```      SUBROUTINE ZLAQR1( 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*16         S1, S2
INTEGER            LDH, N
*     ..
*     .. Array Arguments ..
COMPLEX*16         H( LDH, * ), V( * )
*     ..
*
*       Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 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*16 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*16
*       S2     S1 and S2 are the shifts defining K in (*) above.
*
*       V      (output) COMPLEX*16 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*16         ZERO
PARAMETER          ( ZERO = ( 0.0d0, 0.0d0 ) )
DOUBLE PRECISION   RZERO
PARAMETER          ( RZERO = 0.0d0 )
*     ..
*     .. Local Scalars ..
COMPLEX*16         CDUM
DOUBLE PRECISION   H21S, H31S, S
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, DBLE, DIMAG
*     ..
*     .. Statement Functions ..
DOUBLE PRECISION   CABS1
*     ..
*     .. Statement Function definitions ..
CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( 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

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