N+1: the eigenvalues could not be reordered because some eigen-
values 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 ZGEESX(l)