Add graph references
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Abdelrahman Said
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/* -- translated by f2c (version 20240504).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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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 a
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nd specified shifts.
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=========== DOCUMENTATION ===========
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Online html documentation available at
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http://www.netlib.org/lapack/explore-html/
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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.
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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.
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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.
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f">
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> [TXT]</a>
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> \endhtmlonly
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Definition:
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===========
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SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
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DOUBLE PRECISION SI1, SI2, SR1, SR2
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INTEGER LDH, N
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DOUBLE PRECISION H( LDH, * ), V( * )
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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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Arguments:
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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 of 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.GE.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 of 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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Authors:
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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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> \date September 2012
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> \ingroup doubleOTHERauxiliary
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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 */ int igraphdlaqr1_(integer *n, doublereal *h__, integer *ldh,
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doublereal *sr1, doublereal *si1, doublereal *sr2, doublereal *si2,
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doublereal *v)
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{
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/* System generated locals */
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integer h_dim1, h_offset;
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doublereal d__1, d__2, d__3;
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/* Local variables */
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doublereal s, h21s, h31s;
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/* -- LAPACK auxiliary routine (version 3.4.2) --
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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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September 2012
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================================================================
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Parameter adjustments */
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h_dim1 = *ldh;
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h_offset = 1 + h_dim1;
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h__ -= h_offset;
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--v;
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/* Function Body */
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if (*n == 2) {
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s = (d__1 = h__[h_dim1 + 1] - *sr2, abs(d__1)) + abs(*si2) + (d__2 =
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h__[h_dim1 + 2], abs(d__2));
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if (s == 0.) {
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v[1] = 0.;
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v[2] = 0.;
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} else {
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h21s = h__[h_dim1 + 2] / s;
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v[1] = h21s * h__[(h_dim1 << 1) + 1] + (h__[h_dim1 + 1] - *sr1) *
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((h__[h_dim1 + 1] - *sr2) / s) - *si1 * (*si2 / s);
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v[2] = h21s * (h__[h_dim1 + 1] + h__[(h_dim1 << 1) + 2] - *sr1 - *
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sr2);
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}
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} else {
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s = (d__1 = h__[h_dim1 + 1] - *sr2, abs(d__1)) + abs(*si2) + (d__2 =
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h__[h_dim1 + 2], abs(d__2)) + (d__3 = h__[h_dim1 + 3], abs(
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d__3));
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if (s == 0.) {
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v[1] = 0.;
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v[2] = 0.;
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v[3] = 0.;
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} else {
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h21s = h__[h_dim1 + 2] / s;
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h31s = h__[h_dim1 + 3] / s;
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v[1] = (h__[h_dim1 + 1] - *sr1) * ((h__[h_dim1 + 1] - *sr2) / s)
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- *si1 * (*si2 / s) + h__[(h_dim1 << 1) + 1] * h21s + h__[
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h_dim1 * 3 + 1] * h31s;
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v[2] = h21s * (h__[h_dim1 + 1] + h__[(h_dim1 << 1) + 2] - *sr1 - *
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sr2) + h__[h_dim1 * 3 + 2] * h31s;
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v[3] = h31s * (h__[h_dim1 + 1] + h__[h_dim1 * 3 + 3] - *sr1 - *
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sr2) + h21s * h__[(h_dim1 << 1) + 3];
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}
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}
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return 0;
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} /* igraphdlaqr1_ */
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