dgees(3P) Sun Performance Library dgees(3P)NAMEdgees - compute for an N-by-N real nonsymmetric matrix A, the eigenval‐
ues, the real Schur form T, and, optionally, the matrix of Schur vec‐
tors Z
SYNOPSIS
SUBROUTINE DGEES(JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, WR, WI, Z,
LDZ, WORK, LDWORK, WORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV
INTEGER N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL SELECT
LOGICAL WORK3(*)
DOUBLE PRECISION A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*)
SUBROUTINE DGEES_64(JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, WR, WI, Z,
LDZ, WORK, LDWORK, WORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV
INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL*8 SELECT
LOGICAL*8 WORK3(*)
DOUBLE PRECISION A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE GEES(JOBZ, SORTEV, SELECT, [N], A, [LDA], NOUT, WR, WI, Z,
[LDZ], [WORK], [LDWORK], [WORK3], [INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV
INTEGER :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL :: SELECT
LOGICAL, DIMENSION(:) :: WORK3
REAL(8), DIMENSION(:) :: WR, WI, WORK
REAL(8), DIMENSION(:,:) :: A, Z
SUBROUTINE GEES_64(JOBZ, SORTEV, SELECT, [N], A, [LDA], NOUT, WR, WI,
Z, [LDZ], [WORK], [LDWORK], [WORK3], [INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV
INTEGER(8) :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL(8) :: SELECT
LOGICAL(8), DIMENSION(:) :: WORK3
REAL(8), DIMENSION(:) :: WR, WI, WORK
REAL(8), DIMENSION(:,:) :: A, Z
C INTERFACE
#include <sunperf.h>
void dgees(char jobz, char sortev, int(*select)(double,double), int n,
double *a, int lda, int *nout, double *wr, double *wi, double
*z, int ldz, int *info);
void dgees_64(char jobz, char sortev, long(*select)(double,double),
long n, double *a, long lda, long *nout, double *wr, double
*wi, double *z, long ldz, long *info);
PURPOSEdgees computes for an N-by-N real nonsymmetric matrix A, the eigenval‐
ues, the real Schur form T, and, optionally, the matrix of Schur vec‐
tors Z. This gives the Schur factorization A = Z*T*(Z**T).
Optionally, it also orders the eigenvalues on the diagonal of the real
Schur form so that selected eigenvalues are at the top left. The lead‐
ing columns of Z then form an orthonormal basis for the invariant sub‐
space corresponding to the selected eigenvalues.
A matrix is in real Schur form if it is upper quasi-triangular with
1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the
form
[ a b ]
[ c a ]
where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
ARGUMENTS
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': Eigenvalues are not
ordered;
= 'S': Eigenvalues are ordered (see SELECT).
SELECT (input)
LOGICAL FUNCTION of two DOUBLE PRECISION arguments SELECT
must be declared EXTERNAL in the calling subroutine. If
SORTEV = 'S', SELECT is used to select eigenvalues to sort to
the top left of the Schur form. If SORTEV = 'N', SELECT is
not referenced. An eigenvalue WR(j)+sqrt(-1)*WI(j) is
selected if SELECT(WR(j),WI(j)) is true; i.e., if either one
of a complex conjugate pair of eigenvalues is selected, then
both complex eigenvalues are selected. Note that a selected
complex eigenvalue may no longer satisfy SELECT(WR(j),WI(j))
= .TRUE. after ordering, since ordering may change the value
of complex eigenvalues (especially if the eigenvalue is ill-
conditioned); in this case INFO is set to N+2 (see INFO
below).
N (input) The order of the matrix A. N >= 0.
A (input/output)
DOUBLE PRECISION array, dimension(LDA,N) On entry, the N-by-N
matrix A. On exit, A has been overwritten by its real 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 (after sorting) for which SELECT is true. (Com‐
plex conjugate pairs for which SELECT is true for either ei‐
genvalue count as 2.)
WR (output)
WR and WI contain the real and imaginary parts, respectively,
of the computed eigenvalues in the same order that they
appear on the diagonal of the output Schur form T. Complex
conjugate pairs of eigenvalues will appear consecutively with
the eigenvalue having the positive imaginary part first.
WI (output)
See the description for WR.
Z (output)
If JOBZ = 'V', Z contains the orthogonal matrix Z of Schur
vectors. If JOBZ = 'N', Z is not referenced.
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) contains the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= max(1,3*N). For
good performance, LDWORK must generally be larger.
If LDWORK = -1, then a workspace query is assumed; the rou‐
tine 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.
WORK3 (workspace)
dimension(N) Not referenced if SORTEV = 'N'.
INFO (output)
= 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 WR and WI contain
those eigenvalues which have converged; if JOBZ = 'V', Z con‐
tains 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.
6 Mar 2009 dgees(3P)
