CGEEV - compute for an N-by-N complex nonsymmetric matrix
A, the eigenvalues and, optionally, the left and/or right
eigenvectors
SYNOPSIS
SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL,
VR, LDVR, WORK, LWORK, RWORK, INFO )
CHARACTER JOBVL, JOBVR
INTEGER INFO, LDA, LDVL, LDVR, LWORK, N
REAL RWORK( * )
COMPLEX A( LDA, * ), VL( LDVL, * ), VR( LDVR, *
), W( * ), WORK( * )
PURPOSE
CGEEV computes for an N-by-N complex nonsymmetric matrix
A, the eigenvalues and, optionally, 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 array, dimension (LDA,N)
On entry, the N-by-N 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 array, dimension (N)
W contains the computed eigenvalues.
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 j-
th column of VL.
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1;
if JOBVL = 'V', LDVL >= N.
VR (output) COMPLEX 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 j-
th column of VR.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1;
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 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) REAL array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value.
> 0: if INFO = i, the QR algorithm failed to com
pute all the eigenvalues, and no eigenvectors have
been computed; elements and i+1:N of W contain
eigenvalues which have converged.
Man(1) output converted with
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