/*  -- translated by f2c (version 20191129).

   You must link the resulting object file with libf2c:

  on Microsoft Windows system, link with libf2c.lib;

  on Linux or Unix systems, link with .../path/to/libf2c.a -lm

  or, if you install libf2c.a in a standard place, with -lf2c -lm

  -- in that order, at the end of the command line, as in

    cc *.o -lf2c -lm

  Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

    http://www.netlib.org/f2c/libf2c.zip

*/

#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/   

   > \htmlonly   

   > Download DLARFG + dependencies   

   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfg.

f">   

   > [TGZ]</a>   

   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfg.

f">   

   > [ZIP]</a>   

   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfg.

f">   

   > [TXT]</a>   

   > \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_ */