cggev(3P) Sun Performance Library cggev(3P)NAMEcggev - 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
SYNOPSIS
SUBROUTINE CGGEV(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL,
LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CHARACTER * 1 JOBVL, JOBVR
COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VL(LDVL,*), VR(LDVR,*),
WORK(*)
INTEGER N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL RWORK(*)
SUBROUTINE CGGEV_64(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL,
LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CHARACTER * 1 JOBVL, JOBVR
COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VL(LDVL,*), VR(LDVR,*),
WORK(*)
INTEGER*8 N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL 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, DIMENSION(:) :: ALPHA, BETA, WORK
COMPLEX, DIMENSION(:,:) :: A, B, VL, VR
INTEGER :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL, 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, DIMENSION(:) :: ALPHA, BETA, WORK
COMPLEX, DIMENSION(:,:) :: A, B, VL, VR
INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL, DIMENSION(:) :: RWORK
C INTERFACE
#include <sunperf.h>
void cggev(char jobvl, char jobvr, int n, complex *a, int lda, complex
*b, int ldb, complex *alpha, complex *beta, complex *vl, int
ldvl, complex *vr, int ldvr, int *info);
void cggev_64(char jobvl, char jobvr, long n, complex *a, long lda,
complex *b, long ldb, complex *alpha, complex *beta, complex
*vl, long ldvl, complex *vr, long ldvr, long *info);
PURPOSEcggev 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 singu‐
lar. 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).
ARGUMENTS
JOBVL (input)
= 'N': do not compute the left generalized eigenvectors;
= 'V': compute the left generalized eigenvectors.
JOBVR (input)
= 'N': do not compute the right generalized eigenvectors;
= 'V': compute the right generalized eigenvectors.
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. How‐
ever, ALPHA will be always less than and usually comparable
with norm(A) in magnitude, and BETA always less than and usu‐
ally 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 generally 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 illegal value.
=1,...,N: The QZ iteration failed. No eigenvectors 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.
6 Mar 2009 cggev(3P)
