dlarfg.c

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/* 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 "f2c.h"
#include "blaswrap.h"

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

    /* Builtin functions */
    double d_sign(doublereal *, doublereal *);

    /* Local variables */
    integer j, knt;
    doublereal beta;
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int 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 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");
        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;
    }

    return 0;

/*     End of DLARFG */

} /* dlarfg_ */