zhsein()

subroutine zhsein	(	character	side,
		character	eigsrc,
		character	initv,
		logical, dimension( * )	select,
		integer	n,
		complex*16, dimension( ldh, * )	h,
		integer	ldh,
		complex*16, dimension( * )	w,
		complex*16, dimension( ldvl, * )	vl,
		integer	ldvl,
		complex*16, dimension( ldvr, * )	vr,
		integer	ldvr,
		integer	mm,
		integer	m,
		complex*16, dimension( * )	work,
		double precision, dimension( * )	rwork,
		integer, dimension( * )	ifaill,
		integer, dimension( * )	ifailr,
		integer	info )

ZHSEIN

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Purpose:

!>
!> ZHSEIN uses inverse iteration to find specified right and/or left
!> eigenvectors of a complex upper Hessenberg matrix H.
!>
!> The right eigenvector x and the left eigenvector y of the matrix H
!> corresponding to an eigenvalue w are defined by:
!>
!>              H * x = w * x,     y**h * H = w * y**h
!>
!> where y**h denotes the conjugate transpose of the vector y.
!> 

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]	EIGSRC	!> EIGSRC is CHARACTER*1 !> Specifies the source of eigenvalues supplied in W: !> = 'Q': the eigenvalues were found using ZHSEQR; thus, if !> H has zero subdiagonal elements, and so is !> block-triangular, then the j-th eigenvalue can be !> assumed to be an eigenvalue of the block containing !> the j-th row/column. This property allows ZHSEIN to !> perform inverse iteration on just one diagonal block. !> = 'N': no assumptions are made on the correspondence !> between eigenvalues and diagonal blocks. In this !> case, ZHSEIN must always perform inverse iteration !> using the whole matrix H. !>
[in]	INITV	!> INITV is CHARACTER*1 !> = 'N': no initial vectors are supplied; !> = 'U': user-supplied initial vectors are stored in the arrays !> VL and/or VR. !>
[in]	SELECT	!> SELECT is LOGICAL array, dimension (N) !> Specifies the eigenvectors to be computed. To select the !> eigenvector corresponding to the eigenvalue W(j), !> SELECT(j) must be set to .TRUE.. !>
[in]	N	!> N is INTEGER !> The order of the matrix H. N >= 0. !>
[in]	H	!> H is COMPLEX*16 array, dimension (LDH,N) !> The upper Hessenberg matrix H. !> If a NaN is detected in H, the routine will return with INFO=-6. !>
[in]	LDH	!> LDH is INTEGER !> The leading dimension of the array H. LDH >= max(1,N). !>
[in,out]	W	!> W is COMPLEX*16 array, dimension (N) !> On entry, the eigenvalues of H. !> On exit, the real parts of W may have been altered since !> close eigenvalues are perturbed slightly in searching for !> independent eigenvectors. !>
[in,out]	VL	!> VL is COMPLEX*16 array, dimension (LDVL,MM) !> On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must !> contain starting vectors for the inverse iteration for the !> left eigenvectors; the starting vector for each eigenvector !> must be in the same column in which the eigenvector will be !> stored. !> On exit, if SIDE = 'L' or 'B', the left eigenvectors !> specified by SELECT will be stored consecutively in the !> columns of VL, in the same order as their eigenvalues. !> If SIDE = 'R', VL is not referenced. !>
[in]	LDVL	!> LDVL is INTEGER !> The leading dimension of the array VL. !> LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise. !>
[in,out]	VR	!> VR is COMPLEX*16 array, dimension (LDVR,MM) !> On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must !> contain starting vectors for the inverse iteration for the !> right eigenvectors; the starting vector for each eigenvector !> must be in the same column in which the eigenvector will be !> stored. !> On exit, if SIDE = 'R' or 'B', the right eigenvectors !> specified by SELECT will be stored consecutively in the !> columns of VR, in the same order as their eigenvalues. !> If SIDE = 'L', VR is not referenced. !>
[in]	LDVR	!> LDVR is INTEGER !> The leading dimension of the array VR. !> LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise. !>
[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 required to !> store the eigenvectors (= the number of .TRUE. elements in !> SELECT). !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension (N*N) !>
[out]	RWORK	!> RWORK is DOUBLE PRECISION array, dimension (N) !>
[out]	IFAILL	!> IFAILL is INTEGER array, dimension (MM) !> If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left !> eigenvector in the i-th column of VL (corresponding to the !> eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the !> eigenvector converged satisfactorily. !> If SIDE = 'R', IFAILL is not referenced. !>
[out]	IFAILR	!> IFAILR is INTEGER array, dimension (MM) !> If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right !> eigenvector in the i-th column of VR (corresponding to the !> eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the !> eigenvector converged satisfactorily. !> If SIDE = 'L', IFAILR is not referenced. !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, i is the number of eigenvectors which !> failed to converge; see IFAILL and IFAILR for further !> details. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Each eigenvector is normalized so that the element of largest
!>  magnitude has magnitude 1; here the magnitude of a complex number
!>  (x,y) is taken to be |x|+|y|.
!>