CTGEVC
November 2006
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
factorization 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)
corresponding 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
eigenvectors 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
factorization of a matrix pair (A,B), then Z*X and Q*Y
are the matrices of right and left eigenvectors of (A,B).
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
factorization 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)
corresponding 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
eigenvectors 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
factorization 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, backtransformed 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
computed. 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
factorization, 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
factorization, as computed by CHGEQZ. P must have real diagonal elements. |
| 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
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 contains: if HOWMNY = 'A', the matrix Y of left eigenvectors 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
contain 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 eigenvectors 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. |