text: /* zlarfg.f -- translated by f2c (version 20061008).
     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"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static doublecomplex c_b5 = {1.,0.};
  
  /* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex *
  	x, integer *incx, doublecomplex *tau)
  {
      /* System generated locals */
      integer i__1;
      doublereal d__1, d__2;
      doublecomplex z__1, z__2;
  
      /* Builtin functions */
      double d_imag(doublecomplex *), d_sign(doublereal *, doublereal *);
  
      /* Local variables */
      integer j, knt;
      doublereal beta, alphi, alphr;
      extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 
  	    doublecomplex *, integer *);
      doublereal xnorm;
      extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *), 
  	    dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *);
      doublereal safmin;
      extern /* Subroutine */ int zdscal_(integer *, doublereal *, 
  	    doublecomplex *, integer *);
      doublereal rsafmn;
      extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, 
  	     doublecomplex *);
  
  
  /*  -- LAPACK auxiliary routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  ZLARFG generates a complex elementary reflector H of order n, such */
  /*  that */
  
  /*        H' * ( alpha ) = ( beta ),   H' * H = I. */
  /*             (   x   )   (   0  ) */
  
  /*  where alpha and beta are scalars, with beta real, and x is an */
  /*  (n-1)-element complex vector. H is represented in the form */
  
  /*        H = I - tau * ( 1 ) * ( 1 v' ) , */
  /*                      ( v ) */
  
  /*  where tau is a complex scalar and v is a complex (n-1)-element */
  /*  vector. Note that H is not hermitian. */
  
  /*  If the elements of x are all zero and alpha is real, then tau = 0 */
  /*  and H is taken to be the unit matrix. */
  
  /*  Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 . */
  
  /*  Arguments */
  /*  ========= */
  
  /*  N       (input) INTEGER */
  /*          The order of the elementary reflector. */
  
  /*  ALPHA   (input/output) COMPLEX*16 */
  /*          On entry, the value alpha. */
  /*          On exit, it is overwritten with the value beta. */
  
  /*  X       (input/output) COMPLEX*16 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) COMPLEX*16 */
  /*          The value tau. */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
      /* Parameter adjustments */
      --x;
  
      /* Function Body */
      if (*n <= 0) {
  	tau->r = 0., tau->i = 0.;
  	return 0;
      }
  
      i__1 = *n - 1;
      xnorm = dznrm2_(&i__1, &x[1], incx);
      alphr = alpha->r;
      alphi = d_imag(alpha);
  
      if (xnorm == 0. && alphi == 0.) {
  
  /*        H  =  I */
  
  	tau->r = 0., tau->i = 0.;
      } else {
  
  /*        general case */
  
  	d__1 = dlapy3_(&alphr, &alphi, &xnorm);
  	beta = -d_sign(&d__1, &alphr);
  	safmin = dlamch_("S") / dlamch_("E");
  	rsafmn = 1. / safmin;
  
  	knt = 0;
  	if (abs(beta) < safmin) {
  
  /*           XNORM, BETA may be inaccurate; scale X and recompute them */
  
  L10:
  	    ++knt;
  	    i__1 = *n - 1;
  	    zdscal_(&i__1, &rsafmn, &x[1], incx);
  	    beta *= rsafmn;
  	    alphi *= rsafmn;
  	    alphr *= rsafmn;
  	    if (abs(beta) < safmin) {
  		goto L10;
  	    }
  
  /*           New BETA is at most 1, at least SAFMIN */
  
  	    i__1 = *n - 1;
  	    xnorm = dznrm2_(&i__1, &x[1], incx);
  	    z__1.r = alphr, z__1.i = alphi;
  	    alpha->r = z__1.r, alpha->i = z__1.i;
  	    d__1 = dlapy3_(&alphr, &alphi, &xnorm);
  	    beta = -d_sign(&d__1, &alphr);
  	}
  	d__1 = (beta - alphr) / beta;
  	d__2 = -alphi / beta;
  	z__1.r = d__1, z__1.i = d__2;
  	tau->r = z__1.r, tau->i = z__1.i;
  	z__2.r = alpha->r - beta, z__2.i = alpha->i;
  	zladiv_(&z__1, &c_b5, &z__2);
  	alpha->r = z__1.r, alpha->i = z__1.i;
  	i__1 = *n - 1;
  	zscal_(&i__1, alpha, &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->r = beta, alpha->i = 0.;
      }
  
      return 0;
  
  /*     End of ZLARFG */
  
  } /* zlarfg_ */
  