sgees - ues, the real Schur form T, and, optionally, the matrix of Schur vec- tors Z
SUBROUTINE SGEES(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(*) REAL A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*) SUBROUTINE SGEES_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(*) REAL 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, DIMENSION(:) :: WR, WI, WORK REAL, 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, DIMENSION(:) :: WR, WI, WORK REAL, DIMENSION(:,:) :: A, Z C INTERFACE #include <sunperf.h> void sgees(char jobz, char sortev, int(*select)(float,float), int n, float *a, int lda, int *nout, float *wr, float *wi, float *z, int ldz, int *info); void sgees_64(char jobz, char sortev, long(*select)(float,float), long n, float *a, long lda, long *nout, float *wr, float *wi, float *z, long ldz, long *info);
Oracle Solaris Studio Performance Library sgees(3P)
NAME
sgees - 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 SGEES(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(*)
REAL A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*)
SUBROUTINE SGEES_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(*)
REAL 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, DIMENSION(:) :: WR, WI, WORK
REAL, 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, DIMENSION(:) :: WR, WI, WORK
REAL, DIMENSION(:,:) :: A, Z
C INTERFACE
#include <sunperf.h>
void sgees(char jobz, char sortev, int(*select)(float,float), int n,
float *a, int lda, int *nout, float *wr, float *wi, float *z,
int ldz, int *info);
void sgees_64(char jobz, char sortev, long(*select)(float,float), long
n, float *a, long lda, long *nout, float *wr, float *wi,
float *z, long ldz, long *info);
PURPOSE
sgees 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 REAL 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 ref-
erenced. 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 ei-
genvalue may no longer satisfy SELECT(WR(j),WI(j)) = .TRUE.
after ordering, since ordering may change the value of com-
plex eigenvalues (especially if the eigenvalue is ill-condi-
tioned); 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)
REAL 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.
7 Nov 2015 sgees(3P)