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/* ../../../dependencies/lapack/src/slaic1.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"
/* Table of constant values */
static integer c__1 = 1;
static real c_b5 = 1.f;
/* Subroutine */ int slaic1_(integer *job, integer *j, real *x, real *sest,
real *w, real *gamma, real *sestpr, real *s, real *c__)
{
/* System generated locals */
real r__1, r__2, r__3, r__4;
/* Builtin functions */
double sqrt(doublereal), r_sign(real *, real *);
/* Local variables */
static real b, t, s1, s2, eps, tmp, sine;
extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
static real test, zeta1, zeta2, alpha, norma, absgam, absalp;
extern doublereal slamch_(char *, ftnlen);
static real cosine, absest;
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* October 31, 1992 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLAIC1 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 SLAIC1 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) REAL array, dimension (J) */
/* The j-vector x. */
/* SEST (input) REAL */
/* Estimated singular value of j by j matrix L */
/* W (input) REAL array, dimension (J) */
/* The j-vector w. */
/* GAMMA (input) REAL */
/* The diagonal element gamma. */
/* SESTPR (output) REAL */
/* Estimated singular value of (j+1) by (j+1) matrix Lhat. */
/* S (output) REAL */
/* Sine needed in forming xhat. */
/* C (output) REAL */
/* Cosine needed in forming xhat. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--w;
--x;
/* Function Body */
eps = slamch_("Epsilon", (ftnlen)7);
alpha = sdot_(j, &x[1], &c__1, &w[1], &c__1);
absalp = dabs(alpha);
absgam = dabs(*gamma);
absest = dabs(*sest);
if (*job == 1) {
/* Estimating largest singular value */
/* special cases */
if (*sest == 0.f) {
s1 = dmax(absgam,absalp);
if (s1 == 0.f) {
*s = 0.f;
*c__ = 1.f;
*sestpr = 0.f;
} 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.f;
*c__ = 0.f;
tmp = dmax(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.f;
*c__ = 0.f;
*sestpr = s2;
} else {
*s = 0.f;
*c__ = 1.f;
*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.f);
*sestpr = s2 * *s;
*c__ = *gamma / s2 / *s;
*s = r_sign(&c_b5, &alpha) / *s;
} else {
tmp = s2 / s1;
*c__ = sqrt(tmp * tmp + 1.f);
*sestpr = s1 * *c__;
*s = alpha / s1 / *c__;
*c__ = r_sign(&c_b5, gamma) / *c__;
}
return 0;
} else {
/* normal case */
zeta1 = alpha / absest;
zeta2 = *gamma / absest;
b = (1.f - zeta1 * zeta1 - zeta2 * zeta2) * .5f;
*c__ = zeta1 * zeta1;
if (b > 0.f) {
t = *c__ / (b + sqrt(b * b + *c__));
} else {
t = sqrt(b * b + *c__) - b;
}
sine = -zeta1 / t;
cosine = -zeta2 / (t + 1.f);
tmp = sqrt(sine * sine + cosine * cosine);
*s = sine / tmp;
*c__ = cosine / tmp;
*sestpr = sqrt(t + 1.f) * absest;
return 0;
}
} else if (*job == 2) {
/* Estimating smallest singular value */
/* special cases */
if (*sest == 0.f) {
*sestpr = 0.f;
if (dmax(absgam,absalp) == 0.f) {
sine = 1.f;
cosine = 0.f;
} else {
sine = -(*gamma);
cosine = alpha;
}
/* Computing MAX */
r__1 = dabs(sine), r__2 = dabs(cosine);
s1 = dmax(r__1,r__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.f;
*c__ = 1.f;
*sestpr = absgam;
return 0;
} else if (absalp <= eps * absest) {
s1 = absgam;
s2 = absest;
if (s1 <= s2) {
*s = 0.f;
*c__ = 1.f;
*sestpr = s1;
} else {
*s = 1.f;
*c__ = 0.f;
*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.f);
*sestpr = absest * (tmp / *c__);
*s = -(*gamma / s2) / *c__;
*c__ = r_sign(&c_b5, &alpha) / *c__;
} else {
tmp = s2 / s1;
*s = sqrt(tmp * tmp + 1.f);
*sestpr = absest / *s;
*c__ = alpha / s1 / *s;
*s = -r_sign(&c_b5, gamma) / *s;
}
return 0;
} else {
/* normal case */
zeta1 = alpha / absest;
zeta2 = *gamma / absest;
/* Computing MAX */
r__3 = zeta1 * zeta1 + 1.f + (r__1 = zeta1 * zeta2, dabs(r__1)),
r__4 = (r__2 = zeta1 * zeta2, dabs(r__2)) + zeta2 * zeta2;
norma = dmax(r__3,r__4);
/* See if root is closer to zero or to ONE */
test = (zeta1 - zeta2) * 2.f * (zeta1 + zeta2) + 1.f;
if (test >= 0.f) {
/* root is close to zero, compute directly */
b = (zeta1 * zeta1 + zeta2 * zeta2 + 1.f) * .5f;
*c__ = zeta2 * zeta2;
t = *c__ / (b + sqrt((r__1 = b * b - *c__, dabs(r__1))));
sine = zeta1 / (1.f - t);
cosine = -zeta2 / t;
*sestpr = sqrt(t + eps * 4.f * eps * norma) * absest;
} else {
/* root is closer to ONE, shift by that amount */
b = (zeta2 * zeta2 + zeta1 * zeta1 - 1.f) * .5f;
*c__ = zeta1 * zeta1;
if (b >= 0.f) {
t = -(*c__) / (b + sqrt(b * b + *c__));
} else {
t = b - sqrt(b * b + *c__);
}
sine = -zeta1 / t;
cosine = -zeta2 / (t + 1.f);
*sestpr = sqrt(t + 1.f + eps * 4.f * eps * norma) * absest;
}
tmp = sqrt(sine * sine + cosine * cosine);
*s = sine / tmp;
*c__ = cosine / tmp;
return 0;
}
}
return 0;
/* End of SLAIC1 */
} /* slaic1_ */
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