dgeesx
dgeesx - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
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(*)
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
#include <sunperf.h>
void dgeesx(char jobz, char sortev, logical(*select)(double,double), char sense, int n, double *a, int lda, int *nout, double *wr, double *wi, double *z, int ldz, double *srcone, double *rconv, int *info);
void dgeesx_64(char jobz, char sortev, logical(*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);
dgeesx computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues, the real Schur form T, and, optionally, the matrix of
Schur vectors 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 quantities 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).
-
* JOBZ (input)
-
-
* SORTEV (input)
-
Specifies whether or not to order the eigenvalues on the
diagonal of the Schur form.
-
* SELECT (input)
-
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 (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. (Complex conjugate
pairs for which SELECT is true for either
eigenvalue 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
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 reciprocal
condition 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 computed by this routine. Note that
N+2*NOUT*(N-NOUT) <= N+N*N/2.
For good performance, LDWORK must generally be larger.
-
* IWORK2 (workspace)
-
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)
-
Not referenced if SORTEV = 'N'.
-
* INFO (output)
-