dgeesx(3P) Sun Performance Library dgeesx(3P)NAMEdgeesx - compute for an N-by-N real nonsymmetric matrix A, the eigen‐
values, the real Schur form T, and, optionally, the matrix of Schur
vectors Z
SYNOPSIS
SUBROUTINE DGEESX(JOBZ, SORTEV, SELECT, SENSE, N, A, LDA, NOUT, WR,
WI, Z, LDZ, SRCONE, RCONV, WORK, LDWORK, IWORK2, LDWRK2, BWORK3,
INFO)
CHARACTER * 1 JOBZ, SORTEV, SENSE
INTEGER N, LDA, NOUT, LDZ, LDWORK, LDWRK2, INFO
INTEGER IWORK2(*)
LOGICAL SELECT
LOGICAL BWORK3(*)
DOUBLE PRECISION SRCONE, RCONV
DOUBLE PRECISION A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*)
SUBROUTINE DGEESX_64(JOBZ, SORTEV, SELECT, SENSE, N, A, LDA, NOUT,
WR, WI, Z, LDZ, SRCONE, RCONV, WORK, LDWORK, IWORK2, LDWRK2,
BWORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV, SENSE
INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, LDWRK2, INFO
INTEGER*8 IWORK2(*)
LOGICAL*8 SELECT
LOGICAL*8 BWORK3(*)
DOUBLE PRECISION SRCONE, RCONV
DOUBLE PRECISION A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE GEESX(JOBZ, SORTEV, SELECT, SENSE, [N], A, [LDA], NOUT,
WR, WI, Z, [LDZ], SRCONE, RCONV, [WORK], [LDWORK], [IWORK2],
[LDWRK2], [BWORK3], [INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV, SENSE
INTEGER :: N, LDA, NOUT, LDZ, LDWORK, LDWRK2, INFO
INTEGER, DIMENSION(:) :: IWORK2
LOGICAL :: SELECT
LOGICAL, DIMENSION(:) :: BWORK3
REAL(8) :: SRCONE, RCONV
REAL(8), DIMENSION(:) :: WR, WI, WORK
REAL(8), DIMENSION(:,:) :: A, Z
SUBROUTINE GEESX_64(JOBZ, SORTEV, SELECT, SENSE, [N], A, [LDA], NOUT,
WR, WI, Z, [LDZ], SRCONE, RCONV, [WORK], [LDWORK], [IWORK2],
[LDWRK2], [BWORK3], [INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV, SENSE
INTEGER(8) :: N, LDA, NOUT, LDZ, LDWORK, LDWRK2, INFO
INTEGER(8), DIMENSION(:) :: IWORK2
LOGICAL(8) :: SELECT
LOGICAL(8), DIMENSION(:) :: BWORK3
REAL(8) :: SRCONE, RCONV
REAL(8), DIMENSION(:) :: WR, WI, WORK
REAL(8), DIMENSION(:,:) :: A, Z
C INTERFACE
#include <sunperf.h>
void dgeesx(char jobz, char sortev, int(*select)(double,double), char
sense, int n, double *a, int lda, int *nout, double *wr, dou‐
ble *wi, double *z, int ldz, double *srcone, double *rconv,
int *info);
void dgeesx_64(char jobz, char sortev, long(*select)(double,double),
char sense, long n, double *a, long lda, long *nout, double
*wr, double *wi, double *z, long ldz, double *srcone, double
*rconv, long *info);
PURPOSEdgeesx 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; 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 quan‐
tities are called s and sep respectively).
A real 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 are. 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 may be set to N+3 (see INFO below).
SENSE (input)
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', SORTEV
must equal 'S'.
N (input) The order of the matrix A. N >= 0.
A (input/output)
On entry, the N-by-N matrix A. On exit, A is 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 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, and if JOBZ
= 'V', LDZ >= N.
SRCONE (output)
If SENSE = 'E' or 'B', SRCONE contains the reciprocal condi‐
tion 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 reciprocal condi‐
tion number for the selected right invariant subspace. Not
referenced if SENSE = 'N' or 'E'.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= max(1,3*N).
Also, if SENSE = 'E' or 'V' or 'B', LDWORK >= N+2*NOUT*(N-
NOUT), where NOUT is the number of selected eigenvalues com‐
puted by this routine. Note that N+2*NOUT*(N-NOUT) <=
N+N*N/2. For good performance, LDWORK must generally be
larger.
IWORK2 (workspace/output)
Not referenced if SENSE = 'N' or 'E'. On exit, if INFO = 0,
IWORK2(1) returns the optimal LDWRK2.
LDWRK2 (input)
The dimension of the array IWORK2. LDWRK2 >= 1; if SENSE =
'V' or 'B', LDWRK2 >= NOUT*(N-NOUT).
BWORK3 (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 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 reorder‐
ing, 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 dgeesx(3P)
