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/* zlargv.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 zlargv_(integer *n, doublecomplex *x, integer *incx,
doublecomplex *y, integer *incy, doublereal *c__, integer *incc)
{
/* System generated locals */
integer i__1, i__2;
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__;
doublecomplex f, g;
integer i__, j;
doublecomplex r__;
doublereal f2, g2;
integer ic;
doublereal di;
doublecomplex ff;
doublereal cs, dr;
doublecomplex fs, gs;
integer ix, iy;
doublecomplex sn;
doublereal f2s, g2s, eps, scale;
integer count;
doublereal safmn2;
extern doublereal dlapy2_(doublereal *, doublereal *);
doublereal safmx2;
extern doublereal dlamch_(char *);
doublereal safmin;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLARGV generates a vector of complex plane rotations with real */
/* cosines, determined by elements of the complex vectors x and y. */
/* For i = 1,2,...,n */
/* ( c(i) s(i) ) ( x(i) ) = ( r(i) ) */
/* ( -conjg(s(i)) c(i) ) ( y(i) ) = ( 0 ) */
/* where c(i)**2 + ABS(s(i))**2 = 1 */
/* The following conventions are used (these are the same as in ZLARTG, */
/* but differ from the BLAS1 routine ZROTG): */
/* If y(i)=0, then c(i)=1 and s(i)=0. */
/* If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of plane rotations to be generated. */
/* X (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX) */
/* On entry, the vector x. */
/* On exit, x(i) is overwritten by r(i), for i = 1,...,n. */
/* INCX (input) INTEGER */
/* The increment between elements of X. INCX > 0. */
/* Y (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCY) */
/* On entry, the vector y. */
/* On exit, the sines of the plane rotations. */
/* INCY (input) INTEGER */
/* The increment between elements of Y. INCY > 0. */
/* C (output) DOUBLE PRECISION array, dimension (1+(N-1)*INCC) */
/* The cosines of the plane rotations. */
/* INCC (input) INTEGER */
/* The increment between elements of C. INCC > 0. */
/* Further Details */
/* ======= ======= */
/* 6-6-96 - 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 .. */
/* .. */
/* .. Local Scalars .. */
/* LOGICAL FIRST */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Save statement .. */
/* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 */
/* .. */
/* .. Data statements .. */
/* DATA FIRST / .TRUE. / */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* IF( FIRST ) THEN */
/* FIRST = .FALSE. */
/* Parameter adjustments */
--c__;
--y;
--x;
/* Function Body */
safmin = dlamch_("S");
eps = dlamch_("E");
d__1 = dlamch_("B");
i__1 = (integer) (log(safmin / eps) / log(dlamch_("B")) / 2.);
safmn2 = pow_di(&d__1, &i__1);
safmx2 = 1. / safmn2;
/* END IF */
ix = 1;
iy = 1;
ic = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
f.r = x[i__2].r, f.i = x[i__2].i;
i__2 = iy;
g.r = y[i__2].r, g.i = y[i__2].i;
/* Use identical algorithm as in ZLARTG */
/* 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.r = f.r, fs.i = f.i;
gs.r = g.r, gs.i = g.i;
count = 0;
if (scale >= safmx2) {
L10:
++count;
z__1.r = safmn2 * fs.r, z__1.i = safmn2 * fs.i;
fs.r = z__1.r, fs.i = z__1.i;
z__1.r = safmn2 * gs.r, z__1.i = safmn2 * gs.i;
gs.r = z__1.r, gs.i = z__1.i;
scale *= safmn2;
if (scale >= safmx2) {
goto L10;
}
} else if (scale <= safmn2) {
if (g.r == 0. && g.i == 0.) {
cs = 1.;
sn.r = 0., sn.i = 0.;
r__.r = f.r, r__.i = f.i;
goto L50;
}
L20:
--count;
z__1.r = safmx2 * fs.r, z__1.i = safmx2 * fs.i;
fs.r = z__1.r, fs.i = z__1.i;
z__1.r = safmx2 * gs.r, z__1.i = safmx2 * gs.i;
gs.r = z__1.r, gs.i = z__1.i;
scale *= safmx2;
if (scale <= safmn2) {
goto L20;
}
}
/* Computing 2nd power */
d__1 = fs.r;
/* Computing 2nd power */
d__2 = d_imag(&fs);
f2 = d__1 * d__1 + d__2 * d__2;
/* 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 <= max(g2,1.) * safmin) {
/* This is a rare case: F is very small. */
if (f.r == 0. && f.i == 0.) {
cs = 0.;
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__1 = gs.r;
d__2 = d_imag(&gs);
d__ = dlapy2_(&d__1, &d__2);
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;
goto L50;
}
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);
/* 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;
/* Make sure abs(FF) = 1 */
/* Do complex/real division explicitly with 2 real divisions */
/* 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__1 = f.r;
d__2 = d_imag(&f);
d__ = dlapy2_(&d__1, &d__2);
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 {
dr = safmx2 * f.r;
di = safmx2 * d_imag(&f);
d__ = dlapy2_(&dr, &di);
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;
}
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;
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 {
/* This is the most common case. */
/* Neither F2 nor F2/G2 are less than SAFMIN */
/* F2S cannot overflow, and it is accurate */
f2s = sqrt(g2 / f2 + 1.);
/* Do the F2S(real)*FS(complex) multiply with two real */
/* multiplies */
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 = 1. / f2s;
d__ = f2 + g2;
/* Do complex/real division explicitly with two real divisions */
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;
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 != 0) {
if (count > 0) {
i__2 = count;
for (j = 1; j <= i__2; ++j) {
z__1.r = safmx2 * r__.r, z__1.i = safmx2 * r__.i;
r__.r = z__1.r, r__.i = z__1.i;
/* L30: */
}
} else {
i__2 = -count;
for (j = 1; j <= i__2; ++j) {
z__1.r = safmn2 * r__.r, z__1.i = safmn2 * r__.i;
r__.r = z__1.r, r__.i = z__1.i;
/* L40: */
}
}
}
}
L50:
c__[ic] = cs;
i__2 = iy;
y[i__2].r = sn.r, y[i__2].i = sn.i;
i__2 = ix;
x[i__2].r = r__.r, x[i__2].i = r__.i;
ic += *incc;
iy += *incy;
ix += *incx;
/* L60: */
}
return 0;
/* End of ZLARGV */
} /* zlargv_ */
|
