starpu-max/min-dgels/base/SRC/dlaic1.c

/* dlaic1.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 integer c__1 = 1;
static doublereal c_b5 = 1.;

/* Subroutine */ int dlaic1_(integer *job, integer *j, doublereal *x, 
	doublereal *sest, doublereal *w, doublereal *gamma, doublereal *
	sestpr, doublereal *s, doublereal *c__)
{
    /* System generated locals */
    doublereal d__1, d__2, d__3, d__4;

    /* Builtin functions */
    double sqrt(doublereal), d_sign(doublereal *, doublereal *);

    /* Local variables */
    doublereal b, t, s1, s2, eps, tmp;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    doublereal sine, test, zeta1, zeta2, alpha, norma;
    extern doublereal dlamch_(char *);
    doublereal absgam, absalp, cosine, absest;


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

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

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

/*  DLAIC1 applies one step of incremental condition estimation in */
/*  its simplest version: */

/*  Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j */
/*  lower triangular matrix L, such that */
/*           twonorm(L*x) = sest */
/*  Then DLAIC1 computes sestpr, s, c such that */
/*  the vector */
/*                  [ s*x ] */
/*           xhat = [  c  ] */
/*  is an approximate singular vector of */
/*                  [ L     0  ] */
/*           Lhat = [ w' gamma ] */
/*  in the sense that */
/*           twonorm(Lhat*xhat) = sestpr. */

/*  Depending on JOB, an estimate for the largest or smallest singular */
/*  value is computed. */

/*  Note that [s c]' and sestpr**2 is an eigenpair of the system */

/*      diag(sest*sest, 0) + [alpha  gamma] * [ alpha ] */
/*                                            [ gamma ] */

/*  where  alpha =  x'*w. */

/*  Arguments */
/*  ========= */

/*  JOB     (input) INTEGER */
/*          = 1: an estimate for the largest singular value is computed. */
/*          = 2: an estimate for the smallest singular value is computed. */

/*  J       (input) INTEGER */
/*          Length of X and W */

/*  X       (input) DOUBLE PRECISION array, dimension (J) */
/*          The j-vector x. */

/*  SEST    (input) DOUBLE PRECISION */
/*          Estimated singular value of j by j matrix L */

/*  W       (input) DOUBLE PRECISION array, dimension (J) */
/*          The j-vector w. */

/*  GAMMA   (input) DOUBLE PRECISION */
/*          The diagonal element gamma. */

/*  SESTPR  (output) DOUBLE PRECISION */
/*          Estimated singular value of (j+1) by (j+1) matrix Lhat. */

/*  S       (output) DOUBLE PRECISION */
/*          Sine needed in forming xhat. */

/*  C       (output) DOUBLE PRECISION */
/*          Cosine needed in forming xhat. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Executable Statements .. */

    /* Parameter adjustments */
    --w;
    --x;

    /* Function Body */
    eps = dlamch_("Epsilon");
    alpha = ddot_(j, &x[1], &c__1, &w[1], &c__1);

    absalp = abs(alpha);
    absgam = abs(*gamma);
    absest = abs(*sest);

    if (*job == 1) {

/*        Estimating largest singular value */

/*        special cases */

	if (*sest == 0.) {
	    s1 = max(absgam,absalp);
	    if (s1 == 0.) {
		*s = 0.;
		*c__ = 1.;
		*sestpr = 0.;
	    } else {
		*s = alpha / s1;
		*c__ = *gamma / s1;
		tmp = sqrt(*s * *s + *c__ * *c__);
		*s /= tmp;
		*c__ /= tmp;
		*sestpr = s1 * tmp;
	    }
	    return 0;
	} else if (absgam <= eps * absest) {
	    *s = 1.;
	    *c__ = 0.;
	    tmp = max(absest,absalp);
	    s1 = absest / tmp;
	    s2 = absalp / tmp;
	    *sestpr = tmp * sqrt(s1 * s1 + s2 * s2);
	    return 0;
	} else if (absalp <= eps * absest) {
	    s1 = absgam;
	    s2 = absest;
	    if (s1 <= s2) {
		*s = 1.;
		*c__ = 0.;
		*sestpr = s2;
	    } else {
		*s = 0.;
		*c__ = 1.;
		*sestpr = s1;
	    }
	    return 0;
	} else if (absest <= eps * absalp || absest <= eps * absgam) {
	    s1 = absgam;
	    s2 = absalp;
	    if (s1 <= s2) {
		tmp = s1 / s2;
		*s = sqrt(tmp * tmp + 1.);
		*sestpr = s2 * *s;
		*c__ = *gamma / s2 / *s;
		*s = d_sign(&c_b5, &alpha) / *s;
	    } else {
		tmp = s2 / s1;
		*c__ = sqrt(tmp * tmp + 1.);
		*sestpr = s1 * *c__;
		*s = alpha / s1 / *c__;
		*c__ = d_sign(&c_b5, gamma) / *c__;
	    }
	    return 0;
	} else {

/*           normal case */

	    zeta1 = alpha / absest;
	    zeta2 = *gamma / absest;

	    b = (1. - zeta1 * zeta1 - zeta2 * zeta2) * .5;
	    *c__ = zeta1 * zeta1;
	    if (b > 0.) {
		t = *c__ / (b + sqrt(b * b + *c__));
	    } else {
		t = sqrt(b * b + *c__) - b;
	    }

	    sine = -zeta1 / t;
	    cosine = -zeta2 / (t + 1.);
	    tmp = sqrt(sine * sine + cosine * cosine);
	    *s = sine / tmp;
	    *c__ = cosine / tmp;
	    *sestpr = sqrt(t + 1.) * absest;
	    return 0;
	}

    } else if (*job == 2) {

/*        Estimating smallest singular value */

/*        special cases */

	if (*sest == 0.) {
	    *sestpr = 0.;
	    if (max(absgam,absalp) == 0.) {
		sine = 1.;
		cosine = 0.;
	    } else {
		sine = -(*gamma);
		cosine = alpha;
	    }
/* Computing MAX */
	    d__1 = abs(sine), d__2 = abs(cosine);
	    s1 = max(d__1,d__2);
	    *s = sine / s1;
	    *c__ = cosine / s1;
	    tmp = sqrt(*s * *s + *c__ * *c__);
	    *s /= tmp;
	    *c__ /= tmp;
	    return 0;
	} else if (absgam <= eps * absest) {
	    *s = 0.;
	    *c__ = 1.;
	    *sestpr = absgam;
	    return 0;
	} else if (absalp <= eps * absest) {
	    s1 = absgam;
	    s2 = absest;
	    if (s1 <= s2) {
		*s = 0.;
		*c__ = 1.;
		*sestpr = s1;
	    } else {
		*s = 1.;
		*c__ = 0.;
		*sestpr = s2;
	    }
	    return 0;
	} else if (absest <= eps * absalp || absest <= eps * absgam) {
	    s1 = absgam;
	    s2 = absalp;
	    if (s1 <= s2) {
		tmp = s1 / s2;
		*c__ = sqrt(tmp * tmp + 1.);
		*sestpr = absest * (tmp / *c__);
		*s = -(*gamma / s2) / *c__;
		*c__ = d_sign(&c_b5, &alpha) / *c__;
	    } else {
		tmp = s2 / s1;
		*s = sqrt(tmp * tmp + 1.);
		*sestpr = absest / *s;
		*c__ = alpha / s1 / *s;
		*s = -d_sign(&c_b5, gamma) / *s;
	    }
	    return 0;
	} else {

/*           normal case */

	    zeta1 = alpha / absest;
	    zeta2 = *gamma / absest;

/* Computing MAX */
	    d__3 = zeta1 * zeta1 + 1. + (d__1 = zeta1 * zeta2, abs(d__1)), 
		    d__4 = (d__2 = zeta1 * zeta2, abs(d__2)) + zeta2 * zeta2;
	    norma = max(d__3,d__4);

/*           See if root is closer to zero or to ONE */

	    test = (zeta1 - zeta2) * 2. * (zeta1 + zeta2) + 1.;
	    if (test >= 0.) {

/*              root is close to zero, compute directly */

		b = (zeta1 * zeta1 + zeta2 * zeta2 + 1.) * .5;
		*c__ = zeta2 * zeta2;
		t = *c__ / (b + sqrt((d__1 = b * b - *c__, abs(d__1))));
		sine = zeta1 / (1. - t);
		cosine = -zeta2 / t;
		*sestpr = sqrt(t + eps * 4. * eps * norma) * absest;
	    } else {

/*              root is closer to ONE, shift by that amount */

		b = (zeta2 * zeta2 + zeta1 * zeta1 - 1.) * .5;
		*c__ = zeta1 * zeta1;
		if (b >= 0.) {
		    t = -(*c__) / (b + sqrt(b * b + *c__));
		} else {
		    t = b - sqrt(b * b + *c__);
		}
		sine = -zeta1 / t;
		cosine = -zeta2 / (t + 1.);
		*sestpr = sqrt(t + 1. + eps * 4. * eps * norma) * absest;
	    }
	    tmp = sqrt(sine * sine + cosine * cosine);
	    *s = sine / tmp;
	    *c__ = cosine / tmp;
	    return 0;

	}
    }
    return 0;

/*     End of DLAIC1 */

} /* dlaic1_ */