CTGEVC - compute some or all of the right and/or left gen
eralized eigenvectors of a pair of complex upper triangu
lar 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 gen
eralized eigenvectors of a pair of complex upper triangu
lar matrices (A,B). The right generalized eigenvector x
and the left generalized eigenvector y of (A,B) corre
sponding 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 corre
sponding eigenvector.
If all eigenvectors are requested, the routine may either
return the matrices X and/or Y of right or left eigenvec
tors 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 original 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 eigen
vectors of A.
ARGUMENTS
SIDE (input) CHARACTER*1
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
= 'A': compute all right and/or left eigenvectors;
= 'B': compute all right and/or left eigenvectors,
and backtransform 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 computed. If HOWMNY='A' or 'B', SELECT is
not referenced. To select the eigenvector corre
sponding 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 elements.
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 contain 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 con
tains: if HOWMNY = 'A', the matrix Y of left
eigenvectors 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 other
wise.
VR (input/output) COMPLEX array, dimension (LDVR,MM)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B',
VR must contain an N-by-N matrix Q (usually the
unitary matrix Z of right Schur vectors returned
contains: if HOWMNY = 'A', the matrix X of right
eigenvectors 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 other
wise.
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 ille
gal value.
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