dlaqr1()

subroutine dlaqr1	(	integer	n,
		double precision, dimension( ldh, * )	h,
		integer	ldh,
		double precision	sr1,
		double precision	si1,
		double precision	sr2,
		double precision	si2,
		double precision, dimension( * )	v )

DLAQR1 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, DLAQR1 sets v to a
!>      scalar multiple of the first column of the product
!>
!>      (*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
!>
!>      scaling to avoid overflows and most underflows. It
!>      is assumed that either
!>
!>              1) sr1 = sr2 and si1 = -si2
!>          or
!>              2) si1 = si2 = 0.
!>
!>      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 DOUBLE PRECISION 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]	SR1	!> SR1 is DOUBLE PRECISION !>
[in]	SI1	!> SI1 is DOUBLE PRECISION !>
[in]	SR2	!> SR2 is DOUBLE PRECISION !>
[in]	SI2	!> SI2 is DOUBLE PRECISION !> The shifts in (*). !>
[out]	V	!> V is DOUBLE PRECISION 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