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opencv/3rdparty/lapack/dlaed6.c

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#include "clapack.h"
/* Subroutine */ int dlaed6_(integer *kniter, logical *orgati, doublereal *
rho, doublereal *d__, doublereal *z__, doublereal *finit, doublereal *
tau, integer *info)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2, d__3, d__4;
/* Builtin functions */
double sqrt(doublereal), log(doublereal), pow_di(doublereal *, integer *);
/* Local variables */
doublereal a, b, c__, f;
integer i__;
doublereal fc, df, ddf, lbd, eta, ubd, eps, base;
integer iter;
doublereal temp, temp1, temp2, temp3, temp4;
logical scale;
integer niter;
doublereal small1, small2, sminv1, sminv2;
extern doublereal dlamch_(char *);
doublereal dscale[3], sclfac, zscale[3], erretm, sclinv;
/* -- LAPACK routine (version 3.1.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* February 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAED6 computes the positive or negative root (closest to the origin) */
/* of */
/* z(1) z(2) z(3) */
/* f(x) = rho + --------- + ---------- + --------- */
/* d(1)-x d(2)-x d(3)-x */
/* It is assumed that */
/* if ORGATI = .true. the root is between d(2) and d(3); */
/* otherwise it is between d(1) and d(2) */
/* This routine will be called by DLAED4 when necessary. In most cases, */
/* the root sought is the smallest in magnitude, though it might not be */
/* in some extremely rare situations. */
/* Arguments */
/* ========= */
/* KNITER (input) INTEGER */
/* Refer to DLAED4 for its significance. */
/* ORGATI (input) LOGICAL */
/* If ORGATI is true, the needed root is between d(2) and */
/* d(3); otherwise it is between d(1) and d(2). See */
/* DLAED4 for further details. */
/* RHO (input) DOUBLE PRECISION */
/* Refer to the equation f(x) above. */
/* D (input) DOUBLE PRECISION array, dimension (3) */
/* D satisfies d(1) < d(2) < d(3). */
/* Z (input) DOUBLE PRECISION array, dimension (3) */
/* Each of the elements in z must be positive. */
/* FINIT (input) DOUBLE PRECISION */
/* The value of f at 0. It is more accurate than the one */
/* evaluated inside this routine (if someone wants to do */
/* so). */
/* TAU (output) DOUBLE PRECISION */
/* The root of the equation f(x). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* > 0: if INFO = 1, failure to converge */
/* Further Details */
/* =============== */
/* 30/06/99: Based on contributions by */
/* Ren-Cang Li, Computer Science Division, University of California */
/* at Berkeley, USA */
/* 10/02/03: This version has a few statements commented out for thread */
/* safety (machine parameters are computed on each entry). SJH. */
/* 05/10/06: Modified from a new version of Ren-Cang Li, use */
/* Gragg-Thornton-Warner cubic convergent scheme for better stability. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--z__;
--d__;
/* Function Body */
*info = 0;
if (*orgati) {
lbd = d__[2];
ubd = d__[3];
} else {
lbd = d__[1];
ubd = d__[2];
}
if (*finit < 0.) {
lbd = 0.;
} else {
ubd = 0.;
}
niter = 1;
*tau = 0.;
if (*kniter == 2) {
if (*orgati) {
temp = (d__[3] - d__[2]) / 2.;
c__ = *rho + z__[1] / (d__[1] - d__[2] - temp);
a = c__ * (d__[2] + d__[3]) + z__[2] + z__[3];
b = c__ * d__[2] * d__[3] + z__[2] * d__[3] + z__[3] * d__[2];
} else {
temp = (d__[1] - d__[2]) / 2.;
c__ = *rho + z__[3] / (d__[3] - d__[2] - temp);
a = c__ * (d__[1] + d__[2]) + z__[1] + z__[2];
b = c__ * d__[1] * d__[2] + z__[1] * d__[2] + z__[2] * d__[1];
}
/* Computing MAX */
d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__);
temp = max(d__1,d__2);
a /= temp;
b /= temp;
c__ /= temp;
if (c__ == 0.) {
*tau = b / a;
} else if (a <= 0.) {
*tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (
c__ * 2.);
} else {
*tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))
));
}
if (*tau < lbd || *tau > ubd) {
*tau = (lbd + ubd) / 2.;
}
if (d__[1] == *tau || d__[2] == *tau || d__[3] == *tau) {
*tau = 0.;
} else {
temp = *finit + *tau * z__[1] / (d__[1] * (d__[1] - *tau)) + *tau
* z__[2] / (d__[2] * (d__[2] - *tau)) + *tau * z__[3] / (
d__[3] * (d__[3] - *tau));
if (temp <= 0.) {
lbd = *tau;
} else {
ubd = *tau;
}
if (abs(*finit) <= abs(temp)) {
*tau = 0.;
}
}
}
/* get machine parameters for possible scaling to avoid overflow */
/* modified by Sven: parameters SMALL1, SMINV1, SMALL2, */
/* SMINV2, EPS are not SAVEd anymore between one call to the */
/* others but recomputed at each call */
eps = dlamch_("Epsilon");
base = dlamch_("Base");
i__1 = (integer) (log(dlamch_("SafMin")) / log(base) / 3.);
small1 = pow_di(&base, &i__1);
sminv1 = 1. / small1;
small2 = small1 * small1;
sminv2 = sminv1 * sminv1;
/* Determine if scaling of inputs necessary to avoid overflow */
/* when computing 1/TEMP**3 */
if (*orgati) {
/* Computing MIN */
d__3 = (d__1 = d__[2] - *tau, abs(d__1)), d__4 = (d__2 = d__[3] - *
tau, abs(d__2));
temp = min(d__3,d__4);
} else {
/* Computing MIN */
d__3 = (d__1 = d__[1] - *tau, abs(d__1)), d__4 = (d__2 = d__[2] - *
tau, abs(d__2));
temp = min(d__3,d__4);
}
scale = FALSE_;
if (temp <= small1) {
scale = TRUE_;
if (temp <= small2) {
/* Scale up by power of radix nearest 1/SAFMIN**(2/3) */
sclfac = sminv2;
sclinv = small2;
} else {
/* Scale up by power of radix nearest 1/SAFMIN**(1/3) */
sclfac = sminv1;
sclinv = small1;
}
/* Scaling up safe because D, Z, TAU scaled elsewhere to be O(1) */
for (i__ = 1; i__ <= 3; ++i__) {
dscale[i__ - 1] = d__[i__] * sclfac;
zscale[i__ - 1] = z__[i__] * sclfac;
/* L10: */
}
*tau *= sclfac;
lbd *= sclfac;
ubd *= sclfac;
} else {
/* Copy D and Z to DSCALE and ZSCALE */
for (i__ = 1; i__ <= 3; ++i__) {
dscale[i__ - 1] = d__[i__];
zscale[i__ - 1] = z__[i__];
/* L20: */
}
}
fc = 0.;
df = 0.;
ddf = 0.;
for (i__ = 1; i__ <= 3; ++i__) {
temp = 1. / (dscale[i__ - 1] - *tau);
temp1 = zscale[i__ - 1] * temp;
temp2 = temp1 * temp;
temp3 = temp2 * temp;
fc += temp1 / dscale[i__ - 1];
df += temp2;
ddf += temp3;
/* L30: */
}
f = *finit + *tau * fc;
if (abs(f) <= 0.) {
goto L60;
}
if (f <= 0.) {
lbd = *tau;
} else {
ubd = *tau;
}
/* Iteration begins -- Use Gragg-Thornton-Warner cubic convergent */
/* scheme */
/* It is not hard to see that */
/* 1) Iterations will go up monotonically */
/* if FINIT < 0; */
/* 2) Iterations will go down monotonically */
/* if FINIT > 0. */
iter = niter + 1;
for (niter = iter; niter <= 40; ++niter) {
if (*orgati) {
temp1 = dscale[1] - *tau;
temp2 = dscale[2] - *tau;
} else {
temp1 = dscale[0] - *tau;
temp2 = dscale[1] - *tau;
}
a = (temp1 + temp2) * f - temp1 * temp2 * df;
b = temp1 * temp2 * f;
c__ = f - (temp1 + temp2) * df + temp1 * temp2 * ddf;
/* Computing MAX */
d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__);
temp = max(d__1,d__2);
a /= temp;
b /= temp;
c__ /= temp;
if (c__ == 0.) {
eta = b / a;
} else if (a <= 0.) {
eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__
* 2.);
} else {
eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))
);
}
if (f * eta >= 0.) {
eta = -f / df;
}
*tau += eta;
if (*tau < lbd || *tau > ubd) {
*tau = (lbd + ubd) / 2.;
}
fc = 0.;
erretm = 0.;
df = 0.;
ddf = 0.;
for (i__ = 1; i__ <= 3; ++i__) {
temp = 1. / (dscale[i__ - 1] - *tau);
temp1 = zscale[i__ - 1] * temp;
temp2 = temp1 * temp;
temp3 = temp2 * temp;
temp4 = temp1 / dscale[i__ - 1];
fc += temp4;
erretm += abs(temp4);
df += temp2;
ddf += temp3;
/* L40: */
}
f = *finit + *tau * fc;
erretm = (abs(*finit) + abs(*tau) * erretm) * 8. + abs(*tau) * df;
if (abs(f) <= eps * erretm) {
goto L60;
}
if (f <= 0.) {
lbd = *tau;
} else {
ubd = *tau;
}
/* L50: */
}
*info = 1;
L60:
/* Undo scaling */
if (scale) {
*tau *= sclinv;
}
return 0;
/* End of DLAED6 */
} /* dlaed6_ */
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