claqr1()

subroutine claqr1	(	integer	n,
		complex, dimension( ldh, * )	h,
		integer	ldh,
		complex	s1,
		complex	s2,
		complex, dimension( * )	v
	)

CLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

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Purpose:

      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.

Parameters

[in]	N	N is INTEGER Order of the matrix H. N must be either 2 or 3.
[in]	H	H is COMPLEX array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*).
[in]	LDH	LDH is INTEGER The leading dimension of H as declared in the calling procedure. LDH >= N
[in]	S1	S1 is COMPLEX
[in]	S2	S2 is COMPLEX S1 and S2 are the shifts defining K in (*) above.
[out]	V	V is COMPLEX array, 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.

Contributors:

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line 106 of file claqr1.f.

*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      COMPLEX            S1, S2
      INTEGER            LDH, N
*     ..
*     .. Array Arguments ..
      COMPLEX            H( LDH, * ), V( * )
*     ..
*
*  ================================================================
*
*     .. Parameters ..
      COMPLEX            ZERO
      parameter( zero = ( 0.0e0, 0.0e0 ) )
      REAL               RZERO
      parameter( rzero = 0.0e0 )
*     ..
*     .. Local Scalars ..
      COMPLEX            CDUM, H21S, H31S
      REAL               S
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, aimag, real
*     ..
*     .. Statement Functions ..
      REAL               CABS1
*     ..
*     .. Statement Function definitions ..
      cabs1( cdum ) = abs( real( cdum ) ) + abs( aimag( cdum ) )
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( n.NE.2 .AND. n.NE.3 ) THEN
         RETURN
      END IF
*
      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

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