
CGGEV(l) ) CGGEV(l)
NAME
CGGEV  compute for a pair of NbyN 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 JOBVL, JOBVR
INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N
REAL RWORK( * )
COMPLEX A( LDA, * ), ALPHA( * ), B( LDB, * ), BETA( * ), VL( LDVL, * ), VR(
LDVR, * ), WORK( * )
PURPOSE
CGGEV computes for a pair of NbyN complex nonsymmetric matrices (A,B), the generalized
eigenvalues, and optionally, the left and/or right generalized eigenvectors. A general
ized 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 conjugatetranspose of u(j).
ARGUMENTS
JOBVL (input) CHARACTER*1
= 'N': do not compute the left generalized eigenvectors;
= 'V': compute the left generalized eigenvectors.
JOBVR (input) CHARACTER*1
= 'N': do not compute the right generalized eigenvectors;
= 'V': compute the right generalized eigenvectors.
N (input) INTEGER
The order of the matrices A, B, VL, and VR. N >= 0.
A (input/output) COMPLEX array, dimension (LDA, N)
On entry, the matrix A in the pair (A,B). On exit, A has been overwritten.
LDA (input) INTEGER
The leading dimension of A. LDA >= max(1,N).
B (input/output) COMPLEX array, dimension (LDB, N)
On entry, the matrix B in the pair (A,B). On exit, B has been overwritten.
LDB (input) INTEGER
The leading dimension of B. LDB >= max(1,N).
ALPHA (output) COMPLEX array, dimension (N)
BETA (output) COMPLEX array, dimension (N) 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).
VL (output) COMPLEX array, dimension (LDVL,N)
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 eigen
vector will be scaled so the largest component will have abs(real part) +
abs(imag. part) = 1. Not referenced if JOBVL = 'N'.
LDVL (input) INTEGER
The leading dimension of the matrix VL. LDVL >= 1, and if JOBVL = 'V', LDVL >= N.
VR (output) COMPLEX array, dimension (LDVR,N)
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 eigen
vector will be scaled so the largest component will have abs(real part) +
abs(imag. part) = 1. Not referenced if JOBVR = 'N'.
LDVR (input) INTEGER
The leading dimension of the matrix VR. LDVR >= 1, and if JOBVR = 'V', LDVR >= N.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
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/output) REAL array, dimension (8*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith 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.
LAPACK version 3.0 15 June 2000 CGGEV(l) 
