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/* zlaic1.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 zlaic1_(integer *job, integer *j, doublecomplex *x,
doublereal *sest, doublecomplex *w, doublecomplex *gamma, doublereal *
sestpr, doublecomplex *s, doublecomplex *c__)
{
/* System generated locals */
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6;
/* Builtin functions */
double z_abs(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *), z_sqrt(doublecomplex *,
doublecomplex *);
double sqrt(doublereal);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
doublereal b, t, s1, s2, scl, eps, tmp;
doublecomplex sine;
doublereal test, zeta1, zeta2;
doublecomplex alpha;
doublereal norma;
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern doublereal dlamch_(char *);
doublereal absgam, absalp;
doublecomplex cosine;
doublereal absest;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLAIC1 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 ZLAIC1 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*16 array, dimension (J) */
/* The j-vector x. */
/* SEST (input) DOUBLE PRECISION */
/* Estimated singular value of j by j matrix L */
/* W (input) COMPLEX*16 array, dimension (J) */
/* The j-vector w. */
/* GAMMA (input) COMPLEX*16 */
/* The diagonal element gamma. */
/* SESTPR (output) DOUBLE PRECISION */
/* Estimated singular value of (j+1) by (j+1) matrix Lhat. */
/* S (output) COMPLEX*16 */
/* Sine needed in forming xhat. */
/* C (output) COMPLEX*16 */
/* Cosine needed in forming xhat. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--w;
--x;
/* Function Body */
eps = dlamch_("Epsilon");
zdotc_(&z__1, j, &x[1], &c__1, &w[1], &c__1);
alpha.r = z__1.r, alpha.i = z__1.i;
absalp = z_abs(&alpha);
absgam = z_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->r = 0., s->i = 0.;
c__->r = 1., c__->i = 0.;
*sestpr = 0.;
} else {
z__1.r = alpha.r / s1, z__1.i = alpha.i / s1;
s->r = z__1.r, s->i = z__1.i;
z__1.r = gamma->r / s1, z__1.i = gamma->i / s1;
c__->r = z__1.r, c__->i = z__1.i;
d_cnjg(&z__4, s);
z__3.r = s->r * z__4.r - s->i * z__4.i, z__3.i = s->r *
z__4.i + s->i * z__4.r;
d_cnjg(&z__6, c__);
z__5.r = c__->r * z__6.r - c__->i * z__6.i, z__5.i = c__->r *
z__6.i + c__->i * z__6.r;
z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i;
z_sqrt(&z__1, &z__2);
tmp = z__1.r;
z__1.r = s->r / tmp, z__1.i = s->i / tmp;
s->r = z__1.r, s->i = z__1.i;
z__1.r = c__->r / tmp, z__1.i = c__->i / tmp;
c__->r = z__1.r, c__->i = z__1.i;
*sestpr = s1 * tmp;
}
return 0;
} else if (absgam <= eps * absest) {
s->r = 1., s->i = 0.;
c__->r = 0., c__->i = 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->r = 1., s->i = 0.;
c__->r = 0., c__->i = 0.;
*sestpr = s2;
} else {
s->r = 0., s->i = 0.;
c__->r = 1., c__->i = 0.;
*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.);
*sestpr = s2 * scl;
z__2.r = alpha.r / s2, z__2.i = alpha.i / s2;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
s->r = z__1.r, s->i = z__1.i;
z__2.r = gamma->r / s2, z__2.i = gamma->i / s2;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
c__->r = z__1.r, c__->i = z__1.i;
} else {
tmp = s2 / s1;
scl = sqrt(tmp * tmp + 1.);
*sestpr = s1 * scl;
z__2.r = alpha.r / s1, z__2.i = alpha.i / s1;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
s->r = z__1.r, s->i = z__1.i;
z__2.r = gamma->r / s1, z__2.i = gamma->i / s1;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
c__->r = z__1.r, c__->i = z__1.i;
}
return 0;
} else {
/* normal case */
zeta1 = absalp / absest;
zeta2 = absgam / absest;
b = (1. - zeta1 * zeta1 - zeta2 * zeta2) * .5;
d__1 = zeta1 * zeta1;
c__->r = d__1, c__->i = 0.;
if (b > 0.) {
d__1 = b * b;
z__4.r = d__1 + c__->r, z__4.i = c__->i;
z_sqrt(&z__3, &z__4);
z__2.r = b + z__3.r, z__2.i = z__3.i;
z_div(&z__1, c__, &z__2);
t = z__1.r;
} else {
d__1 = b * b;
z__3.r = d__1 + c__->r, z__3.i = c__->i;
z_sqrt(&z__2, &z__3);
z__1.r = z__2.r - b, z__1.i = z__2.i;
t = z__1.r;
}
z__3.r = alpha.r / absest, z__3.i = alpha.i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / t, z__1.i = z__2.i / t;
sine.r = z__1.r, sine.i = z__1.i;
z__3.r = gamma->r / absest, z__3.i = gamma->i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
d__1 = t + 1.;
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
cosine.r = z__1.r, cosine.i = z__1.i;
d_cnjg(&z__4, &sine);
z__3.r = sine.r * z__4.r - sine.i * z__4.i, z__3.i = sine.r *
z__4.i + sine.i * z__4.r;
d_cnjg(&z__6, &cosine);
z__5.r = cosine.r * z__6.r - cosine.i * z__6.i, z__5.i = cosine.r
* z__6.i + cosine.i * z__6.r;
z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i;
z_sqrt(&z__1, &z__2);
tmp = z__1.r;
z__1.r = sine.r / tmp, z__1.i = sine.i / tmp;
s->r = z__1.r, s->i = z__1.i;
z__1.r = cosine.r / tmp, z__1.i = cosine.i / tmp;
c__->r = z__1.r, c__->i = z__1.i;
*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.r = 1., sine.i = 0.;
cosine.r = 0., cosine.i = 0.;
} else {
d_cnjg(&z__2, gamma);
z__1.r = -z__2.r, z__1.i = -z__2.i;
sine.r = z__1.r, sine.i = z__1.i;
d_cnjg(&z__1, &alpha);
cosine.r = z__1.r, cosine.i = z__1.i;
}
/* Computing MAX */
d__1 = z_abs(&sine), d__2 = z_abs(&cosine);
s1 = max(d__1,d__2);
z__1.r = sine.r / s1, z__1.i = sine.i / s1;
s->r = z__1.r, s->i = z__1.i;
z__1.r = cosine.r / s1, z__1.i = cosine.i / s1;
c__->r = z__1.r, c__->i = z__1.i;
d_cnjg(&z__4, s);
z__3.r = s->r * z__4.r - s->i * z__4.i, z__3.i = s->r * z__4.i +
s->i * z__4.r;
d_cnjg(&z__6, c__);
z__5.r = c__->r * z__6.r - c__->i * z__6.i, z__5.i = c__->r *
z__6.i + c__->i * z__6.r;
z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i;
z_sqrt(&z__1, &z__2);
tmp = z__1.r;
z__1.r = s->r / tmp, z__1.i = s->i / tmp;
s->r = z__1.r, s->i = z__1.i;
z__1.r = c__->r / tmp, z__1.i = c__->i / tmp;
c__->r = z__1.r, c__->i = z__1.i;
return 0;
} else if (absgam <= eps * absest) {
s->r = 0., s->i = 0.;
c__->r = 1., c__->i = 0.;
*sestpr = absgam;
return 0;
} else if (absalp <= eps * absest) {
s1 = absgam;
s2 = absest;
if (s1 <= s2) {
s->r = 0., s->i = 0.;
c__->r = 1., c__->i = 0.;
*sestpr = s1;
} else {
s->r = 1., s->i = 0.;
c__->r = 0., c__->i = 0.;
*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.);
*sestpr = absest * (tmp / scl);
d_cnjg(&z__4, gamma);
z__3.r = z__4.r / s2, z__3.i = z__4.i / s2;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
s->r = z__1.r, s->i = z__1.i;
d_cnjg(&z__3, &alpha);
z__2.r = z__3.r / s2, z__2.i = z__3.i / s2;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
c__->r = z__1.r, c__->i = z__1.i;
} else {
tmp = s2 / s1;
scl = sqrt(tmp * tmp + 1.);
*sestpr = absest / scl;
d_cnjg(&z__4, gamma);
z__3.r = z__4.r / s1, z__3.i = z__4.i / s1;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
s->r = z__1.r, s->i = z__1.i;
d_cnjg(&z__3, &alpha);
z__2.r = z__3.r / s1, z__2.i = z__3.i / s1;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
c__->r = z__1.r, c__->i = z__1.i;
}
return 0;
} else {
/* normal case */
zeta1 = absalp / absest;
zeta2 = absgam / absest;
/* Computing MAX */
d__1 = zeta1 * zeta1 + 1. + zeta1 * zeta2, d__2 = zeta1 * zeta2 +
zeta2 * zeta2;
norma = max(d__1,d__2);
/* 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;
d__1 = zeta2 * zeta2;
c__->r = d__1, c__->i = 0.;
d__2 = b * b;
z__2.r = d__2 - c__->r, z__2.i = -c__->i;
d__1 = b + sqrt(z_abs(&z__2));
z__1.r = c__->r / d__1, z__1.i = c__->i / d__1;
t = z__1.r;
z__2.r = alpha.r / absest, z__2.i = alpha.i / absest;
d__1 = 1. - t;
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
sine.r = z__1.r, sine.i = z__1.i;
z__3.r = gamma->r / absest, z__3.i = gamma->i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / t, z__1.i = z__2.i / t;
cosine.r = z__1.r, cosine.i = z__1.i;
*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;
d__1 = zeta1 * zeta1;
c__->r = d__1, c__->i = 0.;
if (b >= 0.) {
z__2.r = -c__->r, z__2.i = -c__->i;
d__1 = b * b;
z__5.r = d__1 + c__->r, z__5.i = c__->i;
z_sqrt(&z__4, &z__5);
z__3.r = b + z__4.r, z__3.i = z__4.i;
z_div(&z__1, &z__2, &z__3);
t = z__1.r;
} else {
d__1 = b * b;
z__3.r = d__1 + c__->r, z__3.i = c__->i;
z_sqrt(&z__2, &z__3);
z__1.r = b - z__2.r, z__1.i = -z__2.i;
t = z__1.r;
}
z__3.r = alpha.r / absest, z__3.i = alpha.i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / t, z__1.i = z__2.i / t;
sine.r = z__1.r, sine.i = z__1.i;
z__3.r = gamma->r / absest, z__3.i = gamma->i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
d__1 = t + 1.;
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
cosine.r = z__1.r, cosine.i = z__1.i;
*sestpr = sqrt(t + 1. + eps * 4. * eps * norma) * absest;
}
d_cnjg(&z__4, &sine);
z__3.r = sine.r * z__4.r - sine.i * z__4.i, z__3.i = sine.r *
z__4.i + sine.i * z__4.r;
d_cnjg(&z__6, &cosine);
z__5.r = cosine.r * z__6.r - cosine.i * z__6.i, z__5.i = cosine.r
* z__6.i + cosine.i * z__6.r;
z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i;
z_sqrt(&z__1, &z__2);
tmp = z__1.r;
z__1.r = sine.r / tmp, z__1.i = sine.i / tmp;
s->r = z__1.r, s->i = z__1.i;
z__1.r = cosine.r / tmp, z__1.i = cosine.i / tmp;
c__->r = z__1.r, c__->i = z__1.i;
return 0;
}
}
return 0;
/* End of ZLAIC1 */
} /* zlaic1_ */
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