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*/
#include "f2c.h"
/* > \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
nd specified shifts.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
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Definition:
===========
SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
DOUBLE PRECISION SI1, SI2, SR1, SR2
INTEGER LDH, N
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 September 2012
> \ingroup doubleOTHERauxiliary
> \par Contributors:
==================
>
> Karen Braman and Ralph Byers, Department of Mathematics,
> University of Kansas, USA
>
=====================================================================
Subroutine */ int igraphdlaqr1_(integer *n, doublereal *h__, integer *ldh,
doublereal *sr1, doublereal *si1, doublereal *sr2, doublereal *si2,
doublereal *v)
{
/* System generated locals */
integer h_dim1, h_offset;
doublereal d__1, d__2, d__3;
/* Local variables */
doublereal s, h21s, h31s;
/* -- LAPACK auxiliary routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
================================================================
Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
--v;
/* Function Body */
if (*n == 2) {
s = (d__1 = h__[h_dim1 + 1] - *sr2, abs(d__1)) + abs(*si2) + (d__2 =
h__[h_dim1 + 2], abs(d__2));
if (s == 0.) {
v[1] = 0.;
v[2] = 0.;
} else {
h21s = h__[h_dim1 + 2] / s;
v[1] = h21s * h__[(h_dim1 << 1) + 1] + (h__[h_dim1 + 1] - *sr1) *
((h__[h_dim1 + 1] - *sr2) / s) - *si1 * (*si2 / s);
v[2] = h21s * (h__[h_dim1 + 1] + h__[(h_dim1 << 1) + 2] - *sr1 - *
sr2);
}
} else {
s = (d__1 = h__[h_dim1 + 1] - *sr2, abs(d__1)) + abs(*si2) + (d__2 =
h__[h_dim1 + 2], abs(d__2)) + (d__3 = h__[h_dim1 + 3], abs(
d__3));
if (s == 0.) {
v[1] = 0.;
v[2] = 0.;
v[3] = 0.;
} else {
h21s = h__[h_dim1 + 2] / s;
h31s = h__[h_dim1 + 3] / s;
v[1] = (h__[h_dim1 + 1] - *sr1) * ((h__[h_dim1 + 1] - *sr2) / s)
- *si1 * (*si2 / s) + h__[(h_dim1 << 1) + 1] * h21s + h__[
h_dim1 * 3 + 1] * h31s;
v[2] = h21s * (h__[h_dim1 + 1] + h__[(h_dim1 << 1) + 2] - *sr1 - *
sr2) + h__[h_dim1 * 3 + 2] * h31s;
v[3] = h31s * (h__[h_dim1 + 1] + h__[h_dim1 * 3 + 3] - *sr1 - *
sr2) + h21s * h__[(h_dim1 << 1) + 3];
}
}
return 0;
} /* igraphdlaqr1_ */