Contents
zggev - compute for a pair of N-by-N complex nonsymmetric
matrices (A,B), the generalized eigenvalues, and optionally,
the left and/or right generalized eigenvectors
SUBROUTINE ZGGEV(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL,
LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CHARACTER * 1 JOBVL, JOBVR
DOUBLE COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*),
VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER N, LDA, LDB, LDVL, LDVR, LWORK, INFO
DOUBLE PRECISION RWORK(*)
SUBROUTINE ZGGEV_64(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL,
LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CHARACTER * 1 JOBVL, JOBVR
DOUBLE COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*),
VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER*8 N, LDA, LDB, LDVL, LDVR, LWORK, INFO
DOUBLE PRECISION RWORK(*)
F95 INTERFACE
SUBROUTINE GGEV(JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHA, BETA,
VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
COMPLEX(8), DIMENSION(:) :: ALPHA, BETA, WORK
COMPLEX(8), DIMENSION(:,:) :: A, B, VL, VR
INTEGER :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL(8), DIMENSION(:) :: RWORK
SUBROUTINE GGEV_64(JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHA,
BETA, VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
COMPLEX(8), DIMENSION(:) :: ALPHA, BETA, WORK
COMPLEX(8), DIMENSION(:,:) :: A, B, VL, VR
INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL(8), DIMENSION(:) :: RWORK
C INTERFACE
#include <sunperf.h>
void zggev(char jobvl, char jobvr, int n, doublecomplex *a,
int lda, doublecomplex *b, int ldb, doublecomplex
*alpha, doublecomplex *beta, doublecomplex *vl,
int ldvl, doublecomplex *vr, int ldvr, int *info);
void zggev_64(char jobvl, char jobvr, long n, doublecomplex
*a, long lda, doublecomplex *b, long ldb, doub-
lecomplex *alpha, doublecomplex *beta, doublecom-
plex *vl, long ldvl, doublecomplex *vr, long ldvr,
long *info);
zggev computes for a pair of N-by-N complex nonsymmetric
matrices (A,B), the generalized eigenvalues, and optionally,
the left and/or right generalized eigenvectors.
A generalized eigenvalue for a pair of matrices (A,B) is a
scalar lambda or a ratio alpha/beta = lambda, such that A -
lambda*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.
The right generalized eigenvector v(j) corresponding to the
generalized eigenvalue lambda(j) of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left generalized eigenvector u(j) corresponding to the
generalized eigenvalues lambda(j) of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B
where u(j)**H is the conjugate-transpose of u(j).
JOBVL (input)
= 'N': do not compute the left generalized eigen-
vectors;
= 'V': compute the left generalized eigenvectors.
JOBVR (input)
= 'N': do not compute the right generalized
eigenvectors;
= 'V': compute the right generalized eigenvec-
tors.
N (input) The order of the matrices A, B, VL, and VR. N >=
0.
A (input/output)
On entry, the matrix A in the pair (A,B). On
exit, A has been overwritten.
LDA (input)
The leading dimension of A. LDA >= max(1,N).
B (input/output)
On entry, the matrix B in the pair (A,B). On
exit, B has been overwritten.
LDB (input)
The leading dimension of B. LDB >= max(1,N).
ALPHA (output)
On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
generalized eigenvalues.
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).
BETA (output)
See description of ALPHA.
VL (output)
If JOBVL = 'V', the left generalized eigenvectors
u(j) are stored one after another in the columns
of VL, in the same order as their eigenvalues.
Each eigenvector will be scaled so the largest
component will have abs(real part) + abs(imag.
part) = 1. Not referenced if JOBVL = 'N'.
LDVL (input)
The leading dimension of the matrix VL. LDVL >= 1,
and if JOBVL = 'V', LDVL >= N.
VR (output)
If JOBVR = 'V', the right generalized eigenvectors
v(j) are stored one after another in the columns
of VR, in the same order as their eigenvalues.
Each eigenvector will be scaled so the largest
component will have abs(real part) + abs(imag.
part) = 1. Not referenced if JOBVR = 'N'.
LDVR (input)
The leading dimension of the matrix VR. LDVR >= 1,
and if JOBVR = 'V', LDVR >= N.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input)
The dimension of the array WORK. LWORK >=
max(1,2*N). For good performance, LWORK must gen-
erally be larger.
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.
RWORK (workspace)
dimension(8*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
=1,...,N: The QZ iteration failed. No eigenvec-
tors have been calculated, but ALPHA(j) and
BETA(j) should be correct for j=INFO+1,...,N. >
N: =N+1: other then QZ iteration failed in
SHGEQZ,
=N+2: error return from STGEVC.