/* claic1.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;
/* Subroutine */ int claic1_(integer *job, integer *j, complex *x, real *sest,
complex *w, complex *gamma, real *sestpr, complex *s, complex *c__)
{
/* System generated locals */
real r__1, r__2;
complex q__1, q__2, q__3, q__4, q__5, q__6;
/* Builtin functions */
double c_abs(complex *);
void r_cnjg(complex *, complex *), c_sqrt(complex *, complex *);
double sqrt(doublereal);
void c_div(complex *, complex *, complex *);
/* Local variables */
real b, t, s1, s2, scl, eps, tmp;
complex sine;
real test, zeta1, zeta2;
complex alpha;
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
real norma, absgam, absalp;
extern doublereal slamch_(char *);
complex cosine;
real absest;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLAIC1 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 CLAIC1 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] * [ conjg(alpha) ] */
/* [ conjg(gamma) ] */
/* where alpha = conjg(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) COMPLEX array, dimension (J) */
/* The j-vector x. */
/* SEST (input) REAL */
/* Estimated singular value of j by j matrix L */
/* W (input) COMPLEX array, dimension (J) */
/* The j-vector w. */
/* GAMMA (input) COMPLEX */
/* The diagonal element gamma. */
/* SESTPR (output) REAL */
/* Estimated singular value of (j+1) by (j+1) matrix Lhat. */
/* S (output) COMPLEX */
/* Sine needed in forming xhat. */
/* C (output) COMPLEX */
/* Cosine needed in forming xhat. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--w;
--x;
/* Function Body */
eps = slamch_("Epsilon");
cdotc_(&q__1, j, &x[1], &c__1, &w[1], &c__1);
alpha.r = q__1.r, alpha.i = q__1.i;
absalp = c_abs(&alpha);
absgam = c_abs(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->r = 0.f, s->i = 0.f;
c__->r = 1.f, c__->i = 0.f;
*sestpr = 0.f;
} else {
q__1.r = alpha.r / s1, q__1.i = alpha.i / s1;
s->r = q__1.r, s->i = q__1.i;
q__1.r = gamma->r / s1, q__1.i = gamma->i / s1;
c__->r = q__1.r, c__->i = q__1.i;
r_cnjg(&q__4, s);
q__3.r = s->r * q__4.r - s->i * q__4.i, q__3.i = s->r *
q__4.i + s->i * q__4.r;
r_cnjg(&q__6, c__);
q__5.r = c__->r * q__6.r - c__->i * q__6.i, q__5.i = c__->r *
q__6.i + c__->i * q__6.r;
q__2.r = q__3.r + q__5.r, q__2.i = q__3.i + q__5.i;
c_sqrt(&q__1, &q__2);
tmp = q__1.r;
q__1.r = s->r / tmp, q__1.i = s->i / tmp;
s->r = q__1.r, s->i = q__1.i;
q__1.r = c__->r / tmp, q__1.i = c__->i / tmp;
c__->r = q__1.r, c__->i = q__1.i;
*sestpr = s1 * tmp;
}
return 0;
} else if (absgam <= eps * absest) {
s->r = 1.f, s->i = 0.f;
c__->r = 0.f, c__->i = 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->r = 1.f, s->i = 0.f;
c__->r = 0.f, c__->i = 0.f;
*sestpr = s2;
} else {
s->r = 0.f, s->i = 0.f;
c__->r = 1.f, c__->i = 0.f;
*sestpr = s1;
}
return 0;
} else if (absest <= eps * absalp || absest <= eps * absgam) {
s1 = absgam;
s2 = absalp;
if (s1 <= s2) {
tmp = s1 / s2;
scl = sqrt(tmp * tmp + 1.f);
*sestpr = s2 * scl;
q__2.r = alpha.r / s2, q__2.i = alpha.i / s2;
q__1.r = q__2.r / scl, q__1.i = q__2.i / scl;
s->r = q__1.r, s->i = q__1.i;
q__2.r = gamma->r / s2, q__2.i = gamma->i / s2;
q__1.r = q__2.r / scl, q__1.i = q__2.i / scl;
c__->r = q__1.r, c__->i = q__1.i;
} else {
tmp = s2 / s1;
scl = sqrt(tmp * tmp + 1.f);
*sestpr = s1 * scl;
q__2.r = alpha.r / s1, q__2.i = alpha.i / s1;
q__1.r = q__2.r / scl, q__1.i = q__2.i / scl;
s->r = q__1.r, s->i = q__1.i;
q__2.r = gamma->r / s1, q__2.i = gamma->i / s1;
q__1.r = q__2.r / scl, q__1.i = q__2.i / scl;
c__->r = q__1.r, c__->i = q__1.i;
}
return 0;
} else {
/* normal case */
zeta1 = absalp / absest;
zeta2 = absgam / absest;
b = (1.f - zeta1 * zeta1 - zeta2 * zeta2) * .5f;
r__1 = zeta1 * zeta1;
c__->r = r__1, c__->i = 0.f;
if (b > 0.f) {
r__1 = b * b;
q__4.r = r__1 + c__->r, q__4.i = c__->i;
c_sqrt(&q__3, &q__4);
q__2.r = b + q__3.r, q__2.i = q__3.i;
c_div(&q__1, c__, &q__2);
t = q__1.r;
} else {
r__1 = b * b;
q__3.r = r__1 + c__->r, q__3.i = c__->i;
c_sqrt(&q__2, &q__3);
q__1.r = q__2.r - b, q__1.i = q__2.i;
t = q__1.r;
}
q__3.r = alpha.r / absest, q__3.i = alpha.i / absest;
q__2.r = -q__3.r, q__2.i = -q__3.i;
q__1.r = q__2.r / t, q__1.i = q__2.i / t;
sine.r = q__1.r, sine.i = q__1.i;
q__3.r = gamma->r / absest, q__3.i = gamma->i / absest;
q__2.r = -q__3.r, q__2.i = -q__3.i;
r__1 = t + 1.f;
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
cosine.r = q__1.r, cosine.i = q__1.i;
r_cnjg(&q__4, &sine);
q__3.r = sine.r * q__4.r - sine.i * q__4.i, q__3.i = sine.r *
q__4.i + sine.i * q__4.r;
r_cnjg(&q__6, &cosine);
q__5.r = cosine.r * q__6.r - cosine.i * q__6.i, q__5.i = cosine.r
* q__6.i + cosine.i * q__6.r;
q__2.r = q__3.r + q__5.r, q__2.i = q__3.i + q__5.i;
c_sqrt(&q__1, &q__2);
tmp = q__1.r;
q__1.r = sine.r / tmp, q__1.i = sine.i / tmp;
s->r = q__1.r, s->i = q__1.i;
q__1.r = cosine.r / tmp, q__1.i = cosine.i / tmp;
c__->r = q__1.r, c__->i = q__1.i;
*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.r = 1.f, sine.i = 0.f;
cosine.r = 0.f, cosine.i = 0.f;
} else {
r_cnjg(&q__2, gamma);
q__1.r = -q__2.r, q__1.i = -q__2.i;
sine.r = q__1.r, sine.i = q__1.i;
r_cnjg(&q__1, &alpha);
cosine.r = q__1.r, cosine.i = q__1.i;
}
/* Computing MAX */
r__1 = c_abs(&sine), r__2 = c_abs(&cosine);
s1 = dmax(r__1,r__2);
q__1.r = sine.r / s1, q__1.i = sine.i / s1;
s->r = q__1.r, s->i = q__1.i;
q__1.r = cosine.r / s1, q__1.i = cosine.i / s1;
c__->r = q__1.r, c__->i = q__1.i;
r_cnjg(&q__4, s);
q__3.r = s->r * q__4.r - s->i * q__4.i, q__3.i = s->r * q__4.i +
s->i * q__4.r;
r_cnjg(&q__6, c__);
q__5.r = c__->r * q__6.r - c__->i * q__6.i, q__5.i = c__->r *
q__6.i + c__->i * q__6.r;
q__2.r = q__3.r + q__5.r, q__2.i = q__3.i + q__5.i;
c_sqrt(&q__1, &q__2);
tmp = q__1.r;
q__1.r = s->r / tmp, q__1.i = s->i / tmp;
s->r = q__1.r, s->i = q__1.i;
q__1.r = c__->r / tmp, q__1.i = c__->i / tmp;
c__->r = q__1.r, c__->i = q__1.i;
return 0;
} else if (absgam <= eps * absest) {
s->r = 0.f, s->i = 0.f;
c__->r = 1.f, c__->i = 0.f;
*sestpr = absgam;
return 0;
} else if (absalp <= eps * absest) {
s1 = absgam;
s2 = absest;
if (s1 <= s2) {
s->r = 0.f, s->i = 0.f;
c__->r = 1.f, c__->i = 0.f;
*sestpr = s1;
} else {
s->r = 1.f, s->i = 0.f;
c__->r = 0.f, c__->i = 0.f;
*sestpr = s2;
}
return 0;
} else if (absest <= eps * absalp || absest <= eps * absgam) {
s1 = absgam;
s2 = absalp;
if (s1 <= s2) {
tmp = s1 / s2;
scl = sqrt(tmp * tmp + 1.f);
*sestpr = absest * (tmp / scl);
r_cnjg(&q__4, gamma);
q__3.r = q__4.r / s2, q__3.i = q__4.i / s2;
q__2.r = -q__3.r, q__2.i = -q__3.i;
q__1.r = q__2.r / scl, q__1.i = q__2.i / scl;
s->r = q__1.r, s->i = q__1.i;
r_cnjg(&q__3, &alpha);
q__2.r = q__3.r / s2, q__2.i = q__3.i / s2;
q__1.r = q__2.r / scl, q__1.i = q__2.i / scl;
c__->r = q__1.r, c__->i = q__1.i;
} else {
tmp = s2 / s1;
scl = sqrt(tmp * tmp + 1.f);
*sestpr = absest / scl;
r_cnjg(&q__4, gamma);
q__3.r = q__4.r / s1, q__3.i = q__4.i / s1;
q__2.r = -q__3.r, q__2.i = -q__3.i;
q__1.r = q__2.r / scl, q__1.i = q__2.i / scl;
s->r = q__1.r, s->i = q__1.i;
r_cnjg(&q__3, &alpha);
q__2.r = q__3.r / s1, q__2.i = q__3.i / s1;
q__1.r = q__2.r / scl, q__1.i = q__2.i / scl;
c__->r = q__1.r, c__->i = q__1.i;
}
return 0;
} else {
/* normal case */
zeta1 = absalp / absest;
zeta2 = absgam / absest;
/* Computing MAX */
r__1 = zeta1 * zeta1 + 1.f + zeta1 * zeta2, r__2 = zeta1 * zeta2
+ zeta2 * zeta2;
norma = dmax(r__1,r__2);
/* 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;
r__1 = zeta2 * zeta2;
c__->r = r__1, c__->i = 0.f;
r__2 = b * b;
q__2.r = r__2 - c__->r, q__2.i = -c__->i;
r__1 = b + sqrt(c_abs(&q__2));
q__1.r = c__->r / r__1, q__1.i = c__->i / r__1;
t = q__1.r;
q__2.r = alpha.r / absest, q__2.i = alpha.i / absest;
r__1 = 1.f - t;
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
sine.r = q__1.r, sine.i = q__1.i;
q__3.r = gamma->r / absest, q__3.i = gamma->i / absest;
q__2.r = -q__3.r, q__2.i = -q__3.i;
q__1.r = q__2.r / t, q__1.i = q__2.i / t;
cosine.r = q__1.r, cosine.i = q__1.i;
*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;
r__1 = zeta1 * zeta1;
c__->r = r__1, c__->i = 0.f;
if (b >= 0.f) {
q__2.r = -c__->r, q__2.i = -c__->i;
r__1 = b * b;
q__5.r = r__1 + c__->r, q__5.i = c__->i;
c_sqrt(&q__4, &q__5);
q__3.r = b + q__4.r, q__3.i = q__4.i;
c_div(&q__1, &q__2, &q__3);
t = q__1.r;
} else {
r__1 = b * b;
q__3.r = r__1 + c__->r, q__3.i = c__->i;
c_sqrt(&q__2, &q__3);
q__1.r = b - q__2.r, q__1.i = -q__2.i;
t = q__1.r;
}
q__3.r = alpha.r / absest, q__3.i = alpha.i / absest;
q__2.r = -q__3.r, q__2.i = -q__3.i;
q__1.r = q__2.r / t, q__1.i = q__2.i / t;
sine.r = q__1.r, sine.i = q__1.i;
q__3.r = gamma->r / absest, q__3.i = gamma->i / absest;
q__2.r = -q__3.r, q__2.i = -q__3.i;
r__1 = t + 1.f;
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
cosine.r = q__1.r, cosine.i = q__1.i;
*sestpr = sqrt(t + 1.f + eps * 4.f * eps * norma) * absest;
}
r_cnjg(&q__4, &sine);
q__3.r = sine.r * q__4.r - sine.i * q__4.i, q__3.i = sine.r *
q__4.i + sine.i * q__4.r;
r_cnjg(&q__6, &cosine);
q__5.r = cosine.r * q__6.r - cosine.i * q__6.i, q__5.i = cosine.r
* q__6.i + cosine.i * q__6.r;
q__2.r = q__3.r + q__5.r, q__2.i = q__3.i + q__5.i;
c_sqrt(&q__1, &q__2);
tmp = q__1.r;
q__1.r = sine.r / tmp, q__1.i = sine.i / tmp;
s->r = q__1.r, s->i = q__1.i;
q__1.r = cosine.r / tmp, q__1.i = cosine.i / tmp;
c__->r = q__1.r, c__->i = q__1.i;
return 0;
}
}
return 0;
/* End of CLAIC1 */
} /* claic1_ */