lapack/clarfg.c

/* clarfg.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 real r_sign(real *a, real *b) {
  real x;
  x = (*a >= 0 ? *a : -*a);
  return (*b >= 0 ? x : -x);
}

/* Table of constant values */

static complex c_b5 = {1.f, 0.f};

/* Subroutine */ void clarfg_(integer *n, complex *alpha, complex *x, integer *incx, complex *tau) {
  /* System generated locals */
  integer i__1;
  real r__1, r__2;
  complex q__1, q__2;

  /* Local variables */
  integer j, knt;
  real beta;
  extern /* Subroutine */ void cscal_(integer *, complex *, complex *, integer *);
  real alphi, alphr, xnorm;
  extern real scnrm2_(integer *, complex *, integer *), slapy3_(real *, real *, real *);
  extern /* Complex */ void cladiv_(complex *, complex *, complex *);
  extern doublereal slamch_(char *);
  extern /* Subroutine */ void csscal_(integer *, real *, complex *, integer *);
  real 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 */
  /*  ======= */

  /*  CLARFG 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 */
  /*          On entry, the value alpha. */
  /*          On exit, it is overwritten with the value beta. */

  /*  X       (input/output) COMPLEX 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 */
  /*          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.f, tau->i = 0.f;
    return;
  }

  i__1 = *n - 1;
  xnorm = scnrm2_(&i__1, &x[1], incx);
  alphr = alpha->r;
  alphi = alpha->i;

  if (xnorm == 0.f && alphi == 0.f) {
    /*        H  =  I */

    tau->r = 0.f, tau->i = 0.f;
  } else {
    /*        general case */

    r__1 = slapy3_(&alphr, &alphi, &xnorm);
    beta = -r_sign(&r__1, &alphr);
    safmin = slamch_("S") / slamch_("E");
    rsafmn = 1.f / safmin;

    knt = 0;
    if (dabs(beta) < safmin) {
      /*           XNORM, BETA may be inaccurate; scale X and recompute them */

    L10:
      ++knt;
      i__1 = *n - 1;
      csscal_(&i__1, &rsafmn, &x[1], incx);
      beta *= rsafmn;
      alphi *= rsafmn;
      alphr *= rsafmn;
      if (dabs(beta) < safmin) {
        goto L10;
      }

      /*           New BETA is at most 1, at least SAFMIN */

      i__1 = *n - 1;
      xnorm = scnrm2_(&i__1, &x[1], incx);
      q__1.r = alphr, q__1.i = alphi;
      alpha->r = q__1.r, alpha->i = q__1.i;
      r__1 = slapy3_(&alphr, &alphi, &xnorm);
      beta = -r_sign(&r__1, &alphr);
    }
    r__1 = (beta - alphr) / beta;
    r__2 = -alphi / beta;
    q__1.r = r__1, q__1.i = r__2;
    tau->r = q__1.r, tau->i = q__1.i;
    q__2.r = alpha->r - beta, q__2.i = alpha->i;
    cladiv_(&q__1, &c_b5, &q__2);
    alpha->r = q__1.r, alpha->i = q__1.i;
    i__1 = *n - 1;
    cscal_(&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.f;
  }

  /*     End of CLARFG */

} /* clarfg_ */