Contents
cgeesx - 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 CGEESX(JOBZ, SORTEV, SELECT, SENSE, N, A, LDA, NOUT, W, Z,
LDZ, RCONE, RCONV, WORK, LDWORK, WORK2, BWORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV, SENSE
COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
INTEGER N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL SELECT
LOGICAL BWORK3(*)
REAL RCONE, RCONV
REAL WORK2(*)
SUBROUTINE CGEESX_64(JOBZ, SORTEV, SELECT, SENSE, N, A, LDA, NOUT, W,
Z, LDZ, RCONE, RCONV, WORK, LDWORK, WORK2, BWORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV, SENSE
COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL*8 SELECT
LOGICAL*8 BWORK3(*)
REAL RCONE, RCONV
REAL WORK2(*)
F95 INTERFACE
SUBROUTINE GEESX(JOBZ, SORTEV, [SELECT], SENSE, [N], A, [LDA], NOUT, W,
Z, [LDZ], RCONE, RCONV, [WORK], [LDWORK], [WORK2], [BWORK3],
[INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV, SENSE
COMPLEX, DIMENSION(:) :: W, WORK
COMPLEX, DIMENSION(:,:) :: A, Z
INTEGER :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL :: SELECT
LOGICAL, DIMENSION(:) :: BWORK3
REAL :: RCONE, RCONV
REAL, DIMENSION(:) :: WORK2
SUBROUTINE GEESX_64(JOBZ, SORTEV, [SELECT], SENSE, [N], A, [LDA], NOUT,
W, Z, [LDZ], RCONE, RCONV, [WORK], [LDWORK], [WORK2], [BWORK3],
[INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV, SENSE
COMPLEX, DIMENSION(:) :: W, WORK
COMPLEX, DIMENSION(:,:) :: A, Z
INTEGER(8) :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL(8) :: SELECT
LOGICAL(8), DIMENSION(:) :: BWORK3
REAL :: RCONE, RCONV
REAL, DIMENSION(:) :: WORK2
C INTERFACE
#include <sunperf.h>
void cgeesx(char jobz, char sortev, int(*select)(complex),
char sense, int n, complex *a, int lda, int *nout,
complex *w, complex *z, int ldz, float *rcone,
float *rconv, int *info);
void cgeesx_64(char jobz, char sortev,
long(*select)(complex), char sense, long n, com-
plex *a, long lda, long *nout, complex *w, complex
*z, long ldz, float *rcone, float *rconv, long
*info);
cgeesx 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 factoriza-
tion 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
leading 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 respec-
tively).
A complex matrix is in Schur form if it is upper triangular.
JOBZ (input)
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.
SORTEV (input)
Specifies whether or not to order the eigenvalues
on the diagonal of the Schur form. = 'N': Eigen-
values 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 subrou-
tine. If SORTEV = 'S', SELECT is used to select
eigenvalues to order to the top left of the Schur
form. If SORTEV = 'N', SELECT is not referenced.
An eigenvalue W(j) is selected if SELECT(W(j)) is
true.
SENSE (input)
Determines which reciprocal condition numbers are
computed. = 'N': None are computed;
= 'E': Computed for average of selected eigen-
values only;
= 'V': Computed for selected right invariant sub-
space only;
= 'B': Computed for both. If SENSE = 'E', 'V' or
'B', SORTEV must equal 'S'.
N (input) 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 is overwritten by its
Schur form T.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
NOUT (output)
If SORTEV = 'N', NOUT = 0. If SORTEV = 'S', NOUT
= number of eigenvalues for which SELECT is true.
W (output)
COMPLEX array, dimension(N) W contains the com-
puted eigenvalues, in the same order that they
appear on the diagonal of the output Schur form T.
Z (output)
COMPLEX array, dimension(LDZ,N) If JOBZ = 'V', Z
contains the unitary matrix Z of Schur vectors.
If JOBZ = 'N', Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1,
and if JOBZ = 'V', LDZ >= N.
RCONE (output)
If SENSE = 'E' or 'B', RCONE contains the recipro-
cal condition number for the average of the
selected eigenvalues. Not referenced if SENSE =
'N' or 'V'.
RCONV (output)
If SENSE = 'V' or 'B', RCONV contains the recipro-
cal condition number for the selected right
invariant subspace. Not referenced if SENSE = 'N'
or 'E'.
WORK (workspace)
COMPLEX array, dimension(LDWORK) On exit, if INFO
= 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >=
max(1,2*N). Also, if SENSE = 'E' or 'V' or 'B',
LDWORK >= 2*NOUT*(N-NOUT), where NOUT is the
number of selected eigenvalues computed by this
routine. Note that 2*NOUT*(N-NOUT) <= N*N/2. For
good performance, LDWORK must generally be larger.
WORK2 (workspace)
REAL array, dimension(N)
BWORK3 (workspace)
LOGICAL array, dimension(N) Not referenced if SOR-
TEV = 'N'.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal 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 con-
tain those eigenvalues which have converged; if
JOBZ = 'V', Z 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 ill-conditioned); =
N+2: after reordering, roundoff changed values of
some complex eigenvalues so that leading eigen-
values in the Schur form no longer satisfy
SELECT=.TRUE. This could also be caused by under-
flow due to scaling.