claqr1.f

          SUBROUTINE CLAQR1( N, H, LDH, S1, S2, V )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          COMPLEX            S1, S2
          INTEGER            LDH, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX            H( LDH, * ), V( * )
    *     ..
    *
    *       Given a 2-by-2 or 3-by-3 matrix H, CLAQR1 sets v to a
    *       scalar multiple of the first column of the product
    *
    *       (*)  K = (H - s1*I)*(H - s2*I)
    *
    *       scaling to avoid overflows and most underflows.
    *
    *       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) COMPLEX 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
    *
    *       S1     (input) COMPLEX
    *       S2     S1 and S2 are the shifts defining K in (*) above.
    *
    *       V      (output) COMPLEX 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 ..
          COMPLEX            ZERO
          PARAMETER          ( ZERO = ( 0.0e0, 0.0e0 ) )
          REAL               RZERO
          PARAMETER          ( RZERO = 0.0e0 )
    *     ..
    *     .. Local Scalars ..
          COMPLEX            CDUM
          REAL               H21S, H31S, S
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, AIMAG, REAL
    *     ..
    *     .. Statement Functions ..
          REAL               CABS1
    *     ..
    *     .. Statement Function definitions ..
          CABS1( CDUM ) = ABS( REAL( CDUM ) ) + ABS( AIMAG( CDUM ) )
    *     ..
    *     .. Executable Statements ..
          IF( N.EQ.2 ) THEN
             S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) )
             IF( S.EQ.RZERO ) THEN
                V( 1 ) = ZERO
                V( 2 ) = ZERO
             ELSE
                H21S = H( 2, 1 ) / S
                V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-S1 )*
         $               ( ( H( 1, 1 )-S2 ) / S )
                V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 )
             END IF
          ELSE
             S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) ) +
         $       CABS1( 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 )-S1 )*( ( H( 1, 1 )-S2 ) / S ) +
         $               H( 1, 2 )*H21S + H( 1, 3 )*H31S
                V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 ) + H( 2, 3 )*H31S
                V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-S1-S2 ) + H21S*H( 3, 2 )
             END IF
          END IF
          END