SLAQR1(3)      LAPACK routine of NEC Numeric Library Collection      SLAQR1(3)



NAME
       SLAQR1

SYNOPSIS
       SUBROUTINE SLAQR1 (N, H, LDH, SR1, SI1, SR2, SI2, V)



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.




ARGUMENTS
           N         (input)
                     N is integer
                         Order of the matrix H. N must be either 2 or 3.

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

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

           SR1       (input)
                     SR1 is REAL

           SI1       (input)
                     SI1 is REAL

           SR2       (input)
                     SR2 is REAL

           SI2       (input)
                     SI2 is REAL
                         The shifts in (*).

           V         (output)
                     V is REAL array of dimension N
                         A scalar multiple of the first column of the
                         matrix K in (*).



LAPACK routine                  31 October 2017                      SLAQR1(3)