151 lines
4.6 KiB
C
151 lines
4.6 KiB
C
/*BHEADER**********************************************************************
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* Copyright (c) 2006 The Regents of the University of California.
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* Produced at the Lawrence Livermore National Laboratory.
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* Written by the HYPRE team. UCRL-CODE-222953.
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* All rights reserved.
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*
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* This file is part of HYPRE (see http://www.llnl.gov/CASC/hypre/).
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* Please see the COPYRIGHT_and_LICENSE file for the copyright notice,
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* disclaimer, contact information and the GNU Lesser General Public License.
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*
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* HYPRE is free software; you can redistribute it and/or modify it under the
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* terms of the GNU General Public License (as published by the Free Software
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* Foundation) version 2.1 dated February 1999.
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*
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* HYPRE is distributed in the hope that it will be useful, but WITHOUT ANY
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* WARRANTY; without even the IMPLIED WARRANTY OF MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the terms and conditions of the GNU General
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* Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, write to the Free Software Foundation,
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* Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*
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* $Revision$
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***********************************************************************EHEADER*/
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#include "hypre_lapack.h"
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#include "f2c.h"
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/* Subroutine */ int dlas2_(doublereal *f, doublereal *g, doublereal *h__,
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doublereal *ssmin, doublereal *ssmax)
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{
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/* -- LAPACK auxiliary routine (version 3.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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September 30, 1994
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Purpose
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=======
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DLAS2 computes the singular values of the 2-by-2 matrix
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[ F G ]
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[ 0 H ].
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On return, SSMIN is the smaller singular value and SSMAX is the
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larger singular value.
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Arguments
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=========
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F (input) DOUBLE PRECISION
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The (1,1) element of the 2-by-2 matrix.
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G (input) DOUBLE PRECISION
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The (1,2) element of the 2-by-2 matrix.
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H (input) DOUBLE PRECISION
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The (2,2) element of the 2-by-2 matrix.
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SSMIN (output) DOUBLE PRECISION
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The smaller singular value.
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SSMAX (output) DOUBLE PRECISION
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The larger singular value.
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Further Details
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===============
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Barring over/underflow, all output quantities are correct to within
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a few units in the last place (ulps), even in the absence of a guard
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digit in addition/subtraction.
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In IEEE arithmetic, the code works correctly if one matrix element is
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infinite.
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Overflow will not occur unless the largest singular value itself
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overflows, or is within a few ulps of overflow. (On machines with
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partial overflow, like the Cray, overflow may occur if the largest
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singular value is within a factor of 2 of overflow.)
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Underflow is harmless if underflow is gradual. Otherwise, results
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may correspond to a matrix modified by perturbations of size near
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the underflow threshold.
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==================================================================== */
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/* System generated locals */
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doublereal d__1, d__2;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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static doublereal fhmn, fhmx, c__, fa, ga, ha, as, at, au;
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fa = abs(*f);
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ga = abs(*g);
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ha = abs(*h__);
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fhmn = min(fa,ha);
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fhmx = max(fa,ha);
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if (fhmn == 0.) {
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*ssmin = 0.;
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if (fhmx == 0.) {
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*ssmax = ga;
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} else {
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/* Computing 2nd power */
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d__1 = min(fhmx,ga) / max(fhmx,ga);
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*ssmax = max(fhmx,ga) * sqrt(d__1 * d__1 + 1.);
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}
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} else {
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if (ga < fhmx) {
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as = fhmn / fhmx + 1.;
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at = (fhmx - fhmn) / fhmx;
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/* Computing 2nd power */
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d__1 = ga / fhmx;
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au = d__1 * d__1;
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c__ = 2. / (sqrt(as * as + au) + sqrt(at * at + au));
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*ssmin = fhmn * c__;
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*ssmax = fhmx / c__;
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} else {
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au = fhmx / ga;
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if (au == 0.) {
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/* Avoid possible harmful underflow if exponent range
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asymmetric (true SSMIN may not underflow even if
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AU underflows) */
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*ssmin = fhmn * fhmx / ga;
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*ssmax = ga;
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} else {
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as = fhmn / fhmx + 1.;
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at = (fhmx - fhmn) / fhmx;
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/* Computing 2nd power */
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d__1 = as * au;
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/* Computing 2nd power */
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d__2 = at * au;
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c__ = 1. / (sqrt(d__1 * d__1 + 1.) + sqrt(d__2 * d__2 + 1.));
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*ssmin = fhmn * c__ * au;
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*ssmin += *ssmin;
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*ssmax = ga / (c__ + c__);
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}
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}
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}
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return 0;
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/* End of DLAS2 */
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} /* dlas2_ */
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