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root/OpenMD/branches/development/src/math/SquareMatrix.hpp

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trunk/src/math/SquareMatrix.hpp (file contents), Revision 151 by tim, Mon Oct 25 22:46:19 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (file contents), Revision 1465 by chuckv, Fri Jul 9 23:08:25 2010 UTC

#	Line 1 | Line 1
1		/*
2	<	* Copyright (C) 2000-2004  Object Oriented Parallel Simulation Engine (OOPSE) project
3	<	*
4	<	* Contact: oopse@oopse.org
5	<	*
6	<	* This program is free software; you can redistribute it and/or
7	<	* modify it under the terms of the GNU Lesser General Public License
8	<	* as published by the Free Software Foundation; either version 2.1
9	<	* of the License, or (at your option) any later version.
10	<	* All we ask is that proper credit is given for our work, which includes
11	<	* - but is not limited to - adding the above copyright notice to the beginning
12	<	* of your source code files, and to any copyright notice that you may distribute
13	<	* with programs based on this work.
14	<	*
15	<	* This program is distributed in the hope that it will be useful,
16	<	* but WITHOUT ANY WARRANTY; without even the implied warranty of
17	<	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
18	<	* GNU Lesser General Public License for more details.
19	<	*
20	<	* You should have received a copy of the GNU Lesser General Public License
21	<	* along with this program; if not, write to the Free Software
22	<	* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
2	>	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3		*
4	+	* The University of Notre Dame grants you ("Licensee") a
5	+	* non-exclusive, royalty free, license to use, modify and
6	+	* redistribute this software in source and binary code form, provided
7	+	* that the following conditions are met:
8	+	*
9	+	* 1. Redistributions of source code must retain the above copyright
10	+	*    notice, this list of conditions and the following disclaimer.
11	+	*
12	+	* 2. Redistributions in binary form must reproduce the above copyright
13	+	*    notice, this list of conditions and the following disclaimer in the
14	+	*    documentation and/or other materials provided with the
15	+	*    distribution.
16	+	*
17	+	* This software is provided "AS IS," without a warranty of any
18	+	* kind. All express or implied conditions, representations and
19	+	* warranties, including any implied warranty of merchantability,
20	+	* fitness for a particular purpose or non-infringement, are hereby
21	+	* excluded.  The University of Notre Dame and its licensors shall not
22	+	* be liable for any damages suffered by licensee as a result of
23	+	* using, modifying or distributing the software or its
24	+	* derivatives. In no event will the University of Notre Dame or its
25	+	* licensors be liable for any lost revenue, profit or data, or for
26	+	* direct, indirect, special, consequential, incidental or punitive
27	+	* damages, however caused and regardless of the theory of liability,
28	+	* arising out of the use of or inability to use software, even if the
29	+	* University of Notre Dame has been advised of the possibility of
30	+	* such damages.
31	+	*
32	+	* SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
33	+	* research, please cite the appropriate papers when you publish your
34	+	* work.  Good starting points are:
35	+	*
36	+	* [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
37	+	* [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
38	+	* [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).
39	+	* [4]  Vardeman & Gezelter, in progress (2009).
40		*/
41	<
41	>
42		/**
43		* @file SquareMatrix.hpp
44		* @author Teng Lin
45		* @date 10/11/2004
46		* @version 1.0
47		*/
48	<	#ifndef MATH_SQUAREMATRIX_HPP
48	>	#ifndef MATH_SQUAREMATRIX_HPP
49		#define MATH_SQUAREMATRIX_HPP
50
51		#include "math/RectMatrix.hpp"
52	+	#include "utils/NumericConstant.hpp"
53
54	<	namespace oopse {
54	>	namespace OpenMD {
55
56	<	/**
57	<	* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
58	<	* @brief A square matrix class
59	<	* @template Real the element type
60	<	* @template Dim the dimension of the square matrix
61	<	*/
62	<	template<typename Real, int Dim>
63	<	class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
64	<	public:
65	<	typedef Real ElemType;
66	<	typedef Real* ElemPoinerType;
56	>	/**
57	>	* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
58	>	* @brief A square matrix class
59	>	* @template Real the element type
60	>	* @template Dim the dimension of the square matrix
61	>	*/
62	>	template<typename Real, int Dim>
63	>	class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
64	>	public:
65	>	typedef Real ElemType;
66	>	typedef Real* ElemPoinerType;
67
68	<	/** default constructor */
69	<	SquareMatrix() {
70	<	for (unsigned int i = 0; i < Dim; i++)
71	<	for (unsigned int j = 0; j < Dim; j++)
72	<	data_[i][j] = 0.0;
73	<	}
68	>	/** default constructor */
69	>	SquareMatrix() {
70	>	for (unsigned int i = 0; i < Dim; i++)
71	>	for (unsigned int j = 0; j < Dim; j++)
72	>	this->data_[i][j] = 0.0;
73	>	}
74
75	<	/** Constructs and initializes every element of this matrix to a scalar */
76	<	SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
77	<	}
75	>	/** Constructs and initializes every element of this matrix to a scalar */
76	>	SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
77	>	}
78
79	<	/** Constructs and initializes from an array */
80	<	SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
81	<	}
79	>	/** Constructs and initializes from an array */
80	>	SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
81	>	}
82
83
84	<	/** copy constructor */
85	<	SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
86	<	}
84	>	/** copy constructor */
85	>	SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
86	>	}
87
88	<	/** copy assignment operator */
89	<	SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
90	<	RectMatrix<Real, Dim, Dim>::operator=(m);
91	<	return *this;
92	<	}
88	>	/** copy assignment operator */
89	>	SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
90	>	RectMatrix<Real, Dim, Dim>::operator=(m);
91	>	return *this;
92	>	}
93
94	<	/** Retunrs  an identity matrix*/
94	>	/** Retunrs  an identity matrix*/
95
96	<	static SquareMatrix<Real, Dim> identity() {
97	<	SquareMatrix<Real, Dim> m;
96	>	static SquareMatrix<Real, Dim> identity() {
97	>	SquareMatrix<Real, Dim> m;
98
99	<	for (unsigned int i = 0; i < Dim; i++)
100	<	for (unsigned int j = 0; j < Dim; j++)
101	<	if (i == j)
102	<	m(i, j) = 1.0;
103	<	else
104	<	m(i, j) = 0.0;
99	>	for (unsigned int i = 0; i < Dim; i++)
100	>	for (unsigned int j = 0; j < Dim; j++)
101	>	if (i == j)
102	>	m(i, j) = 1.0;
103	>	else
104	>	m(i, j) = 0.0;
105
106	<	return m;
107	<	}
106	>	return m;
107	>	}
108
109	<	/**
110	<	* Retunrs  the inversion of this matrix.
111	<	* @todo need implementation
112	<	*/
113	<	SquareMatrix<Real, Dim>  inverse() {
114	<	SquareMatrix<Real, Dim> result;
109	>	/**
110	>	* Retunrs  the inversion of this matrix.
111	>	* @todo need implementation
112	>	*/
113	>	SquareMatrix<Real, Dim>  inverse() {
114	>	SquareMatrix<Real, Dim> result;
115
116	<	return result;
117	<	}
116	>	return result;
117	>	}
118
119	<	/**
120	<	* Returns the determinant of this matrix.
121	<	* @todo need implementation
122	<	*/
123	<	Real determinant() const {
124	<	Real det;
125	<	return det;
126	<	}
119	>	/**
120	>	* Returns the determinant of this matrix.
121	>	* @todo need implementation
122	>	*/
123	>	Real determinant() const {
124	>	Real det;
125	>	return det;
126	>	}
127
128	<	/** Returns the trace of this matrix. */
129	<	Real trace() const {
130	<	Real tmp = 0;
128	>	/** Returns the trace of this matrix. */
129	>	Real trace() const {
130	>	Real tmp = 0;
131
132	<	for (unsigned int i = 0; i < Dim ; i++)
133	<	tmp += data_[i][i];
132	>	for (unsigned int i = 0; i < Dim ; i++)
133	>	tmp += this->data_[i][i];
134
135	<	return tmp;
136	<	}
135	>	return tmp;
136	>	}
137
138	<	/** Tests if this matrix is symmetrix. */
139	<	bool isSymmetric() const {
140	<	for (unsigned int i = 0; i < Dim - 1; i++)
141	<	for (unsigned int j = i; j < Dim; j++)
142	<	if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
143	<	return false;
138	>	/** Tests if this matrix is symmetrix. */
139	>	bool isSymmetric() const {
140	>	for (unsigned int i = 0; i < Dim - 1; i++)
141	>	for (unsigned int j = i; j < Dim; j++)
142	>	if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon)
143	>	return false;
144
145	<	return true;
146	<	}
145	>	return true;
146	>	}
147
148	<	/** Tests if this matrix is orthogonal. */
149	<	bool isOrthogonal() {
150	<	SquareMatrix<Real, Dim> tmp;
148	>	/** Tests if this matrix is orthogonal. */
149	>	bool isOrthogonal() {
150	>	SquareMatrix<Real, Dim> tmp;
151
152	<	tmp = *this * transpose();
152	>	tmp = *this * transpose();
153
154	<	return tmp.isDiagonal();
155	<	}
154	>	return tmp.isDiagonal();
155	>	}
156
157	<	/** Tests if this matrix is diagonal. */
158	<	bool isDiagonal() const {
159	<	for (unsigned int i = 0; i < Dim ; i++)
160	<	for (unsigned int j = 0; j < Dim; j++)
161	<	if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
162	<	return false;
157	>	/** Tests if this matrix is diagonal. */
158	>	bool isDiagonal() const {
159	>	for (unsigned int i = 0; i < Dim ; i++)
160	>	for (unsigned int j = 0; j < Dim; j++)
161	>	if (i !=j && fabs(this->data_[i][j]) > epsilon)
162	>	return false;
163
164	<	return true;
165	<	}
164	>	return true;
165	>	}
166
167	<	/** Tests if this matrix is the unit matrix. */
168	<	bool isUnitMatrix() const {
169	<	if (!isDiagonal())
170	<	return false;
167	>	/** Tests if this matrix is the unit matrix. */
168	>	bool isUnitMatrix() const {
169	>	if (!isDiagonal())
170	>	return false;
171
172	<	for (unsigned int i = 0; i < Dim ; i++)
173	<	if (fabs(data_[i][i] - 1) > oopse::epsilon)
174	<	return false;
172	>	for (unsigned int i = 0; i < Dim ; i++)
173	>	if (fabs(this->data_[i][i] - 1) > epsilon)
174	>	return false;
175
176	<	return true;
177	<	}
176	>	return true;
177	>	}
178
179	<	/** @todo need implementation */
180	<	void diagonalize() {
181	<	//jacobi(m, eigenValues, ortMat);
182	<	}
179	>	/** Return the transpose of this matrix */
180	>	SquareMatrix<Real,  Dim> transpose() const{
181	>	SquareMatrix<Real,  Dim> result;
182	>
183	>	for (unsigned int i = 0; i < Dim; i++)
184	>	for (unsigned int j = 0; j < Dim; j++)
185	>	result(j, i) = this->data_[i][j];
186
187	<	/**
188	<	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
189	<	* real symmetric matrix
190	<	*
191	<	* @return true if success, otherwise return false
192	<	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
193	<	*     overwritten
194	<	* @param w will contain the eigenvalues of the matrix On return of this function
195	<	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
196	<	*    normalized and mutually orthogonal.
197	<	*/
187	>	return result;
188	>	}
189	>
190	>	/** @todo need implementation */
191	>	void diagonalize() {
192	>	//jacobi(m, eigenValues, ortMat);
193	>	}
194	>
195	>	/**
196	>	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
197	>	* real symmetric matrix
198	>	*
199	>	* @return true if success, otherwise return false
200	>	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
201	>	*     overwritten
202	>	* @param w will contain the eigenvalues of the matrix On return of this function
203	>	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
204	>	*    normalized and mutually orthogonal.
205	>	*/
206
207	<	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
208	<	SquareMatrix<Real, Dim>& v);
209	<	};//end SquareMatrix
207	>	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
208	>	SquareMatrix<Real, Dim>& v);
209	>	};//end SquareMatrix
210
211
212	<	/*=========================================================================
212	>	/*=========================================================================
213
214		Program:   Visualization Toolkit
215		Module:    $RCSfile: SquareMatrix.hpp,v $
#	Line 190 | Line 218 | namespace oopse {
218		All rights reserved.
219		See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
220
221	<	This software is distributed WITHOUT ANY WARRANTY; without even
222	<	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
223	<	PURPOSE.  See the above copyright notice for more information.
221	>	This software is distributed WITHOUT ANY WARRANTY; without even
222	>	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
223	>	PURPOSE.  See the above copyright notice for more information.
224
225	<	=========================================================================*/
225	>	=========================================================================*/
226
227	<	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\
228	<	a(k, l)=h+s*(g-h*tau)
227	>	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \
228	>	a(k, l)=h+s*(g-h*tau)
229
230		#define VTK_MAX_ROTATIONS 20
231
232	<	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
233	<	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
234	<	// output eigenvalues in w; and output eigenvectors in v. Resulting
235	<	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
236	<	// normalized.
237	<	template<typename Real, int Dim>
238	<	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
239	<	SquareMatrix<Real, Dim>& v) {
240	<	const int n = Dim;
241	<	int i, j, k, iq, ip, numPos;
242	<	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
243	<	Real bspace[4], zspace[4];
244	<	Real *b = bspace;
245	<	Real *z = zspace;
232	>	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
233	>	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
234	>	// output eigenvalues in w; and output eigenvectors in v. Resulting
235	>	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
236	>	// normalized.
237	>	template<typename Real, int Dim>
238	>	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
239	>	SquareMatrix<Real, Dim>& v) {
240	>	const int n = Dim;
241	>	int i, j, k, iq, ip, numPos;
242	>	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
243	>	Real bspace[4], zspace[4];
244	>	Real *b = bspace;
245	>	Real *z = zspace;
246
247	<	// only allocate memory if the matrix is large
248	<	if (n > 4) {
249	<	b = new Real[n];
250	<	z = new Real[n];
251	<	}
247	>	// only allocate memory if the matrix is large
248	>	if (n > 4) {
249	>	b = new Real[n];
250	>	z = new Real[n];
251	>	}
252
253	<	// initialize
254	<	for (ip=0; ip<n; ip++) {
255	<	for (iq=0; iq<n; iq++) {
256	<	v(ip, iq) = 0.0;
257	<	}
258	<	v(ip, ip) = 1.0;
259	<	}
260	<	for (ip=0; ip<n; ip++) {
261	<	b[ip] = w[ip] = a(ip, ip);
262	<	z[ip] = 0.0;
263	<	}
253	>	// initialize
254	>	for (ip=0; ip<n; ip++) {
255	>	for (iq=0; iq<n; iq++) {
256	>	v(ip, iq) = 0.0;
257	>	}
258	>	v(ip, ip) = 1.0;
259	>	}
260	>	for (ip=0; ip<n; ip++) {
261	>	b[ip] = w[ip] = a(ip, ip);
262	>	z[ip] = 0.0;
263	>	}
264
265	<	// begin rotation sequence
266	<	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
267	<	sm = 0.0;
268	<	for (ip=0; ip<n-1; ip++) {
269	<	for (iq=ip+1; iq<n; iq++) {
270	<	sm += fabs(a(ip, iq));
271	<	}
272	<	}
273	<	if (sm == 0.0) {
274	<	break;
275	<	}
265	>	// begin rotation sequence
266	>	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
267	>	sm = 0.0;
268	>	for (ip=0; ip<n-1; ip++) {
269	>	for (iq=ip+1; iq<n; iq++) {
270	>	sm += fabs(a(ip, iq));
271	>	}
272	>	}
273	>	if (sm == 0.0) {
274	>	break;
275	>	}
276
277	<	if (i < 3) {                                // first 3 sweeps
278	<	tresh = 0.2*sm/(n*n);
279	<	} else {
280	<	tresh = 0.0;
281	<	}
277	>	if (i < 3) {                                // first 3 sweeps
278	>	tresh = 0.2*sm/(n*n);
279	>	} else {
280	>	tresh = 0.0;
281	>	}
282
283	<	for (ip=0; ip<n-1; ip++) {
284	<	for (iq=ip+1; iq<n; iq++) {
285	<	g = 100.0*fabs(a(ip, iq));
283	>	for (ip=0; ip<n-1; ip++) {
284	>	for (iq=ip+1; iq<n; iq++) {
285	>	g = 100.0*fabs(a(ip, iq));
286
287	<	// after 4 sweeps
288	<	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
289	<	&& (fabs(w[iq])+g) == fabs(w[iq])) {
290	<	a(ip, iq) = 0.0;
291	<	} else if (fabs(a(ip, iq)) > tresh) {
292	<	h = w[iq] - w[ip];
293	<	if ( (fabs(h)+g) == fabs(h)) {
294	<	t = (a(ip, iq)) / h;
295	<	} else {
296	<	theta = 0.5*h / (a(ip, iq));
297	<	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
298	<	if (theta < 0.0) {
299	<	t = -t;
300	<	}
301	<	}
302	<	c = 1.0 / sqrt(1+t*t);
303	<	s = t*c;
304	<	tau = s/(1.0+c);
305	<	h = t*a(ip, iq);
306	<	z[ip] -= h;
307	<	z[iq] += h;
308	<	w[ip] -= h;
309	<	w[iq] += h;
310	<	a(ip, iq)=0.0;
287	>	// after 4 sweeps
288	>	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
289	>	&& (fabs(w[iq])+g) == fabs(w[iq])) {
290	>	a(ip, iq) = 0.0;
291	>	} else if (fabs(a(ip, iq)) > tresh) {
292	>	h = w[iq] - w[ip];
293	>	if ( (fabs(h)+g) == fabs(h)) {
294	>	t = (a(ip, iq)) / h;
295	>	} else {
296	>	theta = 0.5*h / (a(ip, iq));
297	>	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
298	>	if (theta < 0.0) {
299	>	t = -t;
300	>	}
301	>	}
302	>	c = 1.0 / sqrt(1+t*t);
303	>	s = t*c;
304	>	tau = s/(1.0+c);
305	>	h = t*a(ip, iq);
306	>	z[ip] -= h;
307	>	z[iq] += h;
308	>	w[ip] -= h;
309	>	w[iq] += h;
310	>	a(ip, iq)=0.0;
311
312	<	// ip already shifted left by 1 unit
313	<	for (j = 0;j <= ip-1;j++) {
314	<	VTK_ROTATE(a,j,ip,j,iq);
315	<	}
316	<	// ip and iq already shifted left by 1 unit
317	<	for (j = ip+1;j <= iq-1;j++) {
318	<	VTK_ROTATE(a,ip,j,j,iq);
319	<	}
320	<	// iq already shifted left by 1 unit
321	<	for (j=iq+1; j<n; j++) {
322	<	VTK_ROTATE(a,ip,j,iq,j);
323	<	}
324	<	for (j=0; j<n; j++) {
325	<	VTK_ROTATE(v,j,ip,j,iq);
326	<	}
327	<	}
328	<	}
329	<	}
312	>	// ip already shifted left by 1 unit
313	>	for (j = 0;j <= ip-1;j++) {
314	>	VTK_ROTATE(a,j,ip,j,iq);
315	>	}
316	>	// ip and iq already shifted left by 1 unit
317	>	for (j = ip+1;j <= iq-1;j++) {
318	>	VTK_ROTATE(a,ip,j,j,iq);
319	>	}
320	>	// iq already shifted left by 1 unit
321	>	for (j=iq+1; j<n; j++) {
322	>	VTK_ROTATE(a,ip,j,iq,j);
323	>	}
324	>	for (j=0; j<n; j++) {
325	>	VTK_ROTATE(v,j,ip,j,iq);
326	>	}
327	>	}
328	>	}
329	>	}
330
331	<	for (ip=0; ip<n; ip++) {
332	<	b[ip] += z[ip];
333	<	w[ip] = b[ip];
334	<	z[ip] = 0.0;
335	<	}
336	<	}
331	>	for (ip=0; ip<n; ip++) {
332	>	b[ip] += z[ip];
333	>	w[ip] = b[ip];
334	>	z[ip] = 0.0;
335	>	}
336	>	}
337
338	<	//// this is NEVER called
339	<	if ( i >= VTK_MAX_ROTATIONS ) {
340	<	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
341	<	return 0;
342	<	}
338	>	//// this is NEVER called
339	>	if ( i >= VTK_MAX_ROTATIONS ) {
340	>	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
341	>	return 0;
342	>	}
343
344	<	// sort eigenfunctions                 these changes do not affect accuracy
345	<	for (j=0; j<n-1; j++) {                  // boundary incorrect
346	<	k = j;
347	<	tmp = w[k];
348	<	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
349	<	if (w[i] >= tmp) {                   // why exchage if same?
350	<	k = i;
351	<	tmp = w[k];
352	<	}
353	<	}
354	<	if (k != j) {
355	<	w[k] = w[j];
356	<	w[j] = tmp;
357	<	for (i=0; i<n; i++) {
358	<	tmp = v(i, j);
359	<	v(i, j) = v(i, k);
360	<	v(i, k) = tmp;
361	<	}
362	<	}
363	<	}
364	<	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
365	<	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
366	<	// reek havoc in hyperstreamline/other stuff. We will select the most
367	<	// positive eigenvector.
368	<	int ceil_half_n = (n >> 1) + (n & 1);
369	<	for (j=0; j<n; j++) {
370	<	for (numPos=0, i=0; i<n; i++) {
371	<	if ( v(i, j) >= 0.0 ) {
372	<	numPos++;
373	<	}
374	<	}
375	<	//    if ( numPos < ceil(double(n)/double(2.0)) )
376	<	if ( numPos < ceil_half_n) {
377	<	for (i=0; i<n; i++) {
378	<	v(i, j) *= -1.0;
379	<	}
380	<	}
381	<	}
344	>	// sort eigenfunctions                 these changes do not affect accuracy
345	>	for (j=0; j<n-1; j++) {                  // boundary incorrect
346	>	k = j;
347	>	tmp = w[k];
348	>	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
349	>	if (w[i] >= tmp) {                   // why exchage if same?
350	>	k = i;
351	>	tmp = w[k];
352	>	}
353	>	}
354	>	if (k != j) {
355	>	w[k] = w[j];
356	>	w[j] = tmp;
357	>	for (i=0; i<n; i++) {
358	>	tmp = v(i, j);
359	>	v(i, j) = v(i, k);
360	>	v(i, k) = tmp;
361	>	}
362	>	}
363	>	}
364	>	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
365	>	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
366	>	// reek havoc in hyperstreamline/other stuff. We will select the most
367	>	// positive eigenvector.
368	>	int ceil_half_n = (n >> 1) + (n & 1);
369	>	for (j=0; j<n; j++) {
370	>	for (numPos=0, i=0; i<n; i++) {
371	>	if ( v(i, j) >= 0.0 ) {
372	>	numPos++;
373	>	}
374	>	}
375	>	//    if ( numPos < ceil(RealType(n)/RealType(2.0)) )
376	>	if ( numPos < ceil_half_n) {
377	>	for (i=0; i<n; i++) {
378	>	v(i, j) *= -1.0;
379	>	}
380	>	}
381	>	}
382
383	<	if (n > 4) {
384	<	delete [] b;
385	<	delete [] z;
358	<	}
359	<	return 1;
383	>	if (n > 4) {
384	>	delete [] b;
385	>	delete [] z;
386		}
387	+	return 1;
388	+	}
389
390
391	+	typedef SquareMatrix<RealType, 6> Mat6x6d;
392		}
393		#endif //MATH_SQUAREMATRIX_HPP
394

Comparing:
trunk/src/math/SquareMatrix.hpp (property svn:keywords), Revision 151 by tim, Mon Oct 25 22:46:19 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (property svn:keywords), Revision 1465 by chuckv, Fri Jul 9 23:08:25 2010 UTC

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