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 (integer N, real, dimension( ldh, * ) H, integer LDH, real SR1, real SI1,
       real SR2, real SI2, 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

Author

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