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

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trunk/src/math/SquareMatrix.hpp (file contents), Revision 123 by tim, Wed Oct 20 18:07:08 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (file contents), Revision 1874 by gezelter, Wed May 15 15:09:35 2013 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, 234107 (2008).
39	+	* [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
40	+	* [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41		*/
42	<
42	>
43		/**
44		* @file SquareMatrix.hpp
45		* @author Teng Lin
46		* @date 10/11/2004
47		* @version 1.0
48		*/
49	<	#ifndef MATH_SQUAREMATRIX_HPP
49	>	#ifndef MATH_SQUAREMATRIX_HPP
50		#define MATH_SQUAREMATRIX_HPP
51
52		#include "math/RectMatrix.hpp"
53	+	#include "utils/NumericConstant.hpp"
54
55	<	namespace oopse {
55	>	namespace OpenMD {
56
57	<	/**
58	<	* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
59	<	* @brief A square matrix class
60	<	* @template Real the element type
61	<	* @template Dim the dimension of the square matrix
62	<	*/
63	<	template<typename Real, int Dim>
64	<	class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
65	<	public:
57	>	/**
58	>	* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
59	>	* @brief A square matrix class
60	>	* \tparam Real the element type
61	>	* \tparam Dim the dimension of the square matrix
62	>	*/
63	>	template<typename Real, int Dim>
64	>	class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
65	>	public:
66	>	typedef Real ElemType;
67	>	typedef Real* ElemPoinerType;
68
69	<	/** default constructor */
70	<	SquareMatrix() {
71	<	for (unsigned int i = 0; i < Dim; i++)
72	<	for (unsigned int j = 0; j < Dim; j++)
73	<	data_[i][j] = 0.0;
74	<	}
69	>	/** default constructor */
70	>	SquareMatrix() {
71	>	for (unsigned int i = 0; i < Dim; i++)
72	>	for (unsigned int j = 0; j < Dim; j++)
73	>	this->data_[i][j] = 0.0;
74	>	}
75
76	<	/** copy constructor */
77	<	SquareMatrix(const RectMatrix<Real, Dim, Dim>& m)  : RectMatrix<Real, Dim, Dim>(m) {
78	<	}
59	<
60	<	/** copy assignment operator */
61	<	SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
62	<	RectMatrix<Real, Dim, Dim>::operator=(m);
63	<	return *this;
64	<	}
65	<
66	<	/** Retunrs  an identity matrix*/
76	>	/** Constructs and initializes every element of this matrix to a scalar */
77	>	SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
78	>	}
79
80	<	static SquareMatrix<Real, Dim> identity() {
81	<	SquareMatrix<Real, Dim> m;
80	>	/** Constructs and initializes from an array */
81	>	SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
82	>	}
83	>
84	>
85	>	/** copy constructor */
86	>	SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
87	>	}
88
89	<	for (unsigned int i = 0; i < Dim; i++)
90	<	for (unsigned int j = 0; j < Dim; j++)
91	<	if (i == j)
92	<	m(i, j) = 1.0;
93	<	else
94	<	m(i, j) = 0.0;
89	>	/** copy assignment operator */
90	>	SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
91	>	RectMatrix<Real, Dim, Dim>::operator=(m);
92	>	return *this;
93	>	}
94	>
95	>	/** Retunrs  an identity matrix*/
96
97	<	return m;
98	<	}
97	>	static SquareMatrix<Real, Dim> identity() {
98	>	SquareMatrix<Real, Dim> m;
99	>
100	>	for (unsigned int i = 0; i < Dim; i++)
101	>	for (unsigned int j = 0; j < Dim; j++)
102	>	if (i == j)
103	>	m(i, j) = 1.0;
104	>	else
105	>	m(i, j) = 0.0;
106
107	<	/**
108	<	* Retunrs  the inversion of this matrix.
83	<	* @todo need implementation
84	<	*/
85	<	SquareMatrix<Real, Dim>  inverse() {
86	<	SquareMatrix<Real, Dim> result;
107	>	return m;
108	>	}
109
110	<	return result;
111	<	}
110	>	/**
111	>	* Retunrs  the inversion of this matrix.
112	>	* @todo need implementation
113	>	*/
114	>	SquareMatrix<Real, Dim>  inverse() {
115	>	SquareMatrix<Real, Dim> result;
116
117	<	/**
118	<	* Returns the determinant of this matrix.
93	<	* @todo need implementation
94	<	*/
95	<	Real determinant() const {
96	<	Real det;
97	<	return det;
98	<	}
117	>	return result;
118	>	}
119
120	<	/** Returns the trace of this matrix. */
121	<	Real trace() const {
122	<	Real tmp = 0;
123	<
124	<	for (unsigned int i = 0; i < Dim ; i++)
125	<	tmp += data_[i][i];
120	>	/**
121	>	* Returns the determinant of this matrix.
122	>	* @todo need implementation
123	>	*/
124	>	Real determinant() const {
125	>	Real det;
126	>	return det;
127	>	}
128	>
129	>	/** Returns the trace of this matrix. */
130	>	Real trace() const {
131	>	Real tmp = 0;
132	>
133	>	for (unsigned int i = 0; i < Dim ; i++)
134	>	tmp += this->data_[i][i];
135
136	<	return tmp;
137	<	}
136	>	return tmp;
137	>	}
138	>
139	>	/**
140	>	* Returns the tensor contraction (double dot product) of two rank 2
141	>	* tensors (or Matrices)
142	>	* @param t1 first tensor
143	>	* @param t2 second tensor
144	>	* @return the tensor contraction (double dot product) of t1 and t2
145	>	*/
146	>	Real doubleDot( const SquareMatrix<Real, Dim>& t1, const SquareMatrix<Real, Dim>& t2 ) {
147	>	Real tmp;
148	>	tmp = 0;
149	>
150	>	for (unsigned int i = 0; i < Dim; i++)
151	>	for (unsigned int j =0; j < Dim; j++)
152	>	tmp += t1[i][j] * t2[i][j];
153	>
154	>	return tmp;
155	>	}
156
110	–	/** Tests if this matrix is symmetrix. */
111	–	bool isSymmetric() const {
112	–	for (unsigned int i = 0; i < Dim - 1; i++)
113	–	for (unsigned int j = i; j < Dim; j++)
114	–	if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
115	–	return false;
116	–
117	–	return true;
118	–	}
157
158	<	/** Tests if this matrix is orthogonal. */
159	<	bool isOrthogonal() {
160	<	SquareMatrix<Real, Dim> tmp;
158	>	/** Tests if this matrix is symmetrix. */
159	>	bool isSymmetric() const {
160	>	for (unsigned int i = 0; i < Dim - 1; i++)
161	>	for (unsigned int j = i; j < Dim; j++)
162	>	if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon)
163	>	return false;
164	>
165	>	return true;
166	>	}
167
168	<	tmp = *this * transpose();
168	>	/** Tests if this matrix is orthogonal. */
169	>	bool isOrthogonal() {
170	>	SquareMatrix<Real, Dim> tmp;
171
172	<	return tmp.isDiagonal();
127	<	}
172	>	tmp = *this * transpose();
173
174	<	/** Tests if this matrix is diagonal. */
175	<	bool isDiagonal() const {
176	<	for (unsigned int i = 0; i < Dim ; i++)
177	<	for (unsigned int j = 0; j < Dim; j++)
178	<	if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
179	<	return false;
174	>	return tmp.isDiagonal();
175	>	}
176	>
177	>	/** Tests if this matrix is diagonal. */
178	>	bool isDiagonal() const {
179	>	for (unsigned int i = 0; i < Dim ; i++)
180	>	for (unsigned int j = 0; j < Dim; j++)
181	>	if (i !=j && fabs(this->data_[i][j]) > epsilon)
182	>	return false;
183	>
184	>	return true;
185	>	}
186	>
187	>	/**
188	>	* Returns a column vector that contains the elements from the
189	>	* diagonal of m in the order R(0) = m(0,0), R(1) = m(1,1), and so
190	>	* on.
191	>	*/
192	>	Vector<Real, Dim> diagonals() const {
193	>	Vector<Real, Dim> result;
194	>	for (unsigned int i = 0; i < Dim; i++) {
195	>	result(i) = this->data_[i][i];
196	>	}
197	>	return result;
198	>	}
199	>
200	>	/** Tests if this matrix is the unit matrix. */
201	>	bool isUnitMatrix() const {
202	>	if (!isDiagonal())
203	>	return false;
204	>
205	>	for (unsigned int i = 0; i < Dim ; i++)
206	>	if (fabs(this->data_[i][i] - 1) > epsilon)
207	>	return false;
208
209	<	return true;
210	<	}
209	>	return true;
210	>	}
211
212	<	/** Tests if this matrix is the unit matrix. */
213	<	bool isUnitMatrix() const {
214	<	if (!isDiagonal())
142	<	return false;
143	<
144	<	for (unsigned int i = 0; i < Dim ; i++)
145	<	if (fabs(data_[i][i] - 1) > oopse::epsilon)
146	<	return false;
212	>	/** Return the transpose of this matrix */
213	>	SquareMatrix<Real,  Dim> transpose() const{
214	>	SquareMatrix<Real,  Dim> result;
215
216	<	return true;
217	<	}
216	>	for (unsigned int i = 0; i < Dim; i++)
217	>	for (unsigned int j = 0; j < Dim; j++)
218	>	result(j, i) = this->data_[i][j];
219
220	<	/** @todo need implementation */
221	<	void diagonalize() {
222	<	//jacobi(m, eigenValues, ortMat);
223	<	}
220	>	return result;
221	>	}
222	>
223	>	/** @todo need implementation */
224	>	void diagonalize() {
225	>	//jacobi(m, eigenValues, ortMat);
226	>	}
227
228	<	/**
229	<	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
230	<	* real symmetric matrix
231	<	*
232	<	* @return true if success, otherwise return false
233	<	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
234	<	*     overwritten
235	<	* @param w will contain the eigenvalues of the matrix On return of this function
236	<	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
237	<	*    normalized and mutually orthogonal.
238	<	*/
239	<
240	<	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
241	<	SquareMatrix<Real, Dim>& v);
242	<	};//end SquareMatrix
228	>	/**
229	>	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
230	>	* real symmetric matrix
231	>	*
232	>	* @return true if success, otherwise return false
233	>	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
234	>	*     overwritten
235	>	* @param d will contain the eigenvalues of the matrix On return of this function
236	>	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
237	>	*    normalized and mutually orthogonal.
238	>	*/
239	>
240	>	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
241	>	SquareMatrix<Real, Dim>& v);
242	>	};//end SquareMatrix
243
244
245	<	/*=========================================================================
245	>	/*=========================================================================
246
247		Program:   Visualization Toolkit
248		Module:    $RCSfile: SquareMatrix.hpp,v $
#	Line 179 | Line 251 | namespace oopse {
251		All rights reserved.
252		See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
253
254	<	This software is distributed WITHOUT ANY WARRANTY; without even
255	<	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
256	<	PURPOSE.  See the above copyright notice for more information.
254	>	This software is distributed WITHOUT ANY WARRANTY; without even
255	>	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
256	>	PURPOSE.  See the above copyright notice for more information.
257
258	<	=========================================================================*/
258	>	=========================================================================*/
259
260	<	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\
261	<	a(k, l)=h+s*(g-h*tau)
260	>	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \
261	>	a(k, l)=h+s*(g-h*tau)
262
263		#define VTK_MAX_ROTATIONS 20
264
265	<	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
266	<	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
267	<	// output eigenvalues in w; and output eigenvectors in v. Resulting
268	<	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
269	<	// normalized.
270	<	template<typename Real, int Dim>
271	<	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
272	<	SquareMatrix<Real, Dim>& v) {
273	<	const int n = Dim;
274	<	int i, j, k, iq, ip, numPos;
275	<	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
276	<	Real bspace[4], zspace[4];
277	<	Real *b = bspace;
278	<	Real *z = zspace;
265	>	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
266	>	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
267	>	// output eigenvalues in w; and output eigenvectors in v. Resulting
268	>	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
269	>	// normalized.
270	>	template<typename Real, int Dim>
271	>	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
272	>	SquareMatrix<Real, Dim>& v) {
273	>	const int n = Dim;
274	>	int i, j, k, iq, ip, numPos;
275	>	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
276	>	Real bspace[4], zspace[4];
277	>	Real *b = bspace;
278	>	Real *z = zspace;
279
280	<	// only allocate memory if the matrix is large
281	<	if (n > 4)
282	<	{
283	<	b = new Real[n];
284	<	z = new Real[n];
213	<	}
280	>	// only allocate memory if the matrix is large
281	>	if (n > 4) {
282	>	b = new Real[n];
283	>	z = new Real[n];
284	>	}
285
286	<	// initialize
287	<	for (ip=0; ip<n; ip++)
288	<	{
289	<	for (iq=0; iq<n; iq++)
290	<	{
291	<	v(ip, iq) = 0.0;
292	<	}
293	<	v(ip, ip) = 1.0;
294	<	}
295	<	for (ip=0; ip<n; ip++)
296	<	{
226	<	b[ip] = w[ip] = a(ip, ip);
227	<	z[ip] = 0.0;
228	<	}
286	>	// initialize
287	>	for (ip=0; ip<n; ip++) {
288	>	for (iq=0; iq<n; iq++) {
289	>	v(ip, iq) = 0.0;
290	>	}
291	>	v(ip, ip) = 1.0;
292	>	}
293	>	for (ip=0; ip<n; ip++) {
294	>	b[ip] = w[ip] = a(ip, ip);
295	>	z[ip] = 0.0;
296	>	}
297
298	<	// begin rotation sequence
299	<	for (i=0; i<VTK_MAX_ROTATIONS; i++)
300	<	{
301	<	sm = 0.0;
302	<	for (ip=0; ip<n-1; ip++)
303	<	{
304	<	for (iq=ip+1; iq<n; iq++)
305	<	{
306	<	sm += fabs(a(ip, iq));
307	<	}
308	<	}
241	<	if (sm == 0.0)
242	<	{
243	<	break;
244	<	}
298	>	// begin rotation sequence
299	>	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
300	>	sm = 0.0;
301	>	for (ip=0; ip<n-1; ip++) {
302	>	for (iq=ip+1; iq<n; iq++) {
303	>	sm += fabs(a(ip, iq));
304	>	}
305	>	}
306	>	if (sm == 0.0) {
307	>	break;
308	>	}
309
310	<	if (i < 3)                                // first 3 sweeps
311	<	{
312	<	tresh = 0.2*sm/(n*n);
313	<	}
314	<	else
251	<	{
252	<	tresh = 0.0;
253	<	}
310	>	if (i < 3) {                                // first 3 sweeps
311	>	tresh = 0.2*sm/(n*n);
312	>	} else {
313	>	tresh = 0.0;
314	>	}
315
316	<	for (ip=0; ip<n-1; ip++)
317	<	{
318	<	for (iq=ip+1; iq<n; iq++)
258	<	{
259	<	g = 100.0*fabs(a(ip, iq));
316	>	for (ip=0; ip<n-1; ip++) {
317	>	for (iq=ip+1; iq<n; iq++) {
318	>	g = 100.0*fabs(a(ip, iq));
319
320	<	// after 4 sweeps
321	<	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
322	<	&& (fabs(w[iq])+g) == fabs(w[iq]))
323	<	{
324	<	a(ip, iq) = 0.0;
325	<	}
326	<	else if (fabs(a(ip, iq)) > tresh)
327	<	{
328	<	h = w[iq] - w[ip];
329	<	if ( (fabs(h)+g) == fabs(h))
330	<	{
331	<	t = (a(ip, iq)) / h;
332	<	}
333	<	else
334	<	{
335	<	theta = 0.5*h / (a(ip, iq));
336	<	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
337	<	if (theta < 0.0)
338	<	{
339	<	t = -t;
340	<	}
341	<	}
342	<	c = 1.0 / sqrt(1+t*t);
343	<	s = t*c;
285	<	tau = s/(1.0+c);
286	<	h = t*a(ip, iq);
287	<	z[ip] -= h;
288	<	z[iq] += h;
289	<	w[ip] -= h;
290	<	w[iq] += h;
291	<	a(ip, iq)=0.0;
320	>	// after 4 sweeps
321	>	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
322	>	&& (fabs(w[iq])+g) == fabs(w[iq])) {
323	>	a(ip, iq) = 0.0;
324	>	} else if (fabs(a(ip, iq)) > tresh) {
325	>	h = w[iq] - w[ip];
326	>	if ( (fabs(h)+g) == fabs(h)) {
327	>	t = (a(ip, iq)) / h;
328	>	} else {
329	>	theta = 0.5*h / (a(ip, iq));
330	>	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
331	>	if (theta < 0.0) {
332	>	t = -t;
333	>	}
334	>	}
335	>	c = 1.0 / sqrt(1+t*t);
336	>	s = t*c;
337	>	tau = s/(1.0+c);
338	>	h = t*a(ip, iq);
339	>	z[ip] -= h;
340	>	z[iq] += h;
341	>	w[ip] -= h;
342	>	w[iq] += h;
343	>	a(ip, iq)=0.0;
344
345	<	// ip already shifted left by 1 unit
346	<	for (j = 0;j <= ip-1;j++)
347	<	{
348	<	VTK_ROTATE(a,j,ip,j,iq);
349	<	}
350	<	// ip and iq already shifted left by 1 unit
351	<	for (j = ip+1;j <= iq-1;j++)
352	<	{
353	<	VTK_ROTATE(a,ip,j,j,iq);
354	<	}
355	<	// iq already shifted left by 1 unit
356	<	for (j=iq+1; j<n; j++)
357	<	{
358	<	VTK_ROTATE(a,ip,j,iq,j);
359	<	}
360	<	for (j=0; j<n; j++)
361	<	{
362	<	VTK_ROTATE(v,j,ip,j,iq);
311	<	}
312	<	}
313	<	}
314	<	}
345	>	// ip already shifted left by 1 unit
346	>	for (j = 0;j <= ip-1;j++) {
347	>	VTK_ROTATE(a,j,ip,j,iq);
348	>	}
349	>	// ip and iq already shifted left by 1 unit
350	>	for (j = ip+1;j <= iq-1;j++) {
351	>	VTK_ROTATE(a,ip,j,j,iq);
352	>	}
353	>	// iq already shifted left by 1 unit
354	>	for (j=iq+1; j<n; j++) {
355	>	VTK_ROTATE(a,ip,j,iq,j);
356	>	}
357	>	for (j=0; j<n; j++) {
358	>	VTK_ROTATE(v,j,ip,j,iq);
359	>	}
360	>	}
361	>	}
362	>	}
363
364	<	for (ip=0; ip<n; ip++)
365	<	{
366	<	b[ip] += z[ip];
367	<	w[ip] = b[ip];
368	<	z[ip] = 0.0;
369	<	}
322	<	}
364	>	for (ip=0; ip<n; ip++) {
365	>	b[ip] += z[ip];
366	>	w[ip] = b[ip];
367	>	z[ip] = 0.0;
368	>	}
369	>	}
370
371	<	//// this is NEVER called
372	<	if ( i >= VTK_MAX_ROTATIONS )
373	<	{
374	<	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
375	<	return 0;
376	<	}
371	>	//// this is NEVER called
372	>	if ( i >= VTK_MAX_ROTATIONS ) {
373	>	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
374	>	if (n > 4) {
375	>	delete[] b;
376	>	delete[] z;
377	>	}
378	>	return 0;
379	>	}
380
381	<	// sort eigenfunctions                 these changes do not affect accuracy
382	<	for (j=0; j<n-1; j++)                  // boundary incorrect
383	<	{
384	<	k = j;
385	<	tmp = w[k];
386	<	for (i=j+1; i<n; i++)                // boundary incorrect, shifted already
387	<	{
388	<	if (w[i] >= tmp)                   // why exchage if same?
389	<	{
390	<	k = i;
391	<	tmp = w[k];
392	<	}
393	<	}
394	<	if (k != j)
395	<	{
396	<	w[k] = w[j];
397	<	w[j] = tmp;
398	<	for (i=0; i<n; i++)
399	<	{
400	<	tmp = v(i, j);
401	<	v(i, j) = v(i, k);
402	<	v(i, k) = tmp;
403	<	}
404	<	}
405	<	}
406	<	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
407	<	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
408	<	// reek havoc in hyperstreamline/other stuff. We will select the most
409	<	// positive eigenvector.
410	<	int ceil_half_n = (n >> 1) + (n & 1);
411	<	for (j=0; j<n; j++)
412	<	{
413	<	for (numPos=0, i=0; i<n; i++)
414	<	{
415	<	if ( v(i, j) >= 0.0 )
416	<	{
417	<	numPos++;
418	<	}
369	<	}
370	<	//    if ( numPos < ceil(double(n)/double(2.0)) )
371	<	if ( numPos < ceil_half_n)
372	<	{
373	<	for(i=0; i<n; i++)
374	<	{
375	<	v(i, j) *= -1.0;
376	<	}
377	<	}
378	<	}
381	>	// sort eigenfunctions                 these changes do not affect accuracy
382	>	for (j=0; j<n-1; j++) {                  // boundary incorrect
383	>	k = j;
384	>	tmp = w[k];
385	>	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
386	>	if (w[i] >= tmp) {                   // why exchage if same?
387	>	k = i;
388	>	tmp = w[k];
389	>	}
390	>	}
391	>	if (k != j) {
392	>	w[k] = w[j];
393	>	w[j] = tmp;
394	>	for (i=0; i<n; i++) {
395	>	tmp = v(i, j);
396	>	v(i, j) = v(i, k);
397	>	v(i, k) = tmp;
398	>	}
399	>	}
400	>	}
401	>	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
402	>	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
403	>	// reek havoc in hyperstreamline/other stuff. We will select the most
404	>	// positive eigenvector.
405	>	int ceil_half_n = (n >> 1) + (n & 1);
406	>	for (j=0; j<n; j++) {
407	>	for (numPos=0, i=0; i<n; i++) {
408	>	if ( v(i, j) >= 0.0 ) {
409	>	numPos++;
410	>	}
411	>	}
412	>	//    if ( numPos < ceil(RealType(n)/RealType(2.0)) )
413	>	if ( numPos < ceil_half_n) {
414	>	for (i=0; i<n; i++) {
415	>	v(i, j) *= -1.0;
416	>	}
417	>	}
418	>	}
419
420	<	if (n > 4)
421	<	{
422	<	delete [] b;
383	<	delete [] z;
384	<	}
385	<	return 1;
420	>	if (n > 4) {
421	>	delete [] b;
422	>	delete [] z;
423		}
424	+	return 1;
425	+	}
426
427
428	+	typedef SquareMatrix<RealType, 6> Mat6x6d;
429		}
430		#endif //MATH_SQUAREMATRIX_HPP
431

Comparing:
trunk/src/math/SquareMatrix.hpp (property svn:keywords), Revision 123 by tim, Wed Oct 20 18:07:08 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (property svn:keywords), Revision 1874 by gezelter, Wed May 15 15:09:35 2013 UTC

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