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

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trunk/src/math/SquareMatrix.hpp (file contents), Revision 385 by tim, Tue Mar 1 20:10:14 2005 UTC vs.
branches/development/src/math/SquareMatrix.hpp (file contents), Revision 1753 by gezelter, Tue Jun 12 13:20:28 2012 UTC

#	Line 1 | Line 1
1	<	/*
1	>	/*
2		* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3		*
4		* The University of Notre Dame grants you ("Licensee") a
#	Line 6 | Line 6
6		* redistribute this software in source and binary code form, provided
7		* that the following conditions are met:
8		*
9	<	* 1. Acknowledgement of the program authors must be made in any
10	<	*    publication of scientific results based in part on use of the
11	<	*    program.  An acceptable form of acknowledgement is citation of
12	<	*    the article in which the program was described (Matthew
13	<	*    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14	<	*    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15	<	*    Parallel Simulation Engine for Molecular Dynamics,"
16	<	*    J. Comput. Chem. 26, pp. 252-271 (2005))
17	<	*
18	<	* 2. Redistributions of source code must retain the above copyright
9	>	* 1. Redistributions of source code must retain the above copyright
10		*    notice, this list of conditions and the following disclaimer.
11		*
12	<	* 3. Redistributions in binary form must reproduce the above copyright
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.
#	Line 37 | Line 28
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]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
40	+	* [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41		*/
42
43		/**
#	Line 45 | Line 46
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:
66	<	typedef Real ElemType;
67	<	typedef Real* ElemPoinerType;
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:
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	<	this->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	<	/** Constructs and initializes every element of this matrix to a scalar */
77	<	SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
78	<	}
76	>	/** Constructs and initializes every element of this matrix to a scalar */
77	>	SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
78	>	}
79
80	<	/** Constructs and initializes from an array */
81	<	SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
82	<	}
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	<	}
85	>	/** copy constructor */
86	>	SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
87	>	}
88
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	<	}
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*/
95	>	/** Retunrs  an identity matrix*/
96
97	<	static SquareMatrix<Real, Dim> identity() {
98	<	SquareMatrix<Real, Dim> m;
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;
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	<	return m;
108	<	}
107	>	return m;
108	>	}
109
110	<	/**
111	<	* Retunrs  the inversion of this matrix.
112	<	* @todo need implementation
113	<	*/
114	<	SquareMatrix<Real, Dim>  inverse() {
115	<	SquareMatrix<Real, Dim> result;
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	<	return result;
118	<	}
117	>	return result;
118	>	}
119
120	<	/**
121	<	* Returns the determinant of this matrix.
122	<	* @todo need implementation
123	<	*/
124	<	Real determinant() const {
125	<	Real det;
126	<	return det;
127	<	}
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;
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];
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
157	<	/** Tests if this matrix is symmetrix. */
158	<	bool isSymmetric() const {
159	<	for (unsigned int i = 0; i < Dim - 1; i++)
160	<	for (unsigned int j = i; j < Dim; j++)
161	<	if (fabs(this->data_[i][j] - this->data_[j][i]) > oopse::epsilon)
162	<	return false;
157	>
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	<	}
165	>	return true;
166	>	}
167
168	<	/** Tests if this matrix is orthogonal. */
169	<	bool isOrthogonal() {
170	<	SquareMatrix<Real, Dim> tmp;
168	>	/** Tests if this matrix is orthogonal. */
169	>	bool isOrthogonal() {
170	>	SquareMatrix<Real, Dim> tmp;
171
172	<	tmp = *this * transpose();
172	>	tmp = *this * transpose();
173
174	<	return tmp.isDiagonal();
175	<	}
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]) > oopse::epsilon)
182	<	return false;
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	<	}
184	>	return true;
185	>	}
186
187	<	/** Tests if this matrix is the unit matrix. */
188	<	bool isUnitMatrix() const {
189	<	if (!isDiagonal())
190	<	return false;
187	>	/** Tests if this matrix is the unit matrix. */
188	>	bool isUnitMatrix() const {
189	>	if (!isDiagonal())
190	>	return false;
191
192	<	for (unsigned int i = 0; i < Dim ; i++)
193	<	if (fabs(this->data_[i][i] - 1) > oopse::epsilon)
194	<	return false;
192	>	for (unsigned int i = 0; i < Dim ; i++)
193	>	if (fabs(this->data_[i][i] - 1) > epsilon)
194	>	return false;
195
196	<	return true;
197	<	}
196	>	return true;
197	>	}
198
199	<	/** Return the transpose of this matrix */
200	<	SquareMatrix<Real,  Dim> transpose() const{
201	<	SquareMatrix<Real,  Dim> result;
199	>	/** Return the transpose of this matrix */
200	>	SquareMatrix<Real,  Dim> transpose() const{
201	>	SquareMatrix<Real,  Dim> result;
202
203	<	for (unsigned int i = 0; i < Dim; i++)
204	<	for (unsigned int j = 0; j < Dim; j++)
205	<	result(j, i) = this->data_[i][j];
203	>	for (unsigned int i = 0; i < Dim; i++)
204	>	for (unsigned int j = 0; j < Dim; j++)
205	>	result(j, i) = this->data_[i][j];
206
207	<	return result;
208	<	}
207	>	return result;
208	>	}
209
210	<	/** @todo need implementation */
211	<	void diagonalize() {
212	<	//jacobi(m, eigenValues, ortMat);
213	<	}
210	>	/** @todo need implementation */
211	>	void diagonalize() {
212	>	//jacobi(m, eigenValues, ortMat);
213	>	}
214
215	<	/**
216	<	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
217	<	* real symmetric matrix
218	<	*
219	<	* @return true if success, otherwise return false
220	<	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
221	<	*     overwritten
222	<	* @param w will contain the eigenvalues of the matrix On return of this function
223	<	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
224	<	*    normalized and mutually orthogonal.
225	<	*/
215	>	/**
216	>	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
217	>	* real symmetric matrix
218	>	*
219	>	* @return true if success, otherwise return false
220	>	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
221	>	*     overwritten
222	>	* @param w will contain the eigenvalues of the matrix On return of this function
223	>	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
224	>	*    normalized and mutually orthogonal.
225	>	*/
226
227	<	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
228	<	SquareMatrix<Real, Dim>& v);
229	<	};//end SquareMatrix
227	>	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
228	>	SquareMatrix<Real, Dim>& v);
229	>	};//end SquareMatrix
230
231
232	<	/*=========================================================================
232	>	/*=========================================================================
233
234		Program:   Visualization Toolkit
235		Module:    $RCSfile: SquareMatrix.hpp,v $
#	Line 217 | Line 238 | namespace oopse {
238		All rights reserved.
239		See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
240
241	<	This software is distributed WITHOUT ANY WARRANTY; without even
242	<	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
243	<	PURPOSE.  See the above copyright notice for more information.
241	>	This software is distributed WITHOUT ANY WARRANTY; without even
242	>	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
243	>	PURPOSE.  See the above copyright notice for more information.
244
245	<	=========================================================================*/
245	>	=========================================================================*/
246
247	<	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\
248	<	a(k, l)=h+s*(g-h*tau)
247	>	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \
248	>	a(k, l)=h+s*(g-h*tau)
249
250		#define VTK_MAX_ROTATIONS 20
251
252	<	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
253	<	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
254	<	// output eigenvalues in w; and output eigenvectors in v. Resulting
255	<	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
256	<	// normalized.
257	<	template<typename Real, int Dim>
258	<	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
259	<	SquareMatrix<Real, Dim>& v) {
260	<	const int n = Dim;
261	<	int i, j, k, iq, ip, numPos;
262	<	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
263	<	Real bspace[4], zspace[4];
264	<	Real *b = bspace;
265	<	Real *z = zspace;
252	>	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
253	>	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
254	>	// output eigenvalues in w; and output eigenvectors in v. Resulting
255	>	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
256	>	// normalized.
257	>	template<typename Real, int Dim>
258	>	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
259	>	SquareMatrix<Real, Dim>& v) {
260	>	const int n = Dim;
261	>	int i, j, k, iq, ip, numPos;
262	>	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
263	>	Real bspace[4], zspace[4];
264	>	Real *b = bspace;
265	>	Real *z = zspace;
266
267	<	// only allocate memory if the matrix is large
268	<	if (n > 4) {
269	<	b = new Real[n];
270	<	z = new Real[n];
271	<	}
267	>	// only allocate memory if the matrix is large
268	>	if (n > 4) {
269	>	b = new Real[n];
270	>	z = new Real[n];
271	>	}
272
273	<	// initialize
274	<	for (ip=0; ip<n; ip++) {
275	<	for (iq=0; iq<n; iq++) {
276	<	v(ip, iq) = 0.0;
277	<	}
278	<	v(ip, ip) = 1.0;
279	<	}
280	<	for (ip=0; ip<n; ip++) {
281	<	b[ip] = w[ip] = a(ip, ip);
282	<	z[ip] = 0.0;
283	<	}
273	>	// initialize
274	>	for (ip=0; ip<n; ip++) {
275	>	for (iq=0; iq<n; iq++) {
276	>	v(ip, iq) = 0.0;
277	>	}
278	>	v(ip, ip) = 1.0;
279	>	}
280	>	for (ip=0; ip<n; ip++) {
281	>	b[ip] = w[ip] = a(ip, ip);
282	>	z[ip] = 0.0;
283	>	}
284
285	<	// begin rotation sequence
286	<	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
287	<	sm = 0.0;
288	<	for (ip=0; ip<n-1; ip++) {
289	<	for (iq=ip+1; iq<n; iq++) {
290	<	sm += fabs(a(ip, iq));
291	<	}
292	<	}
293	<	if (sm == 0.0) {
294	<	break;
295	<	}
285	>	// begin rotation sequence
286	>	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
287	>	sm = 0.0;
288	>	for (ip=0; ip<n-1; ip++) {
289	>	for (iq=ip+1; iq<n; iq++) {
290	>	sm += fabs(a(ip, iq));
291	>	}
292	>	}
293	>	if (sm == 0.0) {
294	>	break;
295	>	}
296
297	<	if (i < 3) {                                // first 3 sweeps
298	<	tresh = 0.2*sm/(n*n);
299	<	} else {
300	<	tresh = 0.0;
301	<	}
297	>	if (i < 3) {                                // first 3 sweeps
298	>	tresh = 0.2*sm/(n*n);
299	>	} else {
300	>	tresh = 0.0;
301	>	}
302
303	<	for (ip=0; ip<n-1; ip++) {
304	<	for (iq=ip+1; iq<n; iq++) {
305	<	g = 100.0*fabs(a(ip, iq));
303	>	for (ip=0; ip<n-1; ip++) {
304	>	for (iq=ip+1; iq<n; iq++) {
305	>	g = 100.0*fabs(a(ip, iq));
306
307	<	// after 4 sweeps
308	<	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
309	<	&& (fabs(w[iq])+g) == fabs(w[iq])) {
310	<	a(ip, iq) = 0.0;
311	<	} else if (fabs(a(ip, iq)) > tresh) {
312	<	h = w[iq] - w[ip];
313	<	if ( (fabs(h)+g) == fabs(h)) {
314	<	t = (a(ip, iq)) / h;
315	<	} else {
316	<	theta = 0.5*h / (a(ip, iq));
317	<	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
318	<	if (theta < 0.0) {
319	<	t = -t;
320	<	}
321	<	}
322	<	c = 1.0 / sqrt(1+t*t);
323	<	s = t*c;
324	<	tau = s/(1.0+c);
325	<	h = t*a(ip, iq);
326	<	z[ip] -= h;
327	<	z[iq] += h;
328	<	w[ip] -= h;
329	<	w[iq] += h;
330	<	a(ip, iq)=0.0;
307	>	// after 4 sweeps
308	>	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
309	>	&& (fabs(w[iq])+g) == fabs(w[iq])) {
310	>	a(ip, iq) = 0.0;
311	>	} else if (fabs(a(ip, iq)) > tresh) {
312	>	h = w[iq] - w[ip];
313	>	if ( (fabs(h)+g) == fabs(h)) {
314	>	t = (a(ip, iq)) / h;
315	>	} else {
316	>	theta = 0.5*h / (a(ip, iq));
317	>	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
318	>	if (theta < 0.0) {
319	>	t = -t;
320	>	}
321	>	}
322	>	c = 1.0 / sqrt(1+t*t);
323	>	s = t*c;
324	>	tau = s/(1.0+c);
325	>	h = t*a(ip, iq);
326	>	z[ip] -= h;
327	>	z[iq] += h;
328	>	w[ip] -= h;
329	>	w[iq] += h;
330	>	a(ip, iq)=0.0;
331
332	<	// ip already shifted left by 1 unit
333	<	for (j = 0;j <= ip-1;j++) {
334	<	VTK_ROTATE(a,j,ip,j,iq);
335	<	}
336	<	// ip and iq already shifted left by 1 unit
337	<	for (j = ip+1;j <= iq-1;j++) {
338	<	VTK_ROTATE(a,ip,j,j,iq);
339	<	}
340	<	// iq already shifted left by 1 unit
341	<	for (j=iq+1; j<n; j++) {
342	<	VTK_ROTATE(a,ip,j,iq,j);
343	<	}
344	<	for (j=0; j<n; j++) {
345	<	VTK_ROTATE(v,j,ip,j,iq);
346	<	}
347	<	}
348	<	}
349	<	}
332	>	// ip already shifted left by 1 unit
333	>	for (j = 0;j <= ip-1;j++) {
334	>	VTK_ROTATE(a,j,ip,j,iq);
335	>	}
336	>	// ip and iq already shifted left by 1 unit
337	>	for (j = ip+1;j <= iq-1;j++) {
338	>	VTK_ROTATE(a,ip,j,j,iq);
339	>	}
340	>	// iq already shifted left by 1 unit
341	>	for (j=iq+1; j<n; j++) {
342	>	VTK_ROTATE(a,ip,j,iq,j);
343	>	}
344	>	for (j=0; j<n; j++) {
345	>	VTK_ROTATE(v,j,ip,j,iq);
346	>	}
347	>	}
348	>	}
349	>	}
350
351	<	for (ip=0; ip<n; ip++) {
352	<	b[ip] += z[ip];
353	<	w[ip] = b[ip];
354	<	z[ip] = 0.0;
355	<	}
356	<	}
351	>	for (ip=0; ip<n; ip++) {
352	>	b[ip] += z[ip];
353	>	w[ip] = b[ip];
354	>	z[ip] = 0.0;
355	>	}
356	>	}
357
358	<	//// this is NEVER called
359	<	if ( i >= VTK_MAX_ROTATIONS ) {
360	<	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
361	<	return 0;
362	<	}
358	>	//// this is NEVER called
359	>	if ( i >= VTK_MAX_ROTATIONS ) {
360	>	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
361	>	return 0;
362	>	}
363
364	<	// sort eigenfunctions                 these changes do not affect accuracy
365	<	for (j=0; j<n-1; j++) {                  // boundary incorrect
366	<	k = j;
367	<	tmp = w[k];
368	<	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
369	<	if (w[i] >= tmp) {                   // why exchage if same?
370	<	k = i;
371	<	tmp = w[k];
372	<	}
373	<	}
374	<	if (k != j) {
375	<	w[k] = w[j];
376	<	w[j] = tmp;
377	<	for (i=0; i<n; i++) {
378	<	tmp = v(i, j);
379	<	v(i, j) = v(i, k);
380	<	v(i, k) = tmp;
381	<	}
382	<	}
383	<	}
384	<	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
385	<	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
386	<	// reek havoc in hyperstreamline/other stuff. We will select the most
387	<	// positive eigenvector.
388	<	int ceil_half_n = (n >> 1) + (n & 1);
389	<	for (j=0; j<n; j++) {
390	<	for (numPos=0, i=0; i<n; i++) {
391	<	if ( v(i, j) >= 0.0 ) {
392	<	numPos++;
393	<	}
394	<	}
395	<	//    if ( numPos < ceil(double(n)/double(2.0)) )
396	<	if ( numPos < ceil_half_n) {
397	<	for (i=0; i<n; i++) {
398	<	v(i, j) *= -1.0;
399	<	}
400	<	}
401	<	}
364	>	// sort eigenfunctions                 these changes do not affect accuracy
365	>	for (j=0; j<n-1; j++) {                  // boundary incorrect
366	>	k = j;
367	>	tmp = w[k];
368	>	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
369	>	if (w[i] >= tmp) {                   // why exchage if same?
370	>	k = i;
371	>	tmp = w[k];
372	>	}
373	>	}
374	>	if (k != j) {
375	>	w[k] = w[j];
376	>	w[j] = tmp;
377	>	for (i=0; i<n; i++) {
378	>	tmp = v(i, j);
379	>	v(i, j) = v(i, k);
380	>	v(i, k) = tmp;
381	>	}
382	>	}
383	>	}
384	>	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
385	>	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
386	>	// reek havoc in hyperstreamline/other stuff. We will select the most
387	>	// positive eigenvector.
388	>	int ceil_half_n = (n >> 1) + (n & 1);
389	>	for (j=0; j<n; j++) {
390	>	for (numPos=0, i=0; i<n; i++) {
391	>	if ( v(i, j) >= 0.0 ) {
392	>	numPos++;
393	>	}
394	>	}
395	>	//    if ( numPos < ceil(RealType(n)/RealType(2.0)) )
396	>	if ( numPos < ceil_half_n) {
397	>	for (i=0; i<n; i++) {
398	>	v(i, j) *= -1.0;
399	>	}
400	>	}
401	>	}
402
403	<	if (n > 4) {
404	<	delete [] b;
405	<	delete [] z;
385	<	}
386	<	return 1;
403	>	if (n > 4) {
404	>	delete [] b;
405	>	delete [] z;
406		}
407	+	return 1;
408	+	}
409
410
411	+	typedef SquareMatrix<RealType, 6> Mat6x6d;
412		}
413		#endif //MATH_SQUAREMATRIX_HPP
414

Comparing:
trunk/src/math/SquareMatrix.hpp (property svn:keywords), Revision 385 by tim, Tue Mar 1 20:10:14 2005 UTC vs.
branches/development/src/math/SquareMatrix.hpp (property svn:keywords), Revision 1753 by gezelter, Tue Jun 12 13:20:28 2012 UTC

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