/* -- translated by f2c (version 20100827).
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
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*/
#include "f2c.h"
/* > \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.
=========== DOCUMENTATION ===========
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Definition:
===========
SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
DN2, G, TAU )
LOGICAL IEEE
INTEGER I0, ITER, N0, NDIV, NFAIL, PP
DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G,
$ QMAX, SIGMA, TAU
DOUBLE PRECISION Z( * )
> \par Purpose:
=============
>
> \verbatim
>
> DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
> In case of failure it changes shifts, and tries again until output
> is positive.
> \endverbatim
Arguments:
==========
> \param[in] I0
> \verbatim
> I0 is INTEGER
> First index.
> \endverbatim
>
> \param[in,out] N0
> \verbatim
> N0 is INTEGER
> Last index.
> \endverbatim
>
> \param[in] Z
> \verbatim
> Z is DOUBLE PRECISION array, dimension ( 4*N )
> Z holds the qd array.
> \endverbatim
>
> \param[in,out] PP
> \verbatim
> PP is INTEGER
> PP=0 for ping, PP=1 for pong.
> PP=2 indicates that flipping was applied to the Z array
> and that the initial tests for deflation should not be
> performed.
> \endverbatim
>
> \param[out] DMIN
> \verbatim
> DMIN is DOUBLE PRECISION
> Minimum value of d.
> \endverbatim
>
> \param[out] SIGMA
> \verbatim
> SIGMA is DOUBLE PRECISION
> Sum of shifts used in current segment.
> \endverbatim
>
> \param[in,out] DESIG
> \verbatim
> DESIG is DOUBLE PRECISION
> Lower order part of SIGMA
> \endverbatim
>
> \param[in] QMAX
> \verbatim
> QMAX is DOUBLE PRECISION
> Maximum value of q.
> \endverbatim
>
> \param[out] NFAIL
> \verbatim
> NFAIL is INTEGER
> Number of times shift was too big.
> \endverbatim
>
> \param[out] ITER
> \verbatim
> ITER is INTEGER
> Number of iterations.
> \endverbatim
>
> \param[out] NDIV
> \verbatim
> NDIV is INTEGER
> Number of divisions.
> \endverbatim
>
> \param[in] IEEE
> \verbatim
> IEEE is LOGICAL
> Flag for IEEE or non IEEE arithmetic (passed to DLASQ5).
> \endverbatim
>
> \param[in,out] TTYPE
> \verbatim
> TTYPE is INTEGER
> Shift type.
> \endverbatim
>
> \param[in,out] DMIN1
> \verbatim
> DMIN1 is DOUBLE PRECISION
> \endverbatim
>
> \param[in,out] DMIN2
> \verbatim
> DMIN2 is DOUBLE PRECISION
> \endverbatim
>
> \param[in,out] DN
> \verbatim
> DN is DOUBLE PRECISION
> \endverbatim
>
> \param[in,out] DN1
> \verbatim
> DN1 is DOUBLE PRECISION
> \endverbatim
>
> \param[in,out] DN2
> \verbatim
> DN2 is DOUBLE PRECISION
> \endverbatim
>
> \param[in,out] G
> \verbatim
> G is DOUBLE PRECISION
> \endverbatim
>
> \param[in,out] TAU
> \verbatim
> TAU is DOUBLE PRECISION
>
> These are passed as arguments in order to save their values
> between calls to DLASQ3.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup auxOTHERcomputational
=====================================================================
Subroutine */ int igraphdlasq3_(integer *i0, integer *n0, doublereal *z__,
integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
doublereal *qmax, integer *nfail, integer *iter, integer *ndiv,
logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2,
doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g,
doublereal *tau)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal s, t;
integer j4, nn;
doublereal eps, tol;
integer n0in, ipn4;
doublereal tol2, temp;
extern /* Subroutine */ int igraphdlasq4_(integer *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *), igraphdlasq5_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, logical *
, doublereal *), igraphdlasq6_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *);
extern doublereal igraphdlamch_(char *);
extern logical igraphdisnan_(doublereal *);
/* -- LAPACK computational routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
Parameter adjustments */
--z__;
/* Function Body */
n0in = *n0;
eps = igraphdlamch_("Precision");
tol = eps * 100.;
/* Computing 2nd power */
d__1 = tol;
tol2 = d__1 * d__1;
/* Check for deflation. */
L10:
if (*n0 < *i0) {
return 0;
}
if (*n0 == *i0) {
goto L20;
}
nn = (*n0 << 2) + *pp;
if (*n0 == *i0 + 1) {
goto L40;
}
/* Check whether E(N0-1) is negligible, 1 eigenvalue. */
if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) -
4] > tol2 * z__[nn - 7]) {
goto L30;
}
L20:
z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma;
--(*n0);
goto L10;
/* Check whether E(N0-2) is negligible, 2 eigenvalues. */
L30:
if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[
nn - 11]) {
goto L50;
}
L40:
if (z__[nn - 3] > z__[nn - 7]) {
s = z__[nn - 3];
z__[nn - 3] = z__[nn - 7];
z__[nn - 7] = s;
}
t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5;
if (z__[nn - 5] > z__[nn - 3] * tol2 && t != 0.) {
s = z__[nn - 3] * (z__[nn - 5] / t);
if (s <= t) {
s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.)));
} else {
s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s)));
}
t = z__[nn - 7] + (s + z__[nn - 5]);
z__[nn - 3] *= z__[nn - 7] / t;
z__[nn - 7] = t;
}
z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma;
z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma;
*n0 += -2;
goto L10;
L50:
if (*pp == 2) {
*pp = 0;
}
/* Reverse the qd-array, if warranted. */
if (*dmin__ <= 0. || *n0 < n0in) {
if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) {
ipn4 = *i0 + *n0 << 2;
i__1 = *i0 + *n0 - 1 << 1;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
temp = z__[j4 - 3];
z__[j4 - 3] = z__[ipn4 - j4 - 3];
z__[ipn4 - j4 - 3] = temp;
temp = z__[j4 - 2];
z__[j4 - 2] = z__[ipn4 - j4 - 2];
z__[ipn4 - j4 - 2] = temp;
temp = z__[j4 - 1];
z__[j4 - 1] = z__[ipn4 - j4 - 5];
z__[ipn4 - j4 - 5] = temp;
temp = z__[j4];
z__[j4] = z__[ipn4 - j4 - 4];
z__[ipn4 - j4 - 4] = temp;
/* L60: */
}
if (*n0 - *i0 <= 4) {
z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1];
z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp];
}
/* Computing MIN */
d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1];
*dmin2 = min(d__1,d__2);
/* Computing MIN */
d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1]
, d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3];
z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2);
/* Computing MIN */
d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 =
min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4];
z__[(*n0 << 2) - *pp] = min(d__1,d__2);
/* Computing MAX */
d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1,
d__2), d__2 = z__[(*i0 << 2) + *pp + 1];
*qmax = max(d__1,d__2);
*dmin__ = -0.;
}
}
/* Choose a shift. */
igraphdlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2,
tau, ttype, g);
/* Call dqds until DMIN > 0. */
L70:
igraphdlasq5_(i0, n0, &z__[1], pp, tau, sigma, dmin__, dmin1, dmin2, dn, dn1,
dn2, ieee, &eps);
*ndiv += *n0 - *i0 + 2;
++(*iter);
/* Check status. */
if (*dmin__ >= 0. && *dmin1 >= 0.) {
/* Success. */
goto L90;
} else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol
* (*sigma + *dn1) && abs(*dn) < tol * *sigma) {
/* Convergence hidden by negative DN. */
z__[(*n0 - 1 << 2) - *pp + 2] = 0.;
*dmin__ = 0.;
goto L90;
} else if (*dmin__ < 0.) {
/* TAU too big. Select new TAU and try again. */
++(*nfail);
if (*ttype < -22) {
/* Failed twice. Play it safe. */
*tau = 0.;
} else if (*dmin1 > 0.) {
/* Late failure. Gives excellent shift. */
*tau = (*tau + *dmin__) * (1. - eps * 2.);
*ttype += -11;
} else {
/* Early failure. Divide by 4. */
*tau *= .25;
*ttype += -12;
}
goto L70;
} else if (igraphdisnan_(dmin__)) {
/* NaN. */
if (*tau == 0.) {
goto L80;
} else {
*tau = 0.;
goto L70;
}
} else {
/* Possible underflow. Play it safe. */
goto L80;
}
/* Risk of underflow. */
L80:
igraphdlasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2);
*ndiv += *n0 - *i0 + 2;
++(*iter);
*tau = 0.;
L90:
if (*tau < *sigma) {
*desig += *tau;
t = *sigma + *desig;
*desig -= t - *sigma;
} else {
t = *sigma + *tau;
*desig = *sigma - (t - *tau) + *desig;
}
*sigma = t;
return 0;
/* End of DLASQ3 */
} /* igraphdlasq3_ */