NAME

       slaqr1.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slaqr1 (N, H, LDH, SR1, SI1, SR2, SI2, V)
           SLAQR1 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 slaqr1 (integerN, real, dimension( ldh, * )H, integerLDH, realSR1, realSI1, realSR2, realSI2,
       real, dimension( * )V)
       SLAQR1 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, SLAQR1 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 REAL 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 REAL

           SI1

                     SI1 is REAL

           SR2

                     SR2 is REAL

           SI2

                     SI2 is REAL
                         The shifts in (*).

           V

                     V is REAL 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 slaqr1.f.

Author

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2                                    Wed Feb 26 2014                                     slaqr1.f(3)