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/* ../../../dependencies/lapack/src/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"
/* 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 */
static integer j, knt;
static doublereal beta;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
static doublereal xnorm;
extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *,
ftnlen);
static doublereal safmin, rsafmn;
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. 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", (ftnlen)1) / dlamch_("E", (ftnlen)1);
if (abs(beta) < safmin) {
/* XNORM, BETA may be inaccurate; scale X and recompute them */
rsafmn = 1. / safmin;
knt = 0;
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 */
*alpha = beta;
i__1 = knt;
for (j = 1; j <= i__1; ++j) {
*alpha *= safmin;
/* L20: */
}
} else {
*tau = (beta - *alpha) / beta;
i__1 = *n - 1;
d__1 = 1. / (*alpha - beta);
dscal_(&i__1, &d__1, &x[1], incx);
*alpha = beta;
}
}
return 0;
/* End of DLARFG */
} /* dlarfg_ */
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