ctgevc()

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

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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 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).
!> 

Parameters

[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. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.