zlaqr1()

subroutine zlaqr1	(	integer	n,
		complex*16, dimension( ldh, * )	h,
		integer	ldh,
		complex*16	s1,
		complex*16	s2,
		complex*16, dimension( * )	v )

ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

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Purpose:

!>
!>      Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a
!>      scalar multiple of the first column of the product
!>
!>      (*)  K = (H - s1*I)*(H - s2*I)
!>
!>      scaling to avoid overflows and most underflows.
!>
!>      This is useful for starting double implicit shift bulges
!>      in the QR algorithm.
!> 

Parameters

[in]	N	!> N is INTEGER !> Order of the matrix H. N must be either 2 or 3. !>
[in]	H	!> H is COMPLEX*16 array, dimension (LDH,N) !> The 2-by-2 or 3-by-3 matrix H in (*). !>
[in]	LDH	!> LDH is INTEGER !> The leading dimension of H as declared in !> the calling procedure. LDH >= N !>
[in]	S1	!> S1 is COMPLEX*16 !>
[in]	S2	!> S2 is COMPLEX*16 !> !> S1 and S2 are the shifts defining K in (*) above. !>
[out]	V	!> V is COMPLEX*16 array, dimension (N) !> A scalar multiple of the first column of the !> matrix K in (*). !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA