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NAME
CTGEVC - compute selected left and/or right generalized
eigenvectors of a pair of complex upper triangular matrices
(A,B)
SYNOPSIS
SUBROUTINE CTGEVC( JOB, SIDE, SELECT, N, A, LDA, B, LDB, VL,
LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO
)
CHARACTER JOB, SIDE
INTEGER INFO, LDA, LDB, LDVL, LDVR, M, MM, N
LOGICAL SELECT( * )
REAL RWORK( N, * )
COMPLEX A( LDA, * ), B( LDB, * ), VL( LDVL, * ),
VR( LDVR, * ), WORK( N, * )
PURPOSE
CTGEVC computes selected left and/or right generalized
eigenvectors of a pair of complex upper triangular matrices
(A,B). The j-th generalized left and right eigenvectors are
y and x, resp., such that:
H
y (A - wB) = 0 (A - wB)x = 0
H
Note: the left eigenvector is sometimes defined as the row
vector y
but CTGEVC computes the column vector y.
ARGUMENTS
JOB (input) CHARACTER*1
= 'A': compute All (left/right/left+right) general-
ized eigenvectors of (A,B); = 'S': compute Selected
(left/right/left+right) generalized eigenvectors of
(A,B) -- see the description of the argument SELECT;
= 'B' or 'T': compute all (left/right/left+right)
generalized eigenvectors of (A,B), and Back
Transform them using the initial contents of VL/VR
-- see the descriptions of the arguments VL and VR.
SIDE (input) CHARACTER*1
Specifies for which side eigenvectors are to be com-
puted:
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
SELECT (input) LOGICAL array, dimension (N)
If JOB='S', then SELECT specifies the (generalized)
eigenvectors to be computed. To get the eigenvector
corresponding to the j-th eigenvalue, set SELECT(j)
to .TRUE.. If JOB='A', 'B', or 'T', SELECT is not
referenced, and all eigenvectors are selected.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input) COMPLEX array, dimension (LDA,N)
One of the pair of matrices whose generalized eigen-
vectors are to be computed. It must be upper tri-
angular.
LDA (input) INTEGER
The leading dimension of array A. LDA >= max(1, N).
B (input) COMPLEX array, dimension (LDB,N)
The other of the pair of matrices whose generalized
eigenvectors are to be computed. It must be upper
triangular with real diagonal elements.
LDB (input) INTEGER
The leading dimension of array B. LDB >= max(1, N).
VL (input/output) COMPLEX array, dimension (LDVL,MM)
The left eigenvectors (column vectors -- see the
note in "Purpose".) If JOB='A', then all left eigen-
vectors of (A,B) will be computed and stored in VL.
If JOB='S', then only the eigenvectors selected by
SELECT will be computed; the first selected eigen-
vector will go in column 1, the second in column 2,
etc. If JOB='B' or 'T', then all left eigenvectors
of (A,B) will be computed and multiplied (on the
left) by the matrix found in VL on entry to CTGEVC.
Usually, this will be the Q matrix computed by
CGGHRD and CHGEQZ, so that on exit, VL will contain
the left eigenvectors of the original matrix pair.
In any case, each eigenvector will be scaled so the
largest component of each vector has abs(real part)
+ abs(imag. part)=1, *unless* A and B both have a
zero in the diagonal entry corresponding to the
eigenvector, in which case the eigenvector will be
zero. If SIDE = 'R', VL is not referenced.
LDVL (input) INTEGER
The leading dimension of array VL. LDVL >= 1; if
SIDE = 'B' or 'L', LDVL >= N.
VR (input/output) COMPLEX array, dimension (LDVR,MM)
The right eigenvectors. If JOB='A', then all right
eigenvectors of (A,B) will be computed and stored in
VR. If JOB='S', then only the eigenvectors selected
by SELECT will be computed; the first selected
eigenvector will go in column 1, the second in
column 2, etc. If JOB='B' or 'T', then all right
eigenvectors of (A,B) will be computed and multi-
plied (on the left) by the matrix found in VR on
entry to CTGEVC. Usually, this will be the Z matrix
computed by CGGHRD and CHGEQZ, so that on exit, VR
will contain the right eigenvectors of the original
matrix pair. In any case, each eigenvector will be
scaled so the largest component of each vector has
abs(real part) + abs(imag. part)=1, *unless* A and
B both have a zero in the diagonal entry correspond-
ing to the eigenvector, in which case the eigenvec-
tor will be zero. If SIDE = 'L', VR is not refer-
enced.
LDVR (input) INTEGER
The leading dimension of array VR. LDVR >= 1; if
SIDE = 'B' or 'R', LDVR >= N.
MM (input) INTEGER
The number of columns in VL and/or VR. If JOB='A',
'B', or 'T', then MM >= N. If JOB='S', then MM must
be at least the number of .TRUE. values in
SELECT(1:N).
M (output) INTEGER
The number of columns in VL and/or VR actually used
to store the eigenvectors.
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.