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/* lapack/complex16/zlartg.f -- translated by f2c (version 20090411).
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 ZLARTG( F, G, CS, SN, R ) >*/
/* Subroutine */ int zlartg_(doublecomplex *f, doublecomplex *g, doublereal *
cs, doublecomplex *sn, doublecomplex *r__)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
double log(doublereal), pow_di(doublereal *, integer *), d_imag(
doublecomplex *), sqrt(doublereal);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
doublereal d__;
integer i__;
doublereal f2, g2;
doublecomplex ff;
doublereal di, dr;
doublecomplex fs, gs;
doublereal f2s, g2s, eps, scale;
integer count;
doublereal safmn2;
extern doublereal dlapy2_(doublereal *, doublereal *);
doublereal safmx2;
extern doublereal dlamch_(char *, ftnlen);
doublereal safmin;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2006 */
/* .. Scalar Arguments .. */
/*< DOUBLE PRECISION CS >*/
/*< COMPLEX*16 F, G, R, SN >*/
/* .. */
/* Purpose */
/* ======= */
/* ZLARTG generates a plane rotation so that */
/* [ CS SN ] [ F ] [ R ] */
/* [ __ ] . [ ] = [ ] where CS**2 + |SN|**2 = 1. */
/* [ -SN CS ] [ G ] [ 0 ] */
/* This is a faster version of the BLAS1 routine ZROTG, except for */
/* the following differences: */
/* F and G are unchanged on return. */
/* If G=0, then CS=1 and SN=0. */
/* If F=0, then CS=0 and SN is chosen so that R is real. */
/* Arguments */
/* ========= */
/* F (input) COMPLEX*16 */
/* The first component of vector to be rotated. */
/* G (input) COMPLEX*16 */
/* The second component of vector to be rotated. */
/* CS (output) DOUBLE PRECISION */
/* The cosine of the rotation. */
/* SN (output) COMPLEX*16 */
/* The sine of the rotation. */
/* R (output) COMPLEX*16 */
/* The nonzero component of the rotated vector. */
/* Further Details */
/* ======= ======= */
/* 3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel */
/* This version has a few statements commented out for thread safety */
/* (machine parameters are computed on each entry). 10 feb 03, SJH. */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION TWO, ONE, ZERO >*/
/*< PARAMETER ( TWO = 2.0D+0, ONE = 1.0D+0, ZERO = 0.0D+0 ) >*/
/*< COMPLEX*16 CZERO >*/
/*< PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) ) >*/
/* .. */
/* .. Local Scalars .. */
/* LOGICAL FIRST */
/*< INTEGER COUNT, I >*/
/*< >*/
/*< COMPLEX*16 FF, FS, GS >*/
/* .. */
/* .. External Functions .. */
/*< DOUBLE PRECISION DLAMCH, DLAPY2 >*/
/*< EXTERNAL DLAMCH, DLAPY2 >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< >*/
/* .. */
/* .. Statement Functions .. */
/*< DOUBLE PRECISION ABS1, ABSSQ >*/
/* .. */
/* .. Save statement .. */
/* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 */
/* .. */
/* .. Data statements .. */
/* DATA FIRST / .TRUE. / */
/* .. */
/* .. Statement Function definitions .. */
/*< ABS1( FF ) = MAX( ABS( DBLE( FF ) ), ABS( DIMAG( FF ) ) ) >*/
/*< ABSSQ( FF ) = DBLE( FF )**2 + DIMAG( FF )**2 >*/
/* .. */
/* .. Executable Statements .. */
/* IF( FIRST ) THEN */
/*< SAFMIN = DLAMCH( 'S' ) >*/
safmin = dlamch_("S", (ftnlen)1);
/*< EPS = DLAMCH( 'E' ) >*/
eps = dlamch_("E", (ftnlen)1);
/*< >*/
d__1 = dlamch_("B", (ftnlen)1);
i__1 = (integer) (log(safmin / eps) / log(dlamch_("B", (ftnlen)1)) / 2.);
safmn2 = pow_di(&d__1, &i__1);
/*< SAFMX2 = ONE / SAFMN2 >*/
safmx2 = 1. / safmn2;
/* FIRST = .FALSE. */
/* END IF */
/*< SCALE = MAX( ABS1( F ), ABS1( G ) ) >*/
/* Computing MAX */
/* Computing MAX */
d__7 = (d__1 = f->r, abs(d__1)), d__8 = (d__2 = d_imag(f), abs(d__2));
/* Computing MAX */
d__9 = (d__3 = g->r, abs(d__3)), d__10 = (d__4 = d_imag(g), abs(d__4));
d__5 = max(d__7,d__8), d__6 = max(d__9,d__10);
scale = max(d__5,d__6);
/*< FS = F >*/
fs.r = f->r, fs.i = f->i;
/*< GS = G >*/
gs.r = g->r, gs.i = g->i;
/*< COUNT = 0 >*/
count = 0;
/*< IF( SCALE.GE.SAFMX2 ) THEN >*/
if (scale >= safmx2) {
/*< 10 CONTINUE >*/
L10:
/*< COUNT = COUNT + 1 >*/
++count;
/*< FS = FS*SAFMN2 >*/
z__1.r = safmn2 * fs.r, z__1.i = safmn2 * fs.i;
fs.r = z__1.r, fs.i = z__1.i;
/*< GS = GS*SAFMN2 >*/
z__1.r = safmn2 * gs.r, z__1.i = safmn2 * gs.i;
gs.r = z__1.r, gs.i = z__1.i;
/*< SCALE = SCALE*SAFMN2 >*/
scale *= safmn2;
/*< >*/
if (scale >= safmx2) {
goto L10;
}
/*< ELSE IF( SCALE.LE.SAFMN2 ) THEN >*/
} else if (scale <= safmn2) {
/*< IF( G.EQ.CZERO ) THEN >*/
if (g->r == 0. && g->i == 0.) {
/*< CS = ONE >*/
*cs = 1.;
/*< SN = CZERO >*/
sn->r = 0., sn->i = 0.;
/*< R = F >*/
r__->r = f->r, r__->i = f->i;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< 20 CONTINUE >*/
L20:
/*< COUNT = COUNT - 1 >*/
--count;
/*< FS = FS*SAFMX2 >*/
z__1.r = safmx2 * fs.r, z__1.i = safmx2 * fs.i;
fs.r = z__1.r, fs.i = z__1.i;
/*< GS = GS*SAFMX2 >*/
z__1.r = safmx2 * gs.r, z__1.i = safmx2 * gs.i;
gs.r = z__1.r, gs.i = z__1.i;
/*< SCALE = SCALE*SAFMX2 >*/
scale *= safmx2;
/*< >*/
if (scale <= safmn2) {
goto L20;
}
/*< END IF >*/
}
/*< F2 = ABSSQ( FS ) >*/
/* Computing 2nd power */
d__1 = fs.r;
/* Computing 2nd power */
d__2 = d_imag(&fs);
f2 = d__1 * d__1 + d__2 * d__2;
/*< G2 = ABSSQ( GS ) >*/
/* Computing 2nd power */
d__1 = gs.r;
/* Computing 2nd power */
d__2 = d_imag(&gs);
g2 = d__1 * d__1 + d__2 * d__2;
/*< IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN >*/
if (f2 <= max(g2,1.) * safmin) {
/* This is a rare case: F is very small. */
/*< IF( F.EQ.CZERO ) THEN >*/
if (f->r == 0. && f->i == 0.) {
/*< CS = ZERO >*/
*cs = 0.;
/*< R = DLAPY2( DBLE( G ), DIMAG( G ) ) >*/
d__2 = g->r;
d__3 = d_imag(g);
d__1 = dlapy2_(&d__2, &d__3);
r__->r = d__1, r__->i = 0.;
/* Do complex/real division explicitly with two real divisions */
/*< D = DLAPY2( DBLE( GS ), DIMAG( GS ) ) >*/
d__1 = gs.r;
d__2 = d_imag(&gs);
d__ = dlapy2_(&d__1, &d__2);
/*< SN = DCMPLX( DBLE( GS ) / D, -DIMAG( GS ) / D ) >*/
d__1 = gs.r / d__;
d__2 = -d_imag(&gs) / d__;
z__1.r = d__1, z__1.i = d__2;
sn->r = z__1.r, sn->i = z__1.i;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< F2S = DLAPY2( DBLE( FS ), DIMAG( FS ) ) >*/
d__1 = fs.r;
d__2 = d_imag(&fs);
f2s = dlapy2_(&d__1, &d__2);
/* G2 and G2S are accurate */
/* G2 is at least SAFMIN, and G2S is at least SAFMN2 */
/*< G2S = SQRT( G2 ) >*/
g2s = sqrt(g2);
/* Error in CS from underflow in F2S is at most */
/* UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS */
/* If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN, */
/* and so CS .lt. sqrt(SAFMIN) */
/* If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN */
/* and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS) */
/* Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S */
/*< CS = F2S / G2S >*/
*cs = f2s / g2s;
/* Make sure abs(FF) = 1 */
/* Do complex/real division explicitly with 2 real divisions */
/*< IF( ABS1( F ).GT.ONE ) THEN >*/
/* Computing MAX */
d__3 = (d__1 = f->r, abs(d__1)), d__4 = (d__2 = d_imag(f), abs(d__2));
if (max(d__3,d__4) > 1.) {
/*< D = DLAPY2( DBLE( F ), DIMAG( F ) ) >*/
d__1 = f->r;
d__2 = d_imag(f);
d__ = dlapy2_(&d__1, &d__2);
/*< FF = DCMPLX( DBLE( F ) / D, DIMAG( F ) / D ) >*/
d__1 = f->r / d__;
d__2 = d_imag(f) / d__;
z__1.r = d__1, z__1.i = d__2;
ff.r = z__1.r, ff.i = z__1.i;
/*< ELSE >*/
} else {
/*< DR = SAFMX2*DBLE( F ) >*/
dr = safmx2 * f->r;
/*< DI = SAFMX2*DIMAG( F ) >*/
di = safmx2 * d_imag(f);
/*< D = DLAPY2( DR, DI ) >*/
d__ = dlapy2_(&dr, &di);
/*< FF = DCMPLX( DR / D, DI / D ) >*/
d__1 = dr / d__;
d__2 = di / d__;
z__1.r = d__1, z__1.i = d__2;
ff.r = z__1.r, ff.i = z__1.i;
/*< END IF >*/
}
/*< SN = FF*DCMPLX( DBLE( GS ) / G2S, -DIMAG( GS ) / G2S ) >*/
d__1 = gs.r / g2s;
d__2 = -d_imag(&gs) / g2s;
z__2.r = d__1, z__2.i = d__2;
z__1.r = ff.r * z__2.r - ff.i * z__2.i, z__1.i = ff.r * z__2.i + ff.i
* z__2.r;
sn->r = z__1.r, sn->i = z__1.i;
/*< R = CS*F + SN*G >*/
z__2.r = *cs * f->r, z__2.i = *cs * f->i;
z__3.r = sn->r * g->r - sn->i * g->i, z__3.i = sn->r * g->i + sn->i *
g->r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
r__->r = z__1.r, r__->i = z__1.i;
/*< ELSE >*/
} else {
/* This is the most common case. */
/* Neither F2 nor F2/G2 are less than SAFMIN */
/* F2S cannot overflow, and it is accurate */
/*< F2S = SQRT( ONE+G2 / F2 ) >*/
f2s = sqrt(g2 / f2 + 1.);
/* Do the F2S(real)*FS(complex) multiply with two real multiplies */
/*< R = DCMPLX( F2S*DBLE( FS ), F2S*DIMAG( FS ) ) >*/
d__1 = f2s * fs.r;
d__2 = f2s * d_imag(&fs);
z__1.r = d__1, z__1.i = d__2;
r__->r = z__1.r, r__->i = z__1.i;
/*< CS = ONE / F2S >*/
*cs = 1. / f2s;
/*< D = F2 + G2 >*/
d__ = f2 + g2;
/* Do complex/real division explicitly with two real divisions */
/*< SN = DCMPLX( DBLE( R ) / D, DIMAG( R ) / D ) >*/
d__1 = r__->r / d__;
d__2 = d_imag(r__) / d__;
z__1.r = d__1, z__1.i = d__2;
sn->r = z__1.r, sn->i = z__1.i;
/*< SN = SN*DCONJG( GS ) >*/
d_cnjg(&z__2, &gs);
z__1.r = sn->r * z__2.r - sn->i * z__2.i, z__1.i = sn->r * z__2.i +
sn->i * z__2.r;
sn->r = z__1.r, sn->i = z__1.i;
/*< IF( COUNT.NE.0 ) THEN >*/
if (count != 0) {
/*< IF( COUNT.GT.0 ) THEN >*/
if (count > 0) {
/*< DO 30 I = 1, COUNT >*/
i__1 = count;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< R = R*SAFMX2 >*/
z__1.r = safmx2 * r__->r, z__1.i = safmx2 * r__->i;
r__->r = z__1.r, r__->i = z__1.i;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< ELSE >*/
} else {
/*< DO 40 I = 1, -COUNT >*/
i__1 = -count;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< R = R*SAFMN2 >*/
z__1.r = safmn2 * r__->r, z__1.i = safmn2 * r__->i;
r__->r = z__1.r, r__->i = z__1.i;
/*< 40 CONTINUE >*/
/* L40: */
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of ZLARTG */
/*< END >*/
} /* zlartg_ */
#ifdef __cplusplus
}
#endif
|
