dlaqr1 (3)

Functions/Subroutines

subroutine dlaqr1 (N, H, LDH, SR1, SI1, SR2, SI2, 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.

subroutine dlaqr1 (integerN, double precision, dimension( ldh, * )H, integerLDH, double precisionSR1, double precisionSI1, double precisionSR2, double precisionSI2, 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.

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:

N

          N is integer
              Order of the matrix H. N must be either 2 or 3.

H

          H is DOUBLE PRECISION array of dimension (LDH,N)
              The 2-by-2 or 3-by-3 matrix H in (*).

LDH

          LDH is integer
              The leading dimension of H as declared in
              the calling procedure.  LDH.GE.N

SR1

          SR1 is DOUBLE PRECISION

SI1

          SI1 is DOUBLE PRECISION

SR2

          SR2 is DOUBLE PRECISION

SI2

          SI2 is DOUBLE PRECISION
              The shifts in (*).

V

          V is DOUBLE PRECISION array of 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.

Date:

September 2012

Contributors:

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

Definition at line 122 of file dlaqr1.f.

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