claqr1.f.html
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SUBROUTINE <a name="CLAQR1.1"></a><a href="claqr1.f.html#CLAQR1.1">CLAQR1</a>( N, H, LDH, S1, S2, 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> COMPLEX S1, S2
INTEGER LDH, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> COMPLEX 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="CLAQR1.15"></a><a href="claqr1.f.html#CLAQR1.1">CLAQR1</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 - s1*I)*(H - s2*I)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> scaling to avoid overflows and most underflows.
</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) COMPLEX 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"> S1 (input) COMPLEX
</span><span class="comment">*</span><span class="comment"> S2 S1 and S2 are the shifts defining K in (*) above.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> V (output) COMPLEX 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> COMPLEX ZERO
PARAMETER ( ZERO = ( 0.0e0, 0.0e0 ) )
REAL RZERO
PARAMETER ( RZERO = 0.0e0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> COMPLEX CDUM
REAL H21S, H31S, S
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, AIMAG, REAL
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Statement Functions ..
</span> REAL CABS1
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Statement Function definitions ..
</span> CABS1( CDUM ) = ABS( REAL( CDUM ) ) + ABS( AIMAG( CDUM ) )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span> 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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