![]() |
LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
|
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 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).
[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 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'. |
[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 221 of file ctgevc.f.