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184 lines
4.9 KiB
184 lines
4.9 KiB
2 years ago
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*> \brief \b DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DLAQR1 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr1.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr1.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr1.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION SI1, SI2, SR1, SR2
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* INTEGER LDH, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION H( LDH, * ), V( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a
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*> scalar multiple of the first column of the product
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*>
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*> (*) K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
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*>
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*> scaling to avoid overflows and most underflows. It
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*> is assumed that either
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*>
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*> 1) sr1 = sr2 and si1 = -si2
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*> or
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*> 2) si1 = si2 = 0.
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*>
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*> This is useful for starting double implicit shift bulges
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*> in the QR algorithm.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> Order of the matrix H. N must be either 2 or 3.
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*> \endverbatim
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*>
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*> \param[in] H
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*> \verbatim
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*> H is DOUBLE PRECISION array, dimension (LDH,N)
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*> The 2-by-2 or 3-by-3 matrix H in (*).
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*> \endverbatim
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*>
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*> \param[in] LDH
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*> \verbatim
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*> LDH is INTEGER
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*> The leading dimension of H as declared in
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*> the calling procedure. LDH >= N
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*> \endverbatim
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*>
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*> \param[in] SR1
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*> \verbatim
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*> SR1 is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[in] SI1
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*> \verbatim
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*> SI1 is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[in] SR2
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*> \verbatim
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*> SR2 is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[in] SI2
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*> \verbatim
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*> SI2 is DOUBLE PRECISION
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*> The shifts in (*).
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*> \endverbatim
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*>
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*> \param[out] V
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*> \verbatim
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*> V is DOUBLE PRECISION array, dimension (N)
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*> A scalar multiple of the first column of the
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*> matrix K in (*).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup doubleOTHERauxiliary
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*
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*> \par Contributors:
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* ==================
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*>
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*> Karen Braman and Ralph Byers, Department of Mathematics,
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*> University of Kansas, USA
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*>
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* =====================================================================
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SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
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*
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* -- LAPACK auxiliary routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION SI1, SI2, SR1, SR2
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INTEGER LDH, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION H( LDH, * ), V( * )
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* ..
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*
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* ================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0d0 )
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* ..
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* .. Local Scalars ..
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DOUBLE PRECISION H21S, H31S, S
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( N.NE.2 .AND. N.NE.3 ) THEN
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RETURN
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END IF
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*
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IF( N.EQ.2 ) THEN
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S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) )
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IF( S.EQ.ZERO ) THEN
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V( 1 ) = ZERO
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V( 2 ) = ZERO
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ELSE
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H21S = H( 2, 1 ) / S
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V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-SR1 )*
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$ ( ( H( 1, 1 )-SR2 ) / S ) - SI1*( SI2 / S )
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V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 )
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END IF
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ELSE
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S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) ) +
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$ ABS( H( 3, 1 ) )
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IF( S.EQ.ZERO ) THEN
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V( 1 ) = ZERO
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V( 2 ) = ZERO
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V( 3 ) = ZERO
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ELSE
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H21S = H( 2, 1 ) / S
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H31S = H( 3, 1 ) / S
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V( 1 ) = ( H( 1, 1 )-SR1 )*( ( H( 1, 1 )-SR2 ) / S ) -
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$ SI1*( SI2 / S ) + H( 1, 2 )*H21S + H( 1, 3 )*H31S
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V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 ) +
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$ H( 2, 3 )*H31S
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V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-SR1-SR2 ) +
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$ H21S*H( 3, 2 )
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END IF
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END IF
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END
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