CTGEVC(l) ) CTGEVC(l)NAME
CTGEVC - compute some or all of the right and/or left generalized
eigenvectors of a pair of complex upper triangular matrices (A,B)
SYNOPSIS
SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL,
VR, LDVR, MM, M, WORK, RWORK, INFO )
CHARACTER HOWMNY, SIDE
INTEGER INFO, LDA, LDB, LDVL, LDVR, M, MM, N
LOGICAL SELECT( * )
REAL RWORK( * )
COMPLEX A( LDA, * ), B( LDB, * ), VL( LDVL, * ), VR( LDVR, *
), WORK( * )
PURPOSE
CTGEVC computes some or all of the right and/or left generalized eigen‐
vectors of a pair of complex upper triangular matrices (A,B). The
right generalized eigenvector x and the left generalized eigenvector y
of (A,B) corresponding to a generalized eigenvalue w are defined by:
(A - wB) * x = 0 and y**H * (A - wB) = 0
where y**H denotes the conjugate tranpose of y.
If an eigenvalue w is determined by zero diagonal elements of both A
and B, a unit vector is returned as the corresponding eigenvector.
If all eigenvectors are requested, the routine may either return the
matrices X and/or Y of right or left eigenvectors of (A,B), or the
products Z*X and/or Q*Y, where Z and Q are input unitary matrices. If
(A,B) was obtained from the generalized Schur factorization of an orig‐
inal pair of matrices
(A0,B0) = (Q*A*Z**H,Q*B*Z**H),
then Z*X and Q*Y are the matrices of right or left eigenvectors of A.
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, and back‐
transform them using the input matrices supplied 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. If HOWMNY='A' or 'B', SELECT is not referenced. To
select the eigenvector corresponding to the j-th eigenvalue,
SELECT(j) must be set to .TRUE..
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input) COMPLEX array, dimension (LDA,N)
The upper triangular matrix A.
LDA (input) INTEGER
The leading dimension of array A. LDA >= max(1,N).
B (input) COMPLEX array, dimension (LDB,N)
The upper triangular matrix B. B must have real diagonal ele‐
ments.
LDB (input) INTEGER
The leading dimension of array B. LDB >= 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 (A,B); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY =
'S', the left eigenvectors of (A,B) specified by SELECT, stored
consecutively in the columns of VL, in the same order as their
eigenvalues. If SIDE = 'R', VL is not referenced.
LDVL (input) INTEGER
The leading dimension of array VL. LDVL >= max(1,N) if SIDE =
'L' or 'B'; LDVL >= 1 otherwise.
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 (A,B); if HOWMNY = 'B', the matrix Z*X; if HOWMNY =
'S', the right eigenvectors of (A,B) specified by SELECT,
stored consecutively in the columns of VR, in the same order as
their eigenvalues. If SIDE = 'L', VR is not referenced.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= max(1,N) if
SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
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 version 3.0 15 June 2000 CTGEVC(l)
