/* -- translated by f2c (version 20100827).
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*/
#include "f2c.h"
/* > \brief \b DLARFG generates an elementary reflector (Householder matrix).
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
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> \endhtmlonly
Definition:
===========
SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
INTEGER INCX, N
DOUBLE PRECISION ALPHA, TAU
DOUBLE PRECISION X( * )
> \par Purpose:
=============
>
> \verbatim
>
> DLARFG generates a real elementary reflector H of order n, such
> that
>
> H * ( alpha ) = ( beta ), H**T * H = I.
> ( x ) ( 0 )
>
> where alpha and beta are scalars, and x is an (n-1)-element real
> vector. H is represented in the form
>
> H = I - tau * ( 1 ) * ( 1 v**T ) ,
> ( v )
>
> where tau is a real scalar and v is a real (n-1)-element
> vector.
>
> If the elements of x are all zero, then tau = 0 and H is taken to be
> the unit matrix.
>
> Otherwise 1 <= tau <= 2.
> \endverbatim
Arguments:
==========
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the elementary reflector.
> \endverbatim
>
> \param[in,out] ALPHA
> \verbatim
> ALPHA is DOUBLE PRECISION
> On entry, the value alpha.
> On exit, it is overwritten with the value beta.
> \endverbatim
>
> \param[in,out] X
> \verbatim
> X is DOUBLE PRECISION array, dimension
> (1+(N-2)*abs(INCX))
> On entry, the vector x.
> On exit, it is overwritten with the vector v.
> \endverbatim
>
> \param[in] INCX
> \verbatim
> INCX is INTEGER
> The increment between elements of X. INCX > 0.
> \endverbatim
>
> \param[out] TAU
> \verbatim
> TAU is DOUBLE PRECISION
> The value tau.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup doubleOTHERauxiliary
=====================================================================
Subroutine */ int igraphdlarfg_(integer *n, doublereal *alpha, doublereal *x,
integer *incx, doublereal *tau)
{
/* System generated locals */
integer i__1;
doublereal d__1;
/* Builtin functions */
double d_sign(doublereal *, doublereal *);
/* Local variables */
integer j, knt;
doublereal beta;
extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);
extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal xnorm;
extern doublereal igraphdlapy2_(doublereal *, doublereal *), igraphdlamch_(char *);
doublereal safmin, rsafmn;
/* -- 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 */
--x;
/* Function Body */
if (*n <= 1) {
*tau = 0.;
return 0;
}
i__1 = *n - 1;
xnorm = igraphdnrm2_(&i__1, &x[1], incx);
if (xnorm == 0.) {
/* H = I */
*tau = 0.;
} else {
/* general case */
d__1 = igraphdlapy2_(alpha, &xnorm);
beta = -d_sign(&d__1, alpha);
safmin = igraphdlamch_("S") / igraphdlamch_("E");
knt = 0;
if (abs(beta) < safmin) {
/* XNORM, BETA may be inaccurate; scale X and recompute them */
rsafmn = 1. / safmin;
L10:
++knt;
i__1 = *n - 1;
igraphdscal_(&i__1, &rsafmn, &x[1], incx);
beta *= rsafmn;
*alpha *= rsafmn;
if (abs(beta) < safmin) {
goto L10;
}
/* New BETA is at most 1, at least SAFMIN */
i__1 = *n - 1;
xnorm = igraphdnrm2_(&i__1, &x[1], incx);
d__1 = igraphdlapy2_(alpha, &xnorm);
beta = -d_sign(&d__1, alpha);
}
*tau = (beta - *alpha) / beta;
i__1 = *n - 1;
d__1 = 1. / (*alpha - beta);
igraphdscal_(&i__1, &d__1, &x[1], incx);
/* If ALPHA is subnormal, it may lose relative accuracy */
i__1 = knt;
for (j = 1; j <= i__1; ++j) {
beta *= safmin;
/* L20: */
}
*alpha = beta;
}
return 0;
/* End of DLARFG */
} /* igraphdlarfg_ */