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hypre/lapack/dlasq2.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"
/* -- translated by f2c (version 19990503).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "f2c.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c__2 = 2;
static integer c__10 = 10;
static integer c__3 = 3;
static integer c__4 = 4;
static integer c__11 = 11;
/* Subroutine */ int dlasq2_(integer *n, doublereal *z__, integer *info)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static logical ieee;
static integer nbig;
static doublereal dmin__, emin, emax;
static integer ndiv, iter;
static doublereal qmin, temp, qmax, zmax;
static integer splt;
static doublereal d__, e;
static integer k;
static doublereal s, t;
static integer nfail;
static doublereal desig, trace, sigma;
static integer iinfo, i0, i4, n0;
extern /* Subroutine */ int dlasq3_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
integer *, integer *, integer *, logical *);
extern doublereal dlamch_(char *);
static integer pp, iwhila, iwhilb;
static doublereal oldemn, safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *,
integer *);
static doublereal eps, tol;
static integer ipn4;
static doublereal tol2;
/* -- LAPACK 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
=======
DLASQ2 computes all the eigenvalues of the symmetric positive
definite tridiagonal matrix associated with the qd array Z to high
relative accuracy are computed to high relative accuracy, in the
absence of denormalization, underflow and overflow.
To see the relation of Z to the tridiagonal matrix, let L be a
unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and
let U be an upper bidiagonal matrix with 1's above and diagonal
Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the
symmetric tridiagonal to which it is similar.
Note : DLASQ2 defines a logical variable, IEEE, which is true
on machines which follow ieee-754 floating-point standard in their
handling of infinities and NaNs, and false otherwise. This variable
is passed to DLASQ3.
Arguments
=========
N (input) INTEGER
The number of rows and columns in the matrix. N >= 0.
Z (workspace) DOUBLE PRECISION array, dimension ( 4*N )
On entry Z holds the qd array. On exit, entries 1 to N hold
the eigenvalues in decreasing order, Z( 2*N+1 ) holds the
trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If
N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 )
holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of
shifts that failed.
INFO (output) INTEGER
= 0: successful exit
< 0: if the i-th argument is a scalar and had an illegal
value, then INFO = -i, if the i-th argument is an
array and the j-entry had an illegal value, then
INFO = -(i*100+j)
> 0: the algorithm failed
= 1, a split was marked by a positive value in E
= 2, current block of Z not diagonalized after 30*N
iterations (in inner while loop)
= 3, termination criterion of outer while loop not met
(program created more than N unreduced blocks)
Further Details
===============
Local Variables: I0:N0 defines a current unreduced segment of Z.
The shifts are accumulated in SIGMA. Iteration count is in ITER.
Ping-pong is controlled by PP (alternates between 0 and 1).
=====================================================================
Test the input arguments.
(in case DLASQ2 is not called by DLASQ1)
Parameter adjustments */
--z__;
/* Function Body */
*info = 0;
eps = dlamch_("Precision");
safmin = dlamch_("Safe minimum");
tol = eps * 100.;
/* Computing 2nd power */
d__1 = tol;
tol2 = d__1 * d__1;
if (*n < 0) {
*info = -1;
xerbla_("DLASQ2", &c__1);
return 0;
} else if (*n == 0) {
return 0;
} else if (*n == 1) {
/* 1-by-1 case. */
if (z__[1] < 0.) {
*info = -201;
xerbla_("DLASQ2", &c__2);
}
return 0;
} else if (*n == 2) {
/* 2-by-2 case. */
if (z__[2] < 0. || z__[3] < 0.) {
*info = -2;
xerbla_("DLASQ2", &c__2);
return 0;
} else if (z__[3] > z__[1]) {
d__ = z__[3];
z__[3] = z__[1];
z__[1] = d__;
}
z__[5] = z__[1] + z__[2] + z__[3];
if (z__[2] > z__[3] * tol2) {
t = (z__[1] - z__[3] + z__[2]) * .5;
s = z__[3] * (z__[2] / t);
if (s <= t) {
s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.) + 1.)));
} else {
s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s)));
}
t = z__[1] + (s + z__[2]);
z__[3] *= z__[1] / t;
z__[1] = t;
}
z__[2] = z__[3];
z__[6] = z__[2] + z__[1];
return 0;
}
/* Check for negative data and compute sums of q's and e's. */
z__[*n * 2] = 0.;
emin = z__[2];
qmax = 0.;
zmax = 0.;
d__ = 0.;
e = 0.;
i__1 = (*n - 1) << 1;
for (k = 1; k <= i__1; k += 2) {
if (z__[k] < 0.) {
*info = -(k + 200);
xerbla_("DLASQ2", &c__2);
return 0;
} else if (z__[k + 1] < 0.) {
*info = -(k + 201);
xerbla_("DLASQ2", &c__2);
return 0;
}
d__ += z__[k];
e += z__[k + 1];
/* Computing MAX */
d__1 = qmax, d__2 = z__[k];
qmax = max(d__1,d__2);
/* Computing MIN */
d__1 = emin, d__2 = z__[k + 1];
emin = min(d__1,d__2);
/* Computing MAX */
d__1 = max(qmax,zmax), d__2 = z__[k + 1];
zmax = max(d__1,d__2);
/* L10: */
}
if (z__[(*n << 1) - 1] < 0.) {
*info = -((*n << 1) + 199);
xerbla_("DLASQ2", &c__2);
return 0;
}
d__ += z__[(*n << 1) - 1];
/* Computing MAX */
d__1 = qmax, d__2 = z__[(*n << 1) - 1];
qmax = max(d__1,d__2);
zmax = max(qmax,zmax);
/* Check for diagonality. */
if (e == 0.) {
i__1 = *n;
for (k = 2; k <= i__1; ++k) {
z__[k] = z__[(k << 1) - 1];
/* L20: */
}
dlasrt_("D", n, &z__[1], &iinfo);
z__[(*n << 1) - 1] = d__;
return 0;
}
trace = d__ + e;
/* Check for zero data. */
if (trace == 0.) {
z__[(*n << 1) - 1] = 0.;
return 0;
}
/* Check whether the machine is IEEE conformable. */
ieee = ilaenv_(&c__10, "DLASQ2", "N", &c__1, &c__2, &c__3, &c__4, (ftnlen)
6, (ftnlen)1) == 1 && ilaenv_(&c__11, "DLASQ2", "N", &c__1, &c__2,
&c__3, &c__4, (ftnlen)6, (ftnlen)1) == 1;
/* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */
for (k = *n << 1; k >= 2; k += -2) {
z__[k * 2] = 0.;
z__[(k << 1) - 1] = z__[k];
z__[(k << 1) - 2] = 0.;
z__[(k << 1) - 3] = z__[k - 1];
/* L30: */
}
i0 = 1;
n0 = *n;
/* Reverse the qd-array, if warranted. */
if (z__[(i0 << 2) - 3] * 1.5 < z__[(n0 << 2) - 3]) {
ipn4 = (i0 + n0) << 2;
i__1 = (i0 + n0 - 1) << 1;
for (i4 = i0 << 2; i4 <= i__1; i4 += 4) {
temp = z__[i4 - 3];
z__[i4 - 3] = z__[ipn4 - i4 - 3];
z__[ipn4 - i4 - 3] = temp;
temp = z__[i4 - 1];
z__[i4 - 1] = z__[ipn4 - i4 - 5];
z__[ipn4 - i4 - 5] = temp;
/* L40: */
}
}
/* Initial split checking via dqd and Li's test. */
pp = 0;
for (k = 1; k <= 2; ++k) {
d__ = z__[(n0 << 2) + pp - 3];
i__1 = (i0 << 2) + pp;
for (i4 = ((n0 - 1) << 2) + pp; i4 >= i__1; i4 += -4) {
if (z__[i4 - 1] <= tol2 * d__) {
z__[i4 - 1] = 0.;
d__ = z__[i4 - 3];
} else {
d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1]));
}
/* L50: */
}
/* dqd maps Z to ZZ plus Li's test. */
emin = z__[(i0 << 2) + pp + 1];
d__ = z__[(i0 << 2) + pp - 3];
i__1 = ((n0 - 1) << 2) + pp;
for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) {
z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1];
if (z__[i4 - 1] <= tol2 * d__) {
z__[i4 - 1] = 0.;
z__[i4 - (pp << 1) - 2] = d__;
z__[i4 - (pp << 1)] = 0.;
d__ = z__[i4 + 1];
} else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] &&
safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) {
temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2];
z__[i4 - (pp << 1)] = z__[i4 - 1] * temp;
d__ *= temp;
} else {
z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - (
pp << 1) - 2]);
d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]);
}
/* Computing MIN */
d__1 = emin, d__2 = z__[i4 - (pp << 1)];
emin = min(d__1,d__2);
/* L60: */
}
z__[(n0 << 2) - pp - 2] = d__;
/* Now find qmax. */
qmax = z__[(i0 << 2) - pp - 2];
i__1 = (n0 << 2) - pp - 2;
for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) {
/* Computing MAX */
d__1 = qmax, d__2 = z__[i4];
qmax = max(d__1,d__2);
/* L70: */
}
/* Prepare for the next iteration on K. */
pp = 1 - pp;
/* L80: */
}
iter = 2;
nfail = 0;
ndiv = (n0 - i0) << 1;
i__1 = *n + 1;
for (iwhila = 1; iwhila <= i__1; ++iwhila) {
if (n0 < 1) {
goto L150;
}
/* While array unfinished do
E(N0) holds the value of SIGMA when submatrix in I0:N0
splits from the rest of the array, but is negated. */
desig = 0.;
if (n0 == *n) {
sigma = 0.;
} else {
sigma = -z__[(n0 << 2) - 1];
}
if (sigma < 0.) {
*info = 1;
return 0;
}
/* Find last unreduced submatrix's top index I0, find QMAX and
EMIN. Find Gershgorin-type bound if Q's much greater than E's. */
emax = 0.;
if (n0 > i0) {
emin = (d__1 = z__[(n0 << 2) - 5], abs(d__1));
} else {
emin = 0.;
}
qmin = z__[(n0 << 2) - 3];
qmax = qmin;
for (i4 = n0 << 2; i4 >= 8; i4 += -4) {
if (z__[i4 - 5] <= 0.) {
goto L100;
}
if (qmin >= emax * 4.) {
/* Computing MIN */
d__1 = qmin, d__2 = z__[i4 - 3];
qmin = min(d__1,d__2);
/* Computing MAX */
d__1 = emax, d__2 = z__[i4 - 5];
emax = max(d__1,d__2);
}
/* Computing MAX */
d__1 = qmax, d__2 = z__[i4 - 7] + z__[i4 - 5];
qmax = max(d__1,d__2);
/* Computing MIN */
d__1 = emin, d__2 = z__[i4 - 5];
emin = min(d__1,d__2);
/* L90: */
}
i4 = 4;
L100:
i0 = i4 / 4;
/* Store EMIN for passing to DLASQ3. */
z__[(n0 << 2) - 1] = emin;
/* Put -(initial shift) into DMIN.
Computing MAX */
d__1 = 0., d__2 = qmin - sqrt(qmin) * 2. * sqrt(emax);
dmin__ = -max(d__1,d__2);
/* Now I0:N0 is unreduced. PP = 0 for ping, PP = 1 for pong. */
pp = 0;
nbig = (n0 - i0 + 1) * 30;
i__2 = nbig;
for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) {
if (i0 > n0) {
goto L130;
}
/* While submatrix unfinished take a good dqds step. */
dlasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, &
nfail, &iter, &ndiv, &ieee);
pp = 1 - pp;
/* When EMIN is very small check for splits. */
if (pp == 0 && n0 - i0 >= 3) {
if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 *
sigma) {
splt = i0 - 1;
qmax = z__[(i0 << 2) - 3];
emin = z__[(i0 << 2) - 1];
oldemn = z__[i0 * 4];
i__3 = (n0 - 3) << 2;
for (i4 = i0 << 2; i4 <= i__3; i4 += 4) {
if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <=
tol2 * sigma) {
z__[i4 - 1] = -sigma;
splt = i4 / 4;
qmax = 0.;
emin = z__[i4 + 3];
oldemn = z__[i4 + 4];
} else {
/* Computing MAX */
d__1 = qmax, d__2 = z__[i4 + 1];
qmax = max(d__1,d__2);
/* Computing MIN */
d__1 = emin, d__2 = z__[i4 - 1];
emin = min(d__1,d__2);
/* Computing MIN */
d__1 = oldemn, d__2 = z__[i4];
oldemn = min(d__1,d__2);
}
/* L110: */
}
z__[(n0 << 2) - 1] = emin;
z__[n0 * 4] = oldemn;
i0 = splt + 1;
}
}
/* L120: */
}
*info = 2;
return 0;
/* end IWHILB */
L130:
/* L140: */
;
}
*info = 3;
return 0;
/* end IWHILA */
L150:
/* Move q's to the front. */
i__1 = *n;
for (k = 2; k <= i__1; ++k) {
z__[k] = z__[(k << 2) - 3];
/* L160: */
}
/* Sort and compute sum of eigenvalues. */
dlasrt_("D", n, &z__[1], &iinfo);
e = 0.;
for (k = *n; k >= 1; --k) {
e += z__[k];
/* L170: */
}
/* Store trace, sum(eigenvalues) and information on performance. */
z__[(*n << 1) + 1] = trace;
z__[(*n << 1) + 2] = e;
z__[(*n << 1) + 3] = (doublereal) iter;
/* Computing 2nd power */
i__1 = *n;
z__[(*n << 1) + 4] = (doublereal) ndiv / (doublereal) (i__1 * i__1);
z__[(*n << 1) + 5] = nfail * 100. / (doublereal) iter;
return 0;
/* End of DLASQ2 */
} /* dlasq2_ */
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