/* 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_ */
