ESMF_DLAQR1 Subroutine

subroutine ESMF_DLAQR1(N, H, LDH, SR1, SI1, SR2, SI2, V)

\brief \b ESMF_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. \htmlonly Download ESMF_DLAQR1 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

 Given a 2-by-2 or 3-by-3 matrix H, ESMF_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 \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, 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, dimension (N) A scalar multiple of the first column of the matrix K in (*). \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date June 2017 \ingroup doubleOTHERauxiliary \par Contributors:

  Karen Braman and Ralph Byers, Department of Mathematics,
  University of Kansas, USA

Arguments