--- rpl/lapack/lapack/zlaqr1.f 2010/12/21 13:53:51 1.7 +++ rpl/lapack/lapack/zlaqr1.f 2011/11/21 20:43:16 1.8 @@ -1,8 +1,116 @@ +*> \brief \b ZLAQR1 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLAQR1 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, V ) +* +* .. Scalar Arguments .. +* COMPLEX*16 S1, S2 +* INTEGER LDH, N +* .. +* .. Array Arguments .. +* COMPLEX*16 H( LDH, * ), V( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a +*> scalar multiple of the first column of the product +*> +*> (*) K = (H - s1*I)*(H - s2*I) +*> +*> scaling to avoid overflows and most underflows. +*> +*> 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 COMPLEX*16 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] S1 +*> \verbatim +*> S1 is COMPLEX*16 +*> \endverbatim +*> +*> \param[in] S2 +*> \verbatim +*> S2 is COMPLEX*16 +*> +*> S1 and S2 are the shifts defining K in (*) above. +*> \endverbatim +*> +*> \param[out] V +*> \verbatim +*> V is COMPLEX*16 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 complex16OTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Karen Braman and Ralph Byers, Department of Mathematics, +*> University of Kansas, USA +*> +* ===================================================================== SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, 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 .. COMPLEX*16 S1, S2 @@ -12,40 +120,7 @@ COMPLEX*16 H( LDH, * ), V( * ) * .. * -* Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a -* scalar multiple of the first column of the product -* -* (*) K = (H - s1*I)*(H - s2*I) -* -* scaling to avoid overflows and most underflows. -* -* 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) COMPLEX*16 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 -* -* S1 (input) COMPLEX*16 -* S2 S1 and S2 are the shifts defining K in (*) above. -* -* V (output) COMPLEX*16 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 .. COMPLEX*16 ZERO