clargv.c

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/* clargv.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 clargv_(integer *n, complex *x, integer *incx, complex *
        y, integer *incy, real *c__, integer *incc)
{
    /* System generated locals */
    integer i__1, i__2;
    real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8, r__9, r__10;
    complex q__1, q__2, q__3;

    /* Builtin functions */
    double log(doublereal), pow_ri(real *, integer *), r_imag(complex *), 
            sqrt(doublereal);
    void r_cnjg(complex *, complex *);

    /* Local variables */
    real d__;
    complex f, g;
    integer i__, j;
    complex r__;
    real f2, g2;
    integer ic;
    real di;
    complex ff;
    real cs, dr;
    complex fs, gs;
    integer ix, iy;
    complex sn;
    real f2s, g2s, eps, scale;
    integer count;
    real safmn2, safmx2;
    extern doublereal slapy2_(real *, real *), slamch_(char *);
    real safmin;


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  CLARGV 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 CLARTG, */
/*  but differ from the BLAS1 routine CROTG): */
/*     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 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 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) REAL 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 = slamch_("S");
    eps = slamch_("E");
    r__1 = slamch_("B");
    i__1 = (integer) (log(safmin / eps) / log(slamch_("B")) / 2.f);
    safmn2 = pow_ri(&r__1, &i__1);
    safmx2 = 1.f / 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 CLARTG */

/* Computing MAX */
/* Computing MAX */
        r__7 = (r__1 = f.r, dabs(r__1)), r__8 = (r__2 = r_imag(&f), dabs(r__2)
                );
/* Computing MAX */
        r__9 = (r__3 = g.r, dabs(r__3)), r__10 = (r__4 = r_imag(&g), dabs(
                r__4));
        r__5 = dmax(r__7,r__8), r__6 = dmax(r__9,r__10);
        scale = dmax(r__5,r__6);
        fs.r = f.r, fs.i = f.i;
        gs.r = g.r, gs.i = g.i;
        count = 0;
        if (scale >= safmx2) {
L10:
            ++count;
            q__1.r = safmn2 * fs.r, q__1.i = safmn2 * fs.i;
            fs.r = q__1.r, fs.i = q__1.i;
            q__1.r = safmn2 * gs.r, q__1.i = safmn2 * gs.i;
            gs.r = q__1.r, gs.i = q__1.i;
            scale *= safmn2;
            if (scale >= safmx2) {
                goto L10;
            }
        } else if (scale <= safmn2) {
            if (g.r == 0.f && g.i == 0.f) {
                cs = 1.f;
                sn.r = 0.f, sn.i = 0.f;
                r__.r = f.r, r__.i = f.i;
                goto L50;
            }
L20:
            --count;
            q__1.r = safmx2 * fs.r, q__1.i = safmx2 * fs.i;
            fs.r = q__1.r, fs.i = q__1.i;
            q__1.r = safmx2 * gs.r, q__1.i = safmx2 * gs.i;
            gs.r = q__1.r, gs.i = q__1.i;
            scale *= safmx2;
            if (scale <= safmn2) {
                goto L20;
            }
        }
/* Computing 2nd power */
        r__1 = fs.r;
/* Computing 2nd power */
        r__2 = r_imag(&fs);
        f2 = r__1 * r__1 + r__2 * r__2;
/* Computing 2nd power */
        r__1 = gs.r;
/* Computing 2nd power */
        r__2 = r_imag(&gs);
        g2 = r__1 * r__1 + r__2 * r__2;
        if (f2 <= dmax(g2,1.f) * safmin) {

/*           This is a rare case: F is very small. */

            if (f.r == 0.f && f.i == 0.f) {
                cs = 0.f;
                r__2 = g.r;
                r__3 = r_imag(&g);
                r__1 = slapy2_(&r__2, &r__3);
                r__.r = r__1, r__.i = 0.f;
/*              Do complex/real division explicitly with two real */
/*              divisions */
                r__1 = gs.r;
                r__2 = r_imag(&gs);
                d__ = slapy2_(&r__1, &r__2);
                r__1 = gs.r / d__;
                r__2 = -r_imag(&gs) / d__;
                q__1.r = r__1, q__1.i = r__2;
                sn.r = q__1.r, sn.i = q__1.i;
                goto L50;
            }
            r__1 = fs.r;
            r__2 = r_imag(&fs);
            f2s = slapy2_(&r__1, &r__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 */
            r__3 = (r__1 = f.r, dabs(r__1)), r__4 = (r__2 = r_imag(&f), dabs(
                    r__2));
            if (dmax(r__3,r__4) > 1.f) {
                r__1 = f.r;
                r__2 = r_imag(&f);
                d__ = slapy2_(&r__1, &r__2);
                r__1 = f.r / d__;
                r__2 = r_imag(&f) / d__;
                q__1.r = r__1, q__1.i = r__2;
                ff.r = q__1.r, ff.i = q__1.i;
            } else {
                dr = safmx2 * f.r;
                di = safmx2 * r_imag(&f);
                d__ = slapy2_(&dr, &di);
                r__1 = dr / d__;
                r__2 = di / d__;
                q__1.r = r__1, q__1.i = r__2;
                ff.r = q__1.r, ff.i = q__1.i;
            }
            r__1 = gs.r / g2s;
            r__2 = -r_imag(&gs) / g2s;
            q__2.r = r__1, q__2.i = r__2;
            q__1.r = ff.r * q__2.r - ff.i * q__2.i, q__1.i = ff.r * q__2.i + 
                    ff.i * q__2.r;
            sn.r = q__1.r, sn.i = q__1.i;
            q__2.r = cs * f.r, q__2.i = cs * f.i;
            q__3.r = sn.r * g.r - sn.i * g.i, q__3.i = sn.r * g.i + sn.i * 
                    g.r;
            q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
            r__.r = q__1.r, r__.i = q__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.f);
/*           Do the F2S(real)*FS(complex) multiply with two real */
/*           multiplies */
            r__1 = f2s * fs.r;
            r__2 = f2s * r_imag(&fs);
            q__1.r = r__1, q__1.i = r__2;
            r__.r = q__1.r, r__.i = q__1.i;
            cs = 1.f / f2s;
            d__ = f2 + g2;
/*           Do complex/real division explicitly with two real divisions */
            r__1 = r__.r / d__;
            r__2 = r_imag(&r__) / d__;
            q__1.r = r__1, q__1.i = r__2;
            sn.r = q__1.r, sn.i = q__1.i;
            r_cnjg(&q__2, &gs);
            q__1.r = sn.r * q__2.r - sn.i * q__2.i, q__1.i = sn.r * q__2.i + 
                    sn.i * q__2.r;
            sn.r = q__1.r, sn.i = q__1.i;
            if (count != 0) {
                if (count > 0) {
                    i__2 = count;
                    for (j = 1; j <= i__2; ++j) {
                        q__1.r = safmx2 * r__.r, q__1.i = safmx2 * r__.i;
                        r__.r = q__1.r, r__.i = q__1.i;
/* L30: */
                    }
                } else {
                    i__2 = -count;
                    for (j = 1; j <= i__2; ++j) {
                        q__1.r = safmn2 * r__.r, q__1.i = safmn2 * r__.i;
                        r__.r = q__1.r, r__.i = q__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 CLARGV */

} /* clargv_ */