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hypre/lapack/dlasq3.c
hill66 402d34179c Updated license info.
2006-09-22 22:06:21 +00:00

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/*BHEADER**********************************************************************
* Copyright (c) 2006 The Regents of the University of California.
* Produced at the Lawrence Livermore National Laboratory.
* Written by the HYPRE team. UCRL-CODE-222953.
* All rights reserved.
*
* This file is part of HYPRE (see http://www.llnl.gov/CASC/hypre/).
* Please see the COPYRIGHT_and_LICENSE file for the copyright notice,
* disclaimer, contact information and the GNU Lesser General Public License.
*
* HYPRE is free software; you can redistribute it and/or modify it under the
* terms of the GNU General Public License (as published by the Free Software
* Foundation) version 2.1 dated February 1999.
*
* HYPRE is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the IMPLIED WARRANTY OF MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the terms and conditions of the GNU General
* Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* $Revision$
***********************************************************************EHEADER*/
#include "hypre_lapack.h"
#include "f2c.h"
/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__,
integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
doublereal *qmax, integer *nfail, integer *iter, integer *ndiv,
logical *ieee)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
May 17, 2000
Purpose
=======
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.
Arguments
=========
I0 (input) INTEGER
First index.
N0 (input) INTEGER
Last index.
Z (input) DOUBLE PRECISION array, dimension ( 4*N )
Z holds the qd array.
PP (input) INTEGER
PP=0 for ping, PP=1 for pong.
DMIN (output) DOUBLE PRECISION
Minimum value of d.
SIGMA (output) DOUBLE PRECISION
Sum of shifts used in current segment.
DESIG (input/output) DOUBLE PRECISION
Lower order part of SIGMA
QMAX (input) DOUBLE PRECISION
Maximum value of q.
NFAIL (output) INTEGER
Number of times shift was too big.
ITER (output) INTEGER
Number of iterations.
NDIV (output) INTEGER
Number of divisions.
TTYPE (output) INTEGER
Shift type.
IEEE (input) LOGICAL
Flag for IEEE or non IEEE arithmetic (passed to DLASQ5).
=====================================================================
Parameter adjustments */
/* Initialized data */
static integer ttype = 0;
static doublereal dmin1 = 0.;
static doublereal dmin2 = 0.;
static doublereal dn = 0.;
static doublereal dn1 = 0.;
static doublereal dn2 = 0.;
static doublereal tau = 0.;
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static doublereal temp, s, t;
static integer j4;
extern /* Subroutine */ int dlasq4_(integer *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *)
, dlasq5_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, logical *), dlasq6_(
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
extern doublereal dlamch_(char *);
static integer nn;
static doublereal safmin, eps, tol;
static integer n0in, ipn4;
static doublereal tol2;
--z__;
/* Function Body */
n0in = *n0;
eps = dlamch_("Precision");
safmin = dlamch_("Safe minimum");
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;
}
if (z__[nn - 5] > z__[nn - 3] * tol2) {
t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5;
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:
/* 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.;
}
}
/* L70:
Computing MIN */
d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*n0 << 2) + *pp - 9], d__1 =
min(d__1,d__2), d__2 = dmin2 + z__[(*n0 << 2) - *pp];
if (*dmin__ < 0. || safmin * *qmax < min(d__1,d__2)) {
/* Choose a shift. */
dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, &dmin1, &dmin2, &dn, &dn1,
&dn2, &tau, &ttype);
/* Call dqds until DMIN > 0. */
L80:
dlasq5_(i0, n0, &z__[1], pp, &tau, dmin__, &dmin1, &dmin2, &dn, &dn1,
&dn2, ieee);
*ndiv += *n0 - *i0 + 2;
++(*iter);
/* Check status. */
if (*dmin__ >= 0. && dmin1 > 0.) {
/* Success. */
goto L100;
} 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 L100;
} 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 L80;
} else if (*dmin__ != *dmin__) {
/* NaN. */
tau = 0.;
goto L80;
} else {
/* Possible underflow. Play it safe. */
goto L90;
}
}
/* Risk of underflow. */
L90:
dlasq6_(i0, n0, &z__[1], pp, dmin__, &dmin1, &dmin2, &dn, &dn1, &dn2);
*ndiv += *n0 - *i0 + 2;
++(*iter);
tau = 0.;
L100:
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 */
} /* dlasq3_ */
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