lapack/dlarfg.c

/* dlarfg.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 "blaswrap.h"
#include "lapack_datatypes.h"

static inline doublereal d_sign(doublereal *a, doublereal *b) {
  doublereal x;
  x = (*a >= 0 ? *a : -*a);
  return (*b >= 0 ? x : -x);
}

/* Subroutine */ void dlarfg_(integer *n, doublereal *alpha, doublereal *x, integer *incx, doublereal *tau) {
  /* System generated locals */
  integer i__1;
  doublereal d__1;

  /* Local variables */
  integer j, knt;
  doublereal beta;
  extern doublereal dnrm2_(integer *, doublereal *, integer *);
  extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *, integer *);
  doublereal xnorm;
  extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
  doublereal safmin, rsafmn;

  /*  -- LAPACK auxiliary routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */

  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */

  /*  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. */

  /*  ===================================================================== */

  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Executable Statements .. */

  /* Parameter adjustments */
  --x;

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

  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");
    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;
      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 */

    i__1 = knt;
    for (j = 1; j <= i__1; ++j) {
      beta *= safmin;
      /* L20: */
    }
    *alpha = beta;
  }

  /*     End of DLARFG */

} /* dlarfg_ */