zgees - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
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(*)
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
#include <sunperf.h>
void zgees(char jobz, char sortev, logical(*select)(COMPLEX*16), int n, doublecomplex *a, int lda, int *nout, doublecomplex *w, doublecomplex *z, int ldz, int *info);
void zgees_64(char jobz, char sortev, logical(*select)(COMPLEX*16), long n, doublecomplex *a, long lda, long *nout, doublecomplex *w, doublecomplex *z, long ldz, long *info);
zgees computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues, 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.
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.
= 'S': Eigenvalues are ordered (see SELECT).
W(j)
is selected if SELECT(W(j))
is true.
WORK(1)
returns the optimal LDWORK.
If LDWORK = -1, then a workspace query is assumed; the routine 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.
dimension(N)
dimension(N)
Not referenced if SORTEV = 'N'.
= 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 scaling.