dlaqr1.f

          SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          DOUBLE PRECISION   SI1, SI2, SR1, SR2
          INTEGER            LDH, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   H( LDH, * ), V( * )
    *     ..
    *
    *       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.
    *
    *
    *       N      (input) integer
    *              Order of the matrix H. N must be either 2 or 3.
    *
    *       H      (input) DOUBLE PRECISION array of dimension (LDH,N)
    *              The 2-by-2 or 3-by-3 matrix H in (*).
    *
    *       LDH    (input) integer
    *              The leading dimension of H as declared in
    *              the calling procedure.  LDH.GE.N
    *
    *       SR1    (input) DOUBLE PRECISION
    *       SI1    The shifts in (*).
    *       SR2
    *       SI2
    *
    *       V      (output) DOUBLE PRECISION array of dimension N
    *              A scalar multiple of the first column of the
    *              matrix K in (*).
    *
    *     ================================================================
    *     Based on contributions by
    *        Karen Braman and Ralph Byers, Department of Mathematics,
    *        University of Kansas, USA
    *
    *     ================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO
          PARAMETER          ( ZERO = 0.0d0 )
    *     ..
    *     .. Local Scalars ..
          DOUBLE PRECISION   H21S, H31S, S
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS
    *     ..
    *     .. Executable Statements ..
          IF( N.EQ.2 ) THEN
             S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) )
             IF( S.EQ.ZERO ) THEN
                V( 1 ) = ZERO
                V( 2 ) = ZERO
             ELSE
                H21S = H( 2, 1 ) / S
                V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-SR1 )*
         $               ( ( H( 1, 1 )-SR2 ) / S ) - SI1*( SI2 / S )
                V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 )
             END IF
          ELSE
             S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) ) +
         $       ABS( H( 3, 1 ) )
             IF( S.EQ.ZERO ) THEN
                V( 1 ) = ZERO
                V( 2 ) = ZERO
                V( 3 ) = ZERO
             ELSE
                H21S = H( 2, 1 ) / S
                H31S = H( 3, 1 ) / S
                V( 1 ) = ( H( 1, 1 )-SR1 )*( ( H( 1, 1 )-SR2 ) / S ) -
         $               SI1*( SI2 / S ) + H( 1, 2 )*H21S + H( 1, 3 )*H31S
                V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 ) +
         $               H( 2, 3 )*H31S
                V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-SR1-SR2 ) +
         $               H21S*H( 3, 2 )
             END IF
          END IF
          END