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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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