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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
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