*> \brief \b SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SLAQR1 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V ) * * .. Scalar Arguments .. * REAL SI1, SI2, SR1, SR2 * INTEGER LDH, N * .. * .. Array Arguments .. * REAL H( LDH, * ), V( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Given a 2-by-2 or 3-by-3 matrix H, SLAQR1 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. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> Order of the matrix H. N must be either 2 or 3. *> \endverbatim *> *> \param[in] H *> \verbatim *> H is REAL array, dimension (LDH,N) *> The 2-by-2 or 3-by-3 matrix H in (*). *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> The leading dimension of H as declared in *> the calling procedure. LDH.GE.N *> \endverbatim *> *> \param[in] SR1 *> \verbatim *> SR1 is REAL *> \endverbatim *> *> \param[in] SI1 *> \verbatim *> SI1 is REAL *> \endverbatim *> *> \param[in] SR2 *> \verbatim *> SR2 is REAL *> \endverbatim *> *> \param[in] SI2 *> \verbatim *> SI2 is REAL *> The shifts in (*). *> \endverbatim *> *> \param[out] V *> \verbatim *> V is REAL array, dimension (N) *> A scalar multiple of the first column of the *> matrix K in (*). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup realOTHERauxiliary * *> \par Contributors: * ================== *> *> Karen Braman and Ralph Byers, Department of Mathematics, *> University of Kansas, USA *> * ===================================================================== SUBROUTINE SLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. REAL SI1, SI2, SR1, SR2 INTEGER LDH, N * .. * .. Array Arguments .. REAL H( LDH, * ), V( * ) * .. * * ================================================================ * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0e0 ) * .. * .. Local Scalars .. REAL 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