lapack/slarfg.c

/* slarfg.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"

/* Subroutine */ int slarfg_(integer *n, real *alpha, real *x, integer *incx, 
	real *tau)
{
    /* System generated locals */
    integer i__1;
    real r__1;

    /* Builtin functions */
    double r_sign(real *, real *);

    /* Local variables */
    integer j, knt;
    real beta;
    extern doublereal snrm2_(integer *, real *, integer *);
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    real xnorm;
    extern doublereal slapy2_(real *, real *), slamch_(char *);
    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 */
/*  ======= */

/*  SLARFG 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) REAL */
/*          On entry, the value alpha. */
/*          On exit, it is overwritten with the value beta. */

/*  X       (input/output) REAL 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) REAL */
/*          The value tau. */

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

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

    /* Parameter adjustments */
    --x;

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

    i__1 = *n - 1;
    xnorm = snrm2_(&i__1, &x[1], incx);

    if (xnorm == 0.f) {

/*        H  =  I */

	*tau = 0.f;
    } else {

/*        general case */

	r__1 = slapy2_(alpha, &xnorm);
	beta = -r_sign(&r__1, alpha);
	safmin = slamch_("S") / slamch_("E");
	knt = 0;
	if (dabs(beta) < safmin) {

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

	    rsafmn = 1.f / safmin;
L10:
	    ++knt;
	    i__1 = *n - 1;
	    sscal_(&i__1, &rsafmn, &x[1], incx);
	    beta *= rsafmn;
	    *alpha *= rsafmn;
	    if (dabs(beta) < safmin) {
		goto L10;
	    }

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

	    i__1 = *n - 1;
	    xnorm = snrm2_(&i__1, &x[1], incx);
	    r__1 = slapy2_(alpha, &xnorm);
	    beta = -r_sign(&r__1, alpha);
	}
	*tau = (beta - *alpha) / beta;
	i__1 = *n - 1;
	r__1 = 1.f / (*alpha - beta);
	sscal_(&i__1, &r__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 SLARFG */

} /* slarfg_ */