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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine ctgevc | ( | character | side, |
| character | howmny, | ||
| logical, dimension( * ) | select, | ||
| integer | n, | ||
| complex, dimension( lds, * ) | s, | ||
| integer | lds, | ||
| complex, dimension( ldp, * ) | p, | ||
| integer | ldp, | ||
| complex, dimension( ldvl, * ) | vl, | ||
| integer | ldvl, | ||
| complex, dimension( ldvr, * ) | vr, | ||
| integer | ldvr, | ||
| integer | mm, | ||
| integer | m, | ||
| complex, dimension( * ) | work, | ||
| real, dimension( * ) | rwork, | ||
| integer | info | ||
| ) |
CTGEVC
Download CTGEVC + dependencies [TGZ] [ZIP] [TXT]
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 transpose 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). | [in] | SIDE | SIDE is CHARACTER*1
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors. |
| [in] | HOWMNY | HOWMNY is 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. |
| [in] | SELECT | SELECT is 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'. |
| [in] | N | N is INTEGER
The order of the matrices S and P. N >= 0. |
| [in] | S | S is COMPLEX array, dimension (LDS,N)
The upper triangular matrix S from a generalized Schur
factorization, as computed by CHGEQZ. |
| [in] | LDS | LDS is INTEGER
The leading dimension of array S. LDS >= max(1,N). |
| [in] | P | P is 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. |
| [in] | LDP | LDP is INTEGER
The leading dimension of array P. LDP >= max(1,N). |
| [in,out] | VL | VL is 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'. |
| [in] | LDVL | LDVL is INTEGER
The leading dimension of array VL. LDVL >= 1, and if
SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N. |
| [in,out] | VR | VR is COMPLEX array, dimension (LDVR,MM)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
contain an N-by-N matrix Z (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'. |
| [in] | LDVR | LDVR is INTEGER
The leading dimension of the array VR. LDVR >= 1, and if
SIDE = 'R' or 'B', LDVR >= N. |
| [in] | MM | MM is INTEGER
The number of columns in the arrays VL and/or VR. MM >= M. |
| [out] | M | M is 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. |
| [out] | WORK | WORK is COMPLEX array, dimension (2*N) |
| [out] | RWORK | RWORK is REAL array, dimension (2*N) |
| [out] | INFO | INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value. |
Definition at line 217 of file ctgevc.f.
1.9.7