zlahqr()

subroutine zlahqr	(	logical	wantt,
		logical	wantz,
		integer	n,
		integer	ilo,
		integer	ihi,
		complex*16, dimension( ldh, * )	h,
		integer	ldh,
		complex*16, dimension( * )	w,
		integer	iloz,
		integer	ihiz,
		complex*16, dimension( ldz, * )	z,
		integer	ldz,
		integer	info )

ZLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.

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Purpose:

!>
!>    ZLAHQR is an auxiliary routine called by CHSEQR to update the
!>    eigenvalues and Schur decomposition already computed by CHSEQR, by
!>    dealing with the Hessenberg submatrix in rows and columns ILO to
!>    IHI.
!> 

Parameters

[in]	WANTT	!> WANTT is LOGICAL !> = .TRUE. : the full Schur form T is required; !> = .FALSE.: only eigenvalues are required. !>
[in]	WANTZ	!> WANTZ is LOGICAL !> = .TRUE. : the matrix of Schur vectors Z is required; !> = .FALSE.: Schur vectors are not required. !>
[in]	N	!> N is INTEGER !> The order of the matrix H. N >= 0. !>
[in]	ILO	!> ILO is INTEGER !>
[in]	IHI	!> IHI is INTEGER !> It is assumed that H is already upper triangular in rows and !> columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1). !> ZLAHQR works primarily with the Hessenberg submatrix in rows !> and columns ILO to IHI, but applies transformations to all of !> H if WANTT is .TRUE.. !> 1 <= ILO <= max(1,IHI); IHI <= N. !>
[in,out]	H	!> H is COMPLEX*16 array, dimension (LDH,N) !> On entry, the upper Hessenberg matrix H. !> On exit, if INFO is zero and if WANTT is .TRUE., then H !> is upper triangular in rows and columns ILO:IHI. If INFO !> is zero and if WANTT is .FALSE., then the contents of H !> are unspecified on exit. The output state of H in case !> INF is positive is below under the description of INFO. !>
[in]	LDH	!> LDH is INTEGER !> The leading dimension of the array H. LDH >= max(1,N). !>
[out]	W	!> W is COMPLEX*16 array, dimension (N) !> The computed eigenvalues ILO to IHI are stored in the !> corresponding elements of W. If WANTT is .TRUE., the !> eigenvalues are stored in the same order as on the diagonal !> of the Schur form returned in H, with W(i) = H(i,i). !>
[in]	ILOZ	!> ILOZ is INTEGER !>
[in]	IHIZ	!> IHIZ is INTEGER !> Specify the rows of Z to which transformations must be !> applied if WANTZ is .TRUE.. !> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N. !>
[in,out]	Z	!> Z is COMPLEX*16 array, dimension (LDZ,N) !> If WANTZ is .TRUE., on entry Z must contain the current !> matrix Z of transformations accumulated by CHSEQR, and on !> exit Z has been updated; transformations are applied only to !> the submatrix Z(ILOZ:IHIZ,ILO:IHI). !> If WANTZ is .FALSE., Z is not referenced. !>
[in]	LDZ	!> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= max(1,N). !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = i, ZLAHQR failed to compute all the !> eigenvalues ILO to IHI in a total of 30 iterations !> per eigenvalue; elements i+1:ihi of W contain !> those eigenvalues which have been successfully !> computed. !> !> If INFO > 0 and WANTT is .FALSE., then on exit, !> the remaining unconverged eigenvalues are the !> eigenvalues of the upper Hessenberg matrix !> rows and columns ILO through INFO of the final, !> output value of H. !> !> If INFO > 0 and WANTT is .TRUE., then on exit !> (*) (initial value of H)*U = U*(final value of H) !> where U is an orthogonal matrix. The final !> value of H is upper Hessenberg and triangular in !> rows and columns INFO+1 through IHI. !> !> If INFO > 0 and WANTZ is .TRUE., then on exit !> (final value of Z) = (initial value of Z)*U !> where U is the orthogonal matrix in (*) !> (regardless of the value of WANTT.) !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

!>
!>     02-96 Based on modifications by
!>     David Day, Sandia National Laboratory, USA
!>
!>     12-04 Further modifications by
!>     Ralph Byers, University of Kansas, USA
!>     This is a modified version of ZLAHQR from LAPACK version 3.0.
!>     It is (1) more robust against overflow and underflow and
!>     (2) adopts the more conservative Ahues & Tisseur stopping
!>     criterion (LAWN 122, 1997).
!>