NAME

       dlaqr1.f -

SYNOPSIS

   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.

Function/Subroutine Documentation

   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.

Author

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2                                    Wed Feb 26 2014                                     dlaqr1.f(3)