dlaqr1.f.html
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SUBROUTINE <a name="DLAQR1.1"></a><a href="dlaqr1.f.html#DLAQR1.1">DLAQR1</a>( N, H, LDH, SR1, SI1, SR2, SI2, V )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> DOUBLE PRECISION SI1, SI2, SR1, SR2
INTEGER LDH, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION H( LDH, * ), V( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Given a 2-by-2 or 3-by-3 matrix H, <a name="DLAQR1.15"></a><a href="dlaqr1.f.html#DLAQR1.1">DLAQR1</a> sets v to a
</span><span class="comment">*</span><span class="comment"> scalar multiple of the first column of the product
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> (*) K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> scaling to avoid overflows and most underflows. It
</span><span class="comment">*</span><span class="comment"> is assumed that either
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 1) sr1 = sr2 and si1 = -si2
</span><span class="comment">*</span><span class="comment"> or
</span><span class="comment">*</span><span class="comment"> 2) si1 = si2 = 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> This is useful for starting double implicit shift bulges
</span><span class="comment">*</span><span class="comment"> in the QR algorithm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) integer
</span><span class="comment">*</span><span class="comment"> Order of the matrix H. N must be either 2 or 3.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> H (input) DOUBLE PRECISION array of dimension (LDH,N)
</span><span class="comment">*</span><span class="comment"> The 2-by-2 or 3-by-3 matrix H in (*).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDH (input) integer
</span><span class="comment">*</span><span class="comment"> The leading dimension of H as declared in
</span><span class="comment">*</span><span class="comment"> the calling procedure. LDH.GE.N
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SR1 (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> SI1 The shifts in (*).
</span><span class="comment">*</span><span class="comment"> SR2
</span><span class="comment">*</span><span class="comment"> SI2
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> V (output) DOUBLE PRECISION array of dimension N
</span><span class="comment">*</span><span class="comment"> A scalar multiple of the first column of the
</span><span class="comment">*</span><span class="comment"> matrix K in (*).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ================================================================
</span><span class="comment">*</span><span class="comment"> Based on contributions by
</span><span class="comment">*</span><span class="comment"> Karen Braman and Ralph Byers, Department of Mathematics,
</span><span class="comment">*</span><span class="comment"> University of Kansas, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0d0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> DOUBLE PRECISION H21S, H31S, S
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span> 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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