zgges - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the generalized complex Schur form (S, T), and optionally left and/or right Schur vectors (VSL and VSR)
SUBROUTINE ZGGES( JOBVSL, JOBVSR, SORT, DELZTG, N, A, LDA, B, LDB, * SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, * BWORK, INFO) CHARACTER * 1 JOBVSL, JOBVSR, SORT DOUBLE COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) INTEGER N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO LOGICAL DELZTG LOGICAL BWORK(*) DOUBLE PRECISION RWORK(*)
SUBROUTINE ZGGES_64( JOBVSL, JOBVSR, SORT, DELZTG, N, A, LDA, B, * LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, * RWORK, BWORK, INFO) CHARACTER * 1 JOBVSL, JOBVSR, SORT DOUBLE COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) INTEGER*8 N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO LOGICAL*8 DELZTG LOGICAL*8 BWORK(*) DOUBLE PRECISION RWORK(*)
SUBROUTINE GGES( JOBVSL, JOBVSR, SORT, DELZTG, [N], A, [LDA], B, * [LDB], SDIM, ALPHA, BETA, VSL, [LDVSL], VSR, [LDVSR], [WORK], * [LWORK], [RWORK], [BWORK], [INFO]) CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT COMPLEX(8), DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX(8), DIMENSION(:,:) :: A, B, VSL, VSR INTEGER :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO LOGICAL :: DELZTG LOGICAL, DIMENSION(:) :: BWORK REAL(8), DIMENSION(:) :: RWORK
SUBROUTINE GGES_64( JOBVSL, JOBVSR, SORT, DELZTG, [N], A, [LDA], B, * [LDB], SDIM, ALPHA, BETA, VSL, [LDVSL], VSR, [LDVSR], [WORK], * [LWORK], [RWORK], [BWORK], [INFO]) CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT COMPLEX(8), DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX(8), DIMENSION(:,:) :: A, B, VSL, VSR INTEGER(8) :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO LOGICAL(8) :: DELZTG LOGICAL(8), DIMENSION(:) :: BWORK REAL(8), DIMENSION(:) :: RWORK
#include <sunperf.h>
void zgges(char jobvsl, char jobvsr, char sort, logical(*delztg)(COMPLEX*16,COMPLEX*16), int n, doublecomplex *a, int lda, doublecomplex *b, int ldb, int *sdim, doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, int ldvsl, doublecomplex *vsr, int ldvsr, int *info);
void zgges_64(char jobvsl, char jobvsr, char sort, logical(*delztg)(COMPLEX*16,COMPLEX*16), long n, doublecomplex *a, long lda, doublecomplex *b, long ldb, long *sdim, doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, long ldvsl, doublecomplex *vsr, long ldvsr, long *info);
zgges computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the generalized complex Schur form (S, T), and optionally left and/or right Schur vectors (VSL and VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
where (VSR)**H is the conjugate-transpose of VSR.
Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper triangular matrix S and the upper triangular matrix T. The leading columns of VSL and VSR then form an unitary basis for the corresponding left and right eigenspaces (deflating subspaces).
(If only the generalized eigenvalues are needed, use the driver CGGEV instead, which is faster.)
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w or a ratio alpha/beta = w, such that A - w*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even for both being zero.
A pair of matrices (S,T) is in generalized complex Schur form if S and T are upper triangular and, in addition, the diagonal elements of T are non-negative real numbers.
= 'N': do not compute the left Schur vectors;
= 'V': compute the left Schur vectors.
= 'N': do not compute the right Schur vectors;
= 'V': compute the right Schur vectors.
= 'S': Eigenvalues are ordered (see DELZTG).
ALPHA(j)/BETA(j) is selected if
DELZTG(ALPHA(j),BETA(j)) is true.
Note that a selected complex eigenvalue may no longer satisfy
DELZTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since
ordering may change the value of complex eigenvalues
(especially if the eigenvalue is ill-conditioned), in this
case INFO is set to N+2 (See INFO below).
BETA(j) will be non-negative real.
Note: the quotients ALPHA(j)/BETA(j) may easily over- or
underflow, and BETA(j) may even be zero. Thus, the user
should avoid naively computing the ratio alpha/beta.
However, ALPHA will be always less than and usually
comparable with norm(A) in magnitude, and BETA always less
than and usually comparable with norm(B).
WORK(1) returns the optimal LWORK.
If LWORK = -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 LWORK is issued by XERBLA.
dimension(8*N)
dimension(N)
Not referenced if SORT = 'N'.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
=1,...,N: The QZ iteration failed. (A,B) are not in Schur form, but ALPHA(j) and BETA(j) should be correct for j =INFO+1,...,N. > N: =N+1: other than QZ iteration failed in CHGEQZ
=N+2: after reordering, roundoff changed values of some complex eigenvalues so that leading eigenvalues in the Generalized Schur form no longer satisfy DELZTG =.TRUE. This could also be caused due to scaling. =N+3: reordering falied in CTGSEN.