/*  -- translated by f2c (version 20100827).
   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"

/* 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 3.3.1) --   
    -- LAPACK is a software package provided by Univ. of Tennessee,    --   
    -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--   
    -- April 2011                                                      --   


    Purpose   
    =======   

    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.   

    Arguments   
    =========   

    N       (input) INTEGER   
            The order of the elementary reflector.   

    ALPHA   (input/output) DOUBLE PRECISION   
            On entry, the value alpha.   
            On exit, it is overwritten with the value beta.   

    X       (input/output) DOUBLE PRECISION array, dimension   
                           (1+(N-2)*abs(INCX))   
            On entry, the vector x.   
            On exit, it is overwritten with the vector v.   

    INCX    (input) INTEGER   
            The increment between elements of X. INCX > 0.   

    TAU     (output) DOUBLE PRECISION   
            The value tau.   

    =====================================================================   


       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_ */

