--- rpl/lapack/lapack/dlaqr1.f 2010/12/21 13:53:31 1.7 +++ rpl/lapack/lapack/dlaqr1.f 2011/11/21 20:42:56 1.8 @@ -1,8 +1,130 @@ +*> \brief \b DLAQR1 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAQR1 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION SI1, SI2, SR1, SR2 +* INTEGER LDH, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION H( LDH, * ), V( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 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 DOUBLE PRECISION array of 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 DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] SI1 +*> \verbatim +*> SI1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] SR2 +*> \verbatim +*> SR2 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] SI2 +*> \verbatim +*> SI2 is DOUBLE PRECISION +*> The shifts in (*). +*> \endverbatim +*> +*> \param[out] V +*> \verbatim +*> V is DOUBLE PRECISION array of 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 November 2011 +* +*> \ingroup doubleOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Karen Braman and Ralph Byers, Department of Mathematics, +*> University of Kansas, USA +*> +* ===================================================================== SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V ) * -* -- LAPACK auxiliary routine (version 3.2) -- -* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. -* November 2006 +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. DOUBLE PRECISION SI1, SI2, SR1, SR2 @@ -12,47 +134,7 @@ DOUBLE PRECISION H( LDH, * ), V( * ) * .. * -* Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 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. -* -* -* N (input) integer -* Order of the matrix H. N must be either 2 or 3. -* -* H (input) DOUBLE PRECISION 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 -* -* SR1 (input) DOUBLE PRECISION -* SI1 The shifts in (*). -* SR2 -* SI2 -* -* V (output) DOUBLE PRECISION 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 .. DOUBLE PRECISION ZERO