Contents
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(JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, LDZ,
WORK, LDWORK, WORK2, WORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV
COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
INTEGER N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL SELECT
LOGICAL WORK3(*)
REAL WORK2(*)
SUBROUTINE CGEES_64(JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, LDZ,
WORK, LDWORK, WORK2, WORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV
COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL*8 SELECT
LOGICAL*8 WORK3(*)
REAL WORK2(*)
F95 INTERFACE
SUBROUTINE GEES(JOBZ, SORTEV, [SELECT], [N], A, [LDA], [NOUT], W, [Z], [LDZ],
[WORK], [LDWORK], [WORK2], [WORK3], [INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV
COMPLEX, DIMENSION(:) :: W, WORK
COMPLEX, DIMENSION(:,:) :: A, Z
INTEGER :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL :: SELECT
LOGICAL, DIMENSION(:) :: WORK3
REAL, DIMENSION(:) :: WORK2
SUBROUTINE GEES_64(JOBZ, SORTEV, [SELECT], [N], A, [LDA], [NOUT], W, [Z],
[LDZ], [WORK], [LDWORK], [WORK2], [WORK3], [INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV
COMPLEX, DIMENSION(:) :: W, WORK
COMPLEX, DIMENSION(:,:) :: A, Z
INTEGER(8) :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL(8) :: SELECT
LOGICAL(8), DIMENSION(:) :: WORK3
REAL, DIMENSION(:) :: WORK2
C INTERFACE
#include <sunperf.h>
void cgees(char jobz, char sortev, int(*select)(complex),
int n, complex *a, int lda, int *nout, complex *w,
complex *z, int ldz, int *info);
void cgees_64(char jobz, char sortev,
long(*select)(complex), long n, complex *a, long
lda, long *nout, complex *w, complex *z, long ldz,
long *info);
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 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. 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.
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)
SELECT must be declared EXTERNAL in the calling
subroutine. 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 refer-
enced. The eigenvalue W(j) is selected if
SELECT(W(j)) is true.
N (input) The order of the matrix A. N >= 0.
A (input/output)
On entry, the N-by-N matrix A. On exit, A has
been 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)
W contains the computed eigenvalues, in the same
order that they appear on the diagonal of the out-
put Schur form T.
Z (output)
If JOBZ = 'V', Z contains the unitary matrix Z of
Schur vectors. If JOBZ = 'N', Z is not refer-
enced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1;
if JOBZ = 'V', LDZ >= N.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >=
max(1,2*N). For good performance, LDWORK must
generally be larger.
If LDWORK = -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 LDWORK is issued by XERBLA.
WORK2 (workspace)
dimension(N)
WORK3 (workspace)
dimension(N) Not referenced if SORTEV = '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 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 prob-
lem is very ill-conditioned); = N+2: after reord-
ering, 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.