#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x, 
	integer *incx, doublereal *tau)
{
/*  -- LAPACK auxiliary routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    DLARFG generates a real elementary reflector H of order n, such   
    that   

          H * ( alpha ) = ( beta ),   H' * 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' ) ,   
                        ( 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 */
    /* System generated locals */
    integer i__1;
    doublereal d__1;
    /* Builtin functions */
    double d_sign(doublereal *, doublereal *);
    /* Local variables */
    static doublereal beta;
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    static integer j;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    static doublereal xnorm;
    extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
    static doublereal safmin, rsafmn;
    static integer knt;

    --x;

    /* Function Body */
    if (*n <= 1) {
	*tau = 0.;
	return 0;
    }

    i__1 = *n - 1;
    xnorm = dnrm2_(&i__1, &x[1], incx);

    if (xnorm == 0.) {

/*        H  =  I */

	*tau = 0.;
    } else {

/*        general case */

	d__1 = dlapy2_(alpha, &xnorm);
	beta = -d_sign(&d__1, alpha);
	safmin = dlamch_("S") / dlamch_("E");
	if (abs(beta) < safmin) {

/*           XNORM, BETA may be inaccurate; scale X and recompute them */

	    rsafmn = 1. / safmin;
	    knt = 0;
L10:
	    ++knt;
	    i__1 = *n - 1;
	    dscal_(&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 = dnrm2_(&i__1, &x[1], incx);
	    d__1 = dlapy2_(alpha, &xnorm);
	    beta = -d_sign(&d__1, alpha);
	    *tau = (beta - *alpha) / beta;
	    i__1 = *n - 1;
	    d__1 = 1. / (*alpha - beta);
	    dscal_(&i__1, &d__1, &x[1], incx);

/*           If ALPHA is subnormal, it may lose relative accuracy */

	    *alpha = beta;
	    i__1 = knt;
	    for (j = 1; j <= i__1; ++j) {
		*alpha *= safmin;
/* L20: */
	    }
	} else {
	    *tau = (beta - *alpha) / beta;
	    i__1 = *n - 1;
	    d__1 = 1. / (*alpha - beta);
	    dscal_(&i__1, &d__1, &x[1], incx);
	    *alpha = beta;
	}
    }

    return 0;

/*     End of DLARFG */

} /* dlarfg_ */

