CTGEVC(1) LAPACK routine (version 3.2) CTGEVC(1)NAME
CTGEVC - computes some or all of the right and/or left eigenvectors of
a pair of complex matrices (S,P), where S and P are upper triangular
SYNOPSIS
SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL,
VR, LDVR, MM, M, WORK, RWORK, INFO )
CHARACTER HOWMNY, SIDE
INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N
LOGICAL SELECT( * )
REAL RWORK( * )
COMPLEX P( LDP, * ), S( LDS, * ), VL( LDVL, * ), VR( LDVR, *
), WORK( * )
PURPOSE
CTGEVC computes some or all of the right and/or left eigenvectors of a
pair of complex matrices (S,P), where S and P are upper triangular.
Matrix pairs of this type are produced by the generalized Schur factor‐
ization of a complex matrix pair (A,B):
A = Q*S*Z**H, B = Q*P*Z**H
as computed by CGGHRD + CHGEQZ.
The right eigenvector x and the left eigenvector y of (S,P) correspond‐
ing to an eigenvalue w are defined by:
S*x = w*P*x, (y**H)*S = w*(y**H)*P,
where y**H denotes the conjugate tranpose of y.
The eigenvalues are not input to this routine, but are computed
directly from the diagonal elements of S and P.
This routine returns the matrices X and/or Y of right and left eigen‐
vectors of (S,P), or the products Z*X and/or Q*Y,
where Z and Q are input matrices.
If Q and Z are the unitary factors from the generalized Schur factor‐
ization of a matrix pair (A,B), then Z*X and Q*Y
are the matrices of right and left eigenvectors of (A,B).
ARGUMENTS
SIDE (input) CHARACTER*1
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
HOWMNY (input) CHARACTER*1
= 'A': compute all right and/or left eigenvectors;
= 'B': compute all right and/or left eigenvectors, backtrans‐
formed by the matrices in VR and/or VL; = 'S': compute selected
right and/or left eigenvectors, specified by the logical array
SELECT.
SELECT (input) LOGICAL array, dimension (N)
If HOWMNY='S', SELECT specifies the eigenvectors to be com‐
puted. The eigenvector corresponding to the j-th eigenvalue is
computed if SELECT(j) = .TRUE.. Not referenced if HOWMNY = 'A'
or 'B'.
N (input) INTEGER
The order of the matrices S and P. N >= 0.
S (input) COMPLEX array, dimension (LDS,N)
The upper triangular matrix S from a generalized Schur factor‐
ization, as computed by CHGEQZ.
LDS (input) INTEGER
The leading dimension of array S. LDS >= max(1,N).
P (input) COMPLEX array, dimension (LDP,N)
The upper triangular matrix P from a generalized Schur factor‐
ization, as computed by CHGEQZ. P must have real diagonal ele‐
ments.
LDP (input) INTEGER
The leading dimension of array P. LDP >= max(1,N).
VL (input/output) COMPLEX array, dimension (LDVL,MM)
On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must con‐
tain an N-by-N matrix Q (usually the unitary matrix Q of left
Schur vectors returned by CHGEQZ). On exit, if SIDE = 'L' or
'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigen‐
vectors of (S,P); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY =
'S', the left eigenvectors of (S,P) specified by SELECT, stored
consecutively in the columns of VL, in the same order as their
eigenvalues. Not referenced if SIDE = 'R'.
LDVL (input) INTEGER
The leading dimension of array VL. LDVL >= 1, and if SIDE =
'L' or 'l' or 'B' or 'b', LDVL >= N.
VR (input/output) COMPLEX array, dimension (LDVR,MM)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must con‐
tain an N-by-N matrix Q (usually the unitary matrix Z of right
Schur vectors returned by CHGEQZ). On exit, if SIDE = 'R' or
'B', VR contains: if HOWMNY = 'A', the matrix X of right eigen‐
vectors of (S,P); if HOWMNY = 'B', the matrix Z*X; if HOWMNY =
'S', the right eigenvectors of (S,P) specified by SELECT,
stored consecutively in the columns of VR, in the same order as
their eigenvalues. Not referenced if SIDE = 'L'.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1, and if SIDE
= 'R' or 'B', LDVR >= N.
MM (input) INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
M (output) INTEGER
The number of columns in the arrays VL and/or VR actually used
to store the eigenvectors. If HOWMNY = 'A' or 'B', M is set to
N. Each selected eigenvector occupies one column.
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
LAPACK routine (version 3.2) November 2008 CTGEVC(1)