zgees(3P) Sun Performance Library zgees(3P)NAMEzgees - compute for an N-by-N complex nonsymmetric matrix A, the eigen‐
values, the Schur form T, and, optionally, the matrix of Schur vectors
Z
SYNOPSIS
SUBROUTINE ZGEES(JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, LDZ,
WORK, LDWORK, WORK2, WORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV
DOUBLE COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
INTEGER N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL SELECT
LOGICAL WORK3(*)
DOUBLE PRECISION WORK2(*)
SUBROUTINE ZGEES_64(JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, LDZ,
WORK, LDWORK, WORK2, WORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV
DOUBLE COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL*8 SELECT
LOGICAL*8 WORK3(*)
DOUBLE PRECISION 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(8), DIMENSION(:) :: W, WORK
COMPLEX(8), DIMENSION(:,:) :: A, Z
INTEGER :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL :: SELECT
LOGICAL, DIMENSION(:) :: WORK3
REAL(8), 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(8), DIMENSION(:) :: W, WORK
COMPLEX(8), DIMENSION(:,:) :: A, Z
INTEGER(8) :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL(8) :: SELECT
LOGICAL(8), DIMENSION(:) :: WORK3
REAL(8), DIMENSION(:) :: WORK2
C INTERFACE
#include <sunperf.h>
void zgees(char jobz, char sortev, int(*select)(doublecomplex), int n,
doublecomplex *a, int lda, int *nout, doublecomplex *w, dou‐
blecomplex *z, int ldz, int *info);
void zgees_64(char jobz, char sortev, long(*select)(doublecomplex),
long n, doublecomplex *a, long lda, long *nout, doublecomplex
*w, doublecomplex *z, long ldz, long *info);
PURPOSEzgees computes for an N-by-N complex nonsymmetric matrix A, the eigen‐
values, the Schur form T, and, optionally, the matrix of Schur vectors
Z. This gives the Schur factorization 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.
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 one DOUBLE COMPLEX argument 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 ref‐
erenced. 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)
DOUBLE COMPLEX array, dimension(LDA,N) 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)
DOUBLE COMPLEX array, dimension(N) W contains the computed
eigenvalues, in the same order that they appear on the diago‐
nal of the output Schur form T.
Z (output)
DOUBLE COMPLEX array, dimension (LDZ, N) If JOBZ = 'V', Z
contains the unitary 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)
DOUBLE COMPLEX array, dimension(LWORK) 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 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.
WORK2 (workspace)
DOUBLE PRECISION array, dimension(N)
WORK3 (workspace)
LOGICAL array, 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 W contain 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 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 scal‐
ing.
6 Mar 2009 zgees(3P)
