
ZGEEV(l) ) ZGEEV(l)
NAME
ZGEEV  compute for an NbyN complex nonsymmetric matrix A, the eigenvalues and, option
ally, the left and/or right eigenvectors
SYNOPSIS
SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO
)
CHARACTER JOBVL, JOBVR
INTEGER INFO, LDA, LDVL, LDVR, LWORK, N
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), W( * ), WORK( * )
PURPOSE
ZGEEV computes for an NbyN complex nonsymmetric matrix A, the eigenvalues and, option
ally, the left and/or right eigenvectors. The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest
component real.
ARGUMENTS
JOBVL (input) CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of are computed.
JOBVR (input) CHARACTER*1
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the NbyN matrix A. On exit, A has been overwritten.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues.
VL (output) COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = 'V', the left eigenvectors u(j) are stored one after another in the
columns of VL, in the same order as their eigenvalues. If JOBVL = 'N', VL is not
referenced. u(j) = VL(:,j), the jth column of VL.
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N.
VR (output) COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = 'V', the right eigenvectors v(j) are stored one after another in the
columns of VR, in the same order as their eigenvalues. If JOBVR = 'N', VR is not
referenced. v(j) = VR(:,j), the jth column of VR.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1; if JOBVR = 'V', LDVR >= N.
WORK (workspace/output) COMPLEX*16 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) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value.
> 0: if INFO = i, the QR algorithm failed to compute all the eigenvalues, and no
eigenvectors have been computed; elements and i+1:N of W contain eigenvalues which
have converged.
LAPACK version 3.0 15 June 2000 ZGEEV(l) 
