DLAQR1(3)      LAPACK routine of NEC Numeric Library Collection      DLAQR1(3)



NAME
       DLAQR1

SYNOPSIS
       SUBROUTINE DLAQR1 (N, H, LDH, SR1, SI1, SR2, SI2, V)



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.




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

           H         (input)
                     H is DOUBLE PRECISION 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 DOUBLE PRECISION

           SI1       (input)
                     SI1 is DOUBLE PRECISION

           SR2       (input)
                     SR2 is DOUBLE PRECISION

           SI2       (input)
                     SI2 is DOUBLE PRECISION
                         The shifts in (*).

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



LAPACK routine                  31 October 2017                      DLAQR1(3)