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/* lapack/double/dlarfg.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/*< SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) >*/
/* 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 *,
ftnlen);
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 .. */
/*< INTEGER INCX, N >*/
/*< DOUBLE PRECISION ALPHA, TAU >*/
/* .. */
/* .. Array Arguments .. */
/*< DOUBLE PRECISION X( * ) >*/
/* .. */
/* 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 .. */
/*< DOUBLE PRECISION ONE, ZERO >*/
/*< PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER J, KNT >*/
/*< DOUBLE PRECISION BETA, RSAFMN, SAFMIN, XNORM >*/
/* .. */
/* .. External Functions .. */
/*< DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2 >*/
/*< EXTERNAL DLAMCH, DLAPY2, DNRM2 >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, SIGN >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL DSCAL >*/
/* .. */
/* .. Executable Statements .. */
/*< IF( N.LE.1 ) THEN >*/
/* Parameter adjustments */
--x;
/* Function Body */
if (*n <= 1) {
/*< TAU = ZERO >*/
*tau = 0.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< XNORM = DNRM2( N-1, X, INCX ) >*/
i__1 = *n - 1;
xnorm = dnrm2_(&i__1, &x[1], incx);
/*< IF( XNORM.EQ.ZERO ) THEN >*/
if (xnorm == 0.) {
/* H = I */
/*< TAU = ZERO >*/
*tau = 0.;
/*< ELSE >*/
} else {
/* general case */
/*< BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) >*/
d__1 = dlapy2_(alpha, &xnorm);
beta = -d_sign(&d__1, alpha);
/*< SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) >*/
safmin = dlamch_("S", (ftnlen)1) / dlamch_("E", (ftnlen)1);
/*< IF( ABS( BETA ).LT.SAFMIN ) THEN >*/
if (abs(beta) < safmin) {
/* XNORM, BETA may be inaccurate; scale X and recompute them */
/*< RSAFMN = ONE / SAFMIN >*/
rsafmn = 1. / safmin;
/*< KNT = 0 >*/
knt = 0;
/*< 10 CONTINUE >*/
L10:
/*< KNT = KNT + 1 >*/
++knt;
/*< CALL DSCAL( N-1, RSAFMN, X, INCX ) >*/
i__1 = *n - 1;
dscal_(&i__1, &rsafmn, &x[1], incx);
/*< BETA = BETA*RSAFMN >*/
beta *= rsafmn;
/*< ALPHA = ALPHA*RSAFMN >*/
*alpha *= rsafmn;
/*< >*/
if (abs(beta) < safmin) {
goto L10;
}
/* New BETA is at most 1, at least SAFMIN */
/*< XNORM = DNRM2( N-1, X, INCX ) >*/
i__1 = *n - 1;
xnorm = dnrm2_(&i__1, &x[1], incx);
/*< BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) >*/
d__1 = dlapy2_(alpha, &xnorm);
beta = -d_sign(&d__1, alpha);
/*< TAU = ( BETA-ALPHA ) / BETA >*/
*tau = (beta - *alpha) / beta;
/*< CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX ) >*/
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 >*/
*alpha = beta;
/*< DO 20 J = 1, KNT >*/
i__1 = knt;
for (j = 1; j <= i__1; ++j) {
/*< ALPHA = ALPHA*SAFMIN >*/
*alpha *= safmin;
/*< 20 CONTINUE >*/
/* L20: */
}
/*< ELSE >*/
} else {
/*< TAU = ( BETA-ALPHA ) / BETA >*/
*tau = (beta - *alpha) / beta;
/*< CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX ) >*/
i__1 = *n - 1;
d__1 = 1. / (*alpha - beta);
dscal_(&i__1, &d__1, &x[1], incx);
/*< ALPHA = BETA >*/
*alpha = beta;
/*< END IF >*/
}
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of DLARFG */
/*< END >*/
} /* dlarfg_ */
#ifdef __cplusplus
}
#endif
|
