410 lines
9.4 KiB
C
410 lines
9.4 KiB
C
/*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"
|
|
/* -- translated by f2c (version 19990503).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
#include "f2c.h"
|
|
|
|
/* Subroutine */ int dlasq4_(integer *i0, integer *n0, doublereal *z__,
|
|
integer *pp, integer *n0in, doublereal *dmin__, doublereal *dmin1,
|
|
doublereal *dmin2, doublereal *dn, doublereal *dn1, doublereal *dn2,
|
|
doublereal *tau, integer *ttype)
|
|
{
|
|
/* Initialized data */
|
|
|
|
static doublereal g = 0.;
|
|
|
|
/* System generated locals */
|
|
integer i__1;
|
|
doublereal d__1, d__2;
|
|
|
|
/* Builtin functions */
|
|
double sqrt(doublereal);
|
|
|
|
/* Local variables */
|
|
static doublereal s, a2, b1, b2;
|
|
static integer i4, nn, np;
|
|
static doublereal gam, gap1, gap2;
|
|
|
|
|
|
/* -- 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, 1999
|
|
|
|
|
|
Purpose
|
|
=======
|
|
|
|
DLASQ4 computes an approximation TAU to the smallest eigenvalue
|
|
using values of d from the previous transform.
|
|
|
|
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.
|
|
|
|
NOIN (input) INTEGER
|
|
The value of N0 at start of EIGTEST.
|
|
|
|
DMIN (input) DOUBLE PRECISION
|
|
Minimum value of d.
|
|
|
|
DMIN1 (input) DOUBLE PRECISION
|
|
Minimum value of d, excluding D( N0 ).
|
|
|
|
DMIN2 (input) DOUBLE PRECISION
|
|
Minimum value of d, excluding D( N0 ) and D( N0-1 ).
|
|
|
|
DN (input) DOUBLE PRECISION
|
|
d(N)
|
|
|
|
DN1 (input) DOUBLE PRECISION
|
|
d(N-1)
|
|
|
|
DN2 (input) DOUBLE PRECISION
|
|
d(N-2)
|
|
|
|
TAU (output) DOUBLE PRECISION
|
|
This is the shift.
|
|
|
|
TTYPE (output) INTEGER
|
|
Shift type.
|
|
|
|
Further Details
|
|
===============
|
|
CNST1 = 9/16
|
|
|
|
=====================================================================
|
|
|
|
Parameter adjustments */
|
|
--z__;
|
|
|
|
/* Function Body
|
|
|
|
A negative DMIN forces the shift to take that absolute value
|
|
TTYPE records the type of shift. */
|
|
|
|
if (*dmin__ <= 0.) {
|
|
*tau = -(*dmin__);
|
|
*ttype = -1;
|
|
return 0;
|
|
}
|
|
|
|
nn = (*n0 << 2) + *pp;
|
|
if (*n0in == *n0) {
|
|
|
|
/* No eigenvalues deflated. */
|
|
|
|
if (*dmin__ == *dn || *dmin__ == *dn1) {
|
|
|
|
b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]);
|
|
b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]);
|
|
a2 = z__[nn - 7] + z__[nn - 5];
|
|
|
|
/* Cases 2 and 3. */
|
|
|
|
if (*dmin__ == *dn && *dmin1 == *dn1) {
|
|
gap2 = *dmin2 - a2 - *dmin2 * .25;
|
|
if (gap2 > 0. && gap2 > b2) {
|
|
gap1 = a2 - *dn - b2 / gap2 * b2;
|
|
} else {
|
|
gap1 = a2 - *dn - (b1 + b2);
|
|
}
|
|
if (gap1 > 0. && gap1 > b1) {
|
|
/* Computing MAX */
|
|
d__1 = *dn - b1 / gap1 * b1, d__2 = *dmin__ * .5;
|
|
s = max(d__1,d__2);
|
|
*ttype = -2;
|
|
} else {
|
|
s = 0.;
|
|
if (*dn > b1) {
|
|
s = *dn - b1;
|
|
}
|
|
if (a2 > b1 + b2) {
|
|
/* Computing MIN */
|
|
d__1 = s, d__2 = a2 - (b1 + b2);
|
|
s = min(d__1,d__2);
|
|
}
|
|
/* Computing MAX */
|
|
d__1 = s, d__2 = *dmin__ * .333;
|
|
s = max(d__1,d__2);
|
|
*ttype = -3;
|
|
}
|
|
} else {
|
|
|
|
/* Case 4. */
|
|
|
|
*ttype = -4;
|
|
s = *dmin__ * .25;
|
|
if (*dmin__ == *dn) {
|
|
gam = *dn;
|
|
a2 = 0.;
|
|
if (z__[nn - 5] > z__[nn - 7]) {
|
|
return 0;
|
|
}
|
|
b2 = z__[nn - 5] / z__[nn - 7];
|
|
np = nn - 9;
|
|
} else {
|
|
np = nn - (*pp << 1);
|
|
b2 = z__[np - 2];
|
|
gam = *dn1;
|
|
if (z__[np - 4] > z__[np - 2]) {
|
|
return 0;
|
|
}
|
|
a2 = z__[np - 4] / z__[np - 2];
|
|
if (z__[nn - 9] > z__[nn - 11]) {
|
|
return 0;
|
|
}
|
|
b2 = z__[nn - 9] / z__[nn - 11];
|
|
np = nn - 13;
|
|
}
|
|
|
|
/* Approximate contribution to norm squared from I < NN-1. */
|
|
|
|
a2 += b2;
|
|
i__1 = (*i0 << 2) - 1 + *pp;
|
|
for (i4 = np; i4 >= i__1; i4 += -4) {
|
|
if (b2 == 0.) {
|
|
goto L20;
|
|
}
|
|
b1 = b2;
|
|
if (z__[i4] > z__[i4 - 2]) {
|
|
return 0;
|
|
}
|
|
b2 *= z__[i4] / z__[i4 - 2];
|
|
a2 += b2;
|
|
if (max(b2,b1) * 100. < a2 || .563 < a2) {
|
|
goto L20;
|
|
}
|
|
/* L10: */
|
|
}
|
|
L20:
|
|
a2 *= 1.05;
|
|
|
|
/* Rayleigh quotient residual bound. */
|
|
|
|
if (a2 < .563) {
|
|
s = gam * (1. - sqrt(a2)) / (a2 + 1.);
|
|
}
|
|
}
|
|
} else if (*dmin__ == *dn2) {
|
|
|
|
/* Case 5. */
|
|
|
|
*ttype = -5;
|
|
s = *dmin__ * .25;
|
|
|
|
/* Compute contribution to norm squared from I > NN-2. */
|
|
|
|
np = nn - (*pp << 1);
|
|
b1 = z__[np - 2];
|
|
b2 = z__[np - 6];
|
|
gam = *dn2;
|
|
if (z__[np - 8] > b2 || z__[np - 4] > b1) {
|
|
return 0;
|
|
}
|
|
a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.);
|
|
|
|
/* Approximate contribution to norm squared from I < NN-2. */
|
|
|
|
if (*n0 - *i0 > 2) {
|
|
b2 = z__[nn - 13] / z__[nn - 15];
|
|
a2 += b2;
|
|
i__1 = (*i0 << 2) - 1 + *pp;
|
|
for (i4 = nn - 17; i4 >= i__1; i4 += -4) {
|
|
if (b2 == 0.) {
|
|
goto L40;
|
|
}
|
|
b1 = b2;
|
|
if (z__[i4] > z__[i4 - 2]) {
|
|
return 0;
|
|
}
|
|
b2 *= z__[i4] / z__[i4 - 2];
|
|
a2 += b2;
|
|
if (max(b2,b1) * 100. < a2 || .563 < a2) {
|
|
goto L40;
|
|
}
|
|
/* L30: */
|
|
}
|
|
L40:
|
|
a2 *= 1.05;
|
|
}
|
|
|
|
if (a2 < .563) {
|
|
s = gam * (1. - sqrt(a2)) / (a2 + 1.);
|
|
}
|
|
} else {
|
|
|
|
/* Case 6, no information to guide us. */
|
|
|
|
if (*ttype == -6) {
|
|
g += (1. - g) * .333;
|
|
} else if (*ttype == -18) {
|
|
g = .083250000000000005;
|
|
} else {
|
|
g = .25;
|
|
}
|
|
s = g * *dmin__;
|
|
*ttype = -6;
|
|
}
|
|
|
|
} else if (*n0in == *n0 + 1) {
|
|
|
|
/* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */
|
|
|
|
if (*dmin1 == *dn1 && *dmin2 == *dn2) {
|
|
|
|
/* Cases 7 and 8. */
|
|
|
|
*ttype = -7;
|
|
s = *dmin1 * .333;
|
|
if (z__[nn - 5] > z__[nn - 7]) {
|
|
return 0;
|
|
}
|
|
b1 = z__[nn - 5] / z__[nn - 7];
|
|
b2 = b1;
|
|
if (b2 == 0.) {
|
|
goto L60;
|
|
}
|
|
i__1 = (*i0 << 2) - 1 + *pp;
|
|
for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
|
|
a2 = b1;
|
|
if (z__[i4] > z__[i4 - 2]) {
|
|
return 0;
|
|
}
|
|
b1 *= z__[i4] / z__[i4 - 2];
|
|
b2 += b1;
|
|
if (max(b1,a2) * 100. < b2) {
|
|
goto L60;
|
|
}
|
|
/* L50: */
|
|
}
|
|
L60:
|
|
b2 = sqrt(b2 * 1.05);
|
|
/* Computing 2nd power */
|
|
d__1 = b2;
|
|
a2 = *dmin1 / (d__1 * d__1 + 1.);
|
|
gap2 = *dmin2 * .5 - a2;
|
|
if (gap2 > 0. && gap2 > b2 * a2) {
|
|
/* Computing MAX */
|
|
d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2);
|
|
s = max(d__1,d__2);
|
|
} else {
|
|
/* Computing MAX */
|
|
d__1 = s, d__2 = a2 * (1. - b2 * 1.01);
|
|
s = max(d__1,d__2);
|
|
*ttype = -8;
|
|
}
|
|
} else {
|
|
|
|
/* Case 9. */
|
|
|
|
s = *dmin1 * .25;
|
|
if (*dmin1 == *dn1) {
|
|
s = *dmin1 * .5;
|
|
}
|
|
*ttype = -9;
|
|
}
|
|
|
|
} else if (*n0in == *n0 + 2) {
|
|
|
|
/* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN.
|
|
|
|
Cases 10 and 11. */
|
|
|
|
if (*dmin2 == *dn2 && z__[nn - 5] * 2. < z__[nn - 7]) {
|
|
*ttype = -10;
|
|
s = *dmin2 * .333;
|
|
if (z__[nn - 5] > z__[nn - 7]) {
|
|
return 0;
|
|
}
|
|
b1 = z__[nn - 5] / z__[nn - 7];
|
|
b2 = b1;
|
|
if (b2 == 0.) {
|
|
goto L80;
|
|
}
|
|
i__1 = (*i0 << 2) - 1 + *pp;
|
|
for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
|
|
if (z__[i4] > z__[i4 - 2]) {
|
|
return 0;
|
|
}
|
|
b1 *= z__[i4] / z__[i4 - 2];
|
|
b2 += b1;
|
|
if (b1 * 100. < b2) {
|
|
goto L80;
|
|
}
|
|
/* L70: */
|
|
}
|
|
L80:
|
|
b2 = sqrt(b2 * 1.05);
|
|
/* Computing 2nd power */
|
|
d__1 = b2;
|
|
a2 = *dmin2 / (d__1 * d__1 + 1.);
|
|
gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[
|
|
nn - 9]) - a2;
|
|
if (gap2 > 0. && gap2 > b2 * a2) {
|
|
/* Computing MAX */
|
|
d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2);
|
|
s = max(d__1,d__2);
|
|
} else {
|
|
/* Computing MAX */
|
|
d__1 = s, d__2 = a2 * (1. - b2 * 1.01);
|
|
s = max(d__1,d__2);
|
|
}
|
|
} else {
|
|
s = *dmin2 * .25;
|
|
*ttype = -11;
|
|
}
|
|
} else if (*n0in > *n0 + 2) {
|
|
|
|
/* Case 12, more than two eigenvalues deflated. No information. */
|
|
|
|
s = 0.;
|
|
*ttype = -12;
|
|
}
|
|
|
|
*tau = s;
|
|
return 0;
|
|
|
|
/* End of DLASQ4 */
|
|
|
|
} /* dlasq4_ */
|
|
|