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/* 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 "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static complex c_b5 = {1.f,0.f};
/* Subroutine */ int 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;
/* Builtin functions */
double r_imag(complex *), r_sign(real *, real *);
/* Local variables */
integer j, knt;
real beta;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
real alphi, alphr, xnorm;
extern doublereal scnrm2_(integer *, complex *, integer *), slapy3_(real *
, real *, real *);
extern /* Complex */ VOID cladiv_(complex *, complex *, complex *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int 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 0;
}
i__1 = *n - 1;
xnorm = scnrm2_(&i__1, &x[1], incx);
alphr = alpha->r;
alphi = r_imag(alpha);
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;
}
return 0;
/* End of CLARFG */
} /* clarfg_ */
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