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