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

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trunk/src/math/SquareMatrix.hpp (file contents), Revision 146 by tim, Fri Oct 22 23:09:57 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (file contents), Revision 1787 by gezelter, Wed Aug 29 18:13:11 2012 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]  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:
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	<	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	<	}
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	>	}
83	>
84	>
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 += 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(data_[i][j] - data_[j][i]) > oopse::epsilon)
162	<	return false;
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]) > epsilon)
162	>	return false;
163
164	<	return true;
165	<	}
164	>	return true;
165	>	}
166
167	<	/** Tests if this matrix is orthogonal. */
168	<	bool isOrthogonal() {
169	<	SquareMatrix<Real, Dim> tmp;
167	>	/** Tests if this matrix is orthogonal. */
168	>	bool isOrthogonal() {
169	>	SquareMatrix<Real, Dim> tmp;
170
171	<	tmp = *this * transpose();
171	>	tmp = *this * transpose();
172
173	<	return tmp.isDiagonal();
174	<	}
173	>	return tmp.isDiagonal();
174	>	}
175
176	<	/** Tests if this matrix is diagonal. */
177	<	bool isDiagonal() const {
178	<	for (unsigned int i = 0; i < Dim ; i++)
179	<	for (unsigned int j = 0; j < Dim; j++)
180	<	if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
181	<	return false;
176	>	/** Tests if this matrix is diagonal. */
177	>	bool isDiagonal() const {
178	>	for (unsigned int i = 0; i < Dim ; i++)
179	>	for (unsigned int j = 0; j < Dim; j++)
180	>	if (i !=j && fabs(this->data_[i][j]) > epsilon)
181	>	return false;
182
183	<	return true;
184	<	}
183	>	return true;
184	>	}
185
186	<	/** Tests if this matrix is the unit matrix. */
187	<	bool isUnitMatrix() const {
188	<	if (!isDiagonal())
189	<	return false;
186	>	/**
187	>	* Returns a column vector that contains the elements from the
188	>	* diagonal of m in the order R(0) = m(0,0), R(1) = m(1,1), and so
189	>	* on.
190	>	*/
191	>	Vector<Real, Dim> diagonals() const {
192	>	Vector<Real, Dim> result;
193	>	for (unsigned int i = 0; i < Dim; i++) {
194	>	result(i) = this->data_[i][i];
195	>	}
196	>	return result;
197	>	}
198	>
199	>	/** Tests if this matrix is the unit matrix. */
200	>	bool isUnitMatrix() const {
201	>	if (!isDiagonal())
202	>	return false;
203
204	<	for (unsigned int i = 0; i < Dim ; i++)
205	<	if (fabs(data_[i][i] - 1) > oopse::epsilon)
206	<	return false;
204	>	for (unsigned int i = 0; i < Dim ; i++)
205	>	if (fabs(this->data_[i][i] - 1) > epsilon)
206	>	return false;
207
208	<	return true;
209	<	}
208	>	return true;
209	>	}
210
211	<	/** @todo need implementation */
212	<	void diagonalize() {
213	<	//jacobi(m, eigenValues, ortMat);
214	<	}
211	>	/** Return the transpose of this matrix */
212	>	SquareMatrix<Real,  Dim> transpose() const{
213	>	SquareMatrix<Real,  Dim> result;
214	>
215	>	for (unsigned int i = 0; i < Dim; i++)
216	>	for (unsigned int j = 0; j < Dim; j++)
217	>	result(j, i) = this->data_[i][j];
218
219	<	/**
220	<	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
221	<	* real symmetric matrix
222	<	*
223	<	* @return true if success, otherwise return false
224	<	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
225	<	*     overwritten
226	<	* @param w will contain the eigenvalues of the matrix On return of this function
227	<	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
228	<	*    normalized and mutually orthogonal.
229	<	*/
219	>	return result;
220	>	}
221	>
222	>	/** @todo need implementation */
223	>	void diagonalize() {
224	>	//jacobi(m, eigenValues, ortMat);
225	>	}
226	>
227	>	/**
228	>	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
229	>	* real symmetric matrix
230	>	*
231	>	* @return true if success, otherwise return false
232	>	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
233	>	*     overwritten
234	>	* @param w will contain the eigenvalues of the matrix On return of this function
235	>	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
236	>	*    normalized and mutually orthogonal.
237	>	*/
238
239	<	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
240	<	SquareMatrix<Real, Dim>& v);
241	<	};//end SquareMatrix
239	>	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
240	>	SquareMatrix<Real, Dim>& v);
241	>	};//end SquareMatrix
242
243
244	<	/*=========================================================================
244	>	/*=========================================================================
245
246		Program:   Visualization Toolkit
247		Module:    $RCSfile: SquareMatrix.hpp,v $
#	Line 181 | Line 250 | namespace oopse {
250		All rights reserved.
251		See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
252
253	<	This software is distributed WITHOUT ANY WARRANTY; without even
254	<	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
255	<	PURPOSE.  See the above copyright notice for more information.
253	>	This software is distributed WITHOUT ANY WARRANTY; without even
254	>	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
255	>	PURPOSE.  See the above copyright notice for more information.
256
257	<	=========================================================================*/
257	>	=========================================================================*/
258
259	<	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\
260	<	a(k, l)=h+s*(g-h*tau)
259	>	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \
260	>	a(k, l)=h+s*(g-h*tau)
261
262		#define VTK_MAX_ROTATIONS 20
263
264	<	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
265	<	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
266	<	// output eigenvalues in w; and output eigenvectors in v. Resulting
267	<	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
268	<	// normalized.
269	<	template<typename Real, int Dim>
270	<	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
271	<	SquareMatrix<Real, Dim>& v) {
272	<	const int n = Dim;
273	<	int i, j, k, iq, ip, numPos;
274	<	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
275	<	Real bspace[4], zspace[4];
276	<	Real *b = bspace;
277	<	Real *z = zspace;
264	>	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
265	>	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
266	>	// output eigenvalues in w; and output eigenvectors in v. Resulting
267	>	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
268	>	// normalized.
269	>	template<typename Real, int Dim>
270	>	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
271	>	SquareMatrix<Real, Dim>& v) {
272	>	const int n = Dim;
273	>	int i, j, k, iq, ip, numPos;
274	>	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
275	>	Real bspace[4], zspace[4];
276	>	Real *b = bspace;
277	>	Real *z = zspace;
278
279	<	// only allocate memory if the matrix is large
280	<	if (n > 4) {
281	<	b = new Real[n];
282	<	z = new Real[n];
283	<	}
279	>	// only allocate memory if the matrix is large
280	>	if (n > 4) {
281	>	b = new Real[n];
282	>	z = new Real[n];
283	>	}
284
285	<	// initialize
286	<	for (ip=0; ip<n; ip++) {
287	<	for (iq=0; iq<n; iq++) {
288	<	v(ip, iq) = 0.0;
289	<	}
290	<	v(ip, ip) = 1.0;
291	<	}
292	<	for (ip=0; ip<n; ip++) {
293	<	b[ip] = w[ip] = a(ip, ip);
294	<	z[ip] = 0.0;
295	<	}
285	>	// initialize
286	>	for (ip=0; ip<n; ip++) {
287	>	for (iq=0; iq<n; iq++) {
288	>	v(ip, iq) = 0.0;
289	>	}
290	>	v(ip, ip) = 1.0;
291	>	}
292	>	for (ip=0; ip<n; ip++) {
293	>	b[ip] = w[ip] = a(ip, ip);
294	>	z[ip] = 0.0;
295	>	}
296
297	<	// begin rotation sequence
298	<	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
299	<	sm = 0.0;
300	<	for (ip=0; ip<n-1; ip++) {
301	<	for (iq=ip+1; iq<n; iq++) {
302	<	sm += fabs(a(ip, iq));
303	<	}
304	<	}
305	<	if (sm == 0.0) {
306	<	break;
307	<	}
297	>	// begin rotation sequence
298	>	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
299	>	sm = 0.0;
300	>	for (ip=0; ip<n-1; ip++) {
301	>	for (iq=ip+1; iq<n; iq++) {
302	>	sm += fabs(a(ip, iq));
303	>	}
304	>	}
305	>	if (sm == 0.0) {
306	>	break;
307	>	}
308
309	<	if (i < 3) {                                // first 3 sweeps
310	<	tresh = 0.2*sm/(n*n);
311	<	} else {
312	<	tresh = 0.0;
313	<	}
309	>	if (i < 3) {                                // first 3 sweeps
310	>	tresh = 0.2*sm/(n*n);
311	>	} else {
312	>	tresh = 0.0;
313	>	}
314
315	<	for (ip=0; ip<n-1; ip++) {
316	<	for (iq=ip+1; iq<n; iq++) {
317	<	g = 100.0*fabs(a(ip, iq));
315	>	for (ip=0; ip<n-1; ip++) {
316	>	for (iq=ip+1; iq<n; iq++) {
317	>	g = 100.0*fabs(a(ip, iq));
318
319	<	// after 4 sweeps
320	<	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
321	<	&& (fabs(w[iq])+g) == fabs(w[iq])) {
322	<	a(ip, iq) = 0.0;
323	<	} else if (fabs(a(ip, iq)) > tresh) {
324	<	h = w[iq] - w[ip];
325	<	if ( (fabs(h)+g) == fabs(h)) {
326	<	t = (a(ip, iq)) / h;
327	<	} else {
328	<	theta = 0.5*h / (a(ip, iq));
329	<	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
330	<	if (theta < 0.0) {
331	<	t = -t;
332	<	}
333	<	}
334	<	c = 1.0 / sqrt(1+t*t);
335	<	s = t*c;
336	<	tau = s/(1.0+c);
337	<	h = t*a(ip, iq);
338	<	z[ip] -= h;
339	<	z[iq] += h;
340	<	w[ip] -= h;
341	<	w[iq] += h;
342	<	a(ip, iq)=0.0;
319	>	// after 4 sweeps
320	>	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
321	>	&& (fabs(w[iq])+g) == fabs(w[iq])) {
322	>	a(ip, iq) = 0.0;
323	>	} else if (fabs(a(ip, iq)) > tresh) {
324	>	h = w[iq] - w[ip];
325	>	if ( (fabs(h)+g) == fabs(h)) {
326	>	t = (a(ip, iq)) / h;
327	>	} else {
328	>	theta = 0.5*h / (a(ip, iq));
329	>	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
330	>	if (theta < 0.0) {
331	>	t = -t;
332	>	}
333	>	}
334	>	c = 1.0 / sqrt(1+t*t);
335	>	s = t*c;
336	>	tau = s/(1.0+c);
337	>	h = t*a(ip, iq);
338	>	z[ip] -= h;
339	>	z[iq] += h;
340	>	w[ip] -= h;
341	>	w[iq] += h;
342	>	a(ip, iq)=0.0;
343
344	<	// ip already shifted left by 1 unit
345	<	for (j = 0;j <= ip-1;j++) {
346	<	VTK_ROTATE(a,j,ip,j,iq);
347	<	}
348	<	// ip and iq already shifted left by 1 unit
349	<	for (j = ip+1;j <= iq-1;j++) {
350	<	VTK_ROTATE(a,ip,j,j,iq);
351	<	}
352	<	// iq already shifted left by 1 unit
353	<	for (j=iq+1; j<n; j++) {
354	<	VTK_ROTATE(a,ip,j,iq,j);
355	<	}
356	<	for (j=0; j<n; j++) {
357	<	VTK_ROTATE(v,j,ip,j,iq);
358	<	}
359	<	}
360	<	}
361	<	}
344	>	// ip already shifted left by 1 unit
345	>	for (j = 0;j <= ip-1;j++) {
346	>	VTK_ROTATE(a,j,ip,j,iq);
347	>	}
348	>	// ip and iq already shifted left by 1 unit
349	>	for (j = ip+1;j <= iq-1;j++) {
350	>	VTK_ROTATE(a,ip,j,j,iq);
351	>	}
352	>	// iq already shifted left by 1 unit
353	>	for (j=iq+1; j<n; j++) {
354	>	VTK_ROTATE(a,ip,j,iq,j);
355	>	}
356	>	for (j=0; j<n; j++) {
357	>	VTK_ROTATE(v,j,ip,j,iq);
358	>	}
359	>	}
360	>	}
361	>	}
362
363	<	for (ip=0; ip<n; ip++) {
364	<	b[ip] += z[ip];
365	<	w[ip] = b[ip];
366	<	z[ip] = 0.0;
367	<	}
368	<	}
363	>	for (ip=0; ip<n; ip++) {
364	>	b[ip] += z[ip];
365	>	w[ip] = b[ip];
366	>	z[ip] = 0.0;
367	>	}
368	>	}
369
370	<	//// this is NEVER called
371	<	if ( i >= VTK_MAX_ROTATIONS ) {
372	<	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
373	<	return 0;
374	<	}
370	>	//// this is NEVER called
371	>	if ( i >= VTK_MAX_ROTATIONS ) {
372	>	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
373	>	return 0;
374	>	}
375
376	<	// sort eigenfunctions                 these changes do not affect accuracy
377	<	for (j=0; j<n-1; j++) {                  // boundary incorrect
378	<	k = j;
379	<	tmp = w[k];
380	<	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
381	<	if (w[i] >= tmp) {                   // why exchage if same?
382	<	k = i;
383	<	tmp = w[k];
384	<	}
385	<	}
386	<	if (k != j) {
387	<	w[k] = w[j];
388	<	w[j] = tmp;
389	<	for (i=0; i<n; i++) {
390	<	tmp = v(i, j);
391	<	v(i, j) = v(i, k);
392	<	v(i, k) = tmp;
393	<	}
394	<	}
395	<	}
396	<	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
397	<	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
398	<	// reek havoc in hyperstreamline/other stuff. We will select the most
399	<	// positive eigenvector.
400	<	int ceil_half_n = (n >> 1) + (n & 1);
401	<	for (j=0; j<n; j++) {
402	<	for (numPos=0, i=0; i<n; i++) {
403	<	if ( v(i, j) >= 0.0 ) {
404	<	numPos++;
405	<	}
406	<	}
407	<	//    if ( numPos < ceil(double(n)/double(2.0)) )
408	<	if ( numPos < ceil_half_n) {
409	<	for (i=0; i<n; i++) {
410	<	v(i, j) *= -1.0;
411	<	}
412	<	}
413	<	}
376	>	// sort eigenfunctions                 these changes do not affect accuracy
377	>	for (j=0; j<n-1; j++) {                  // boundary incorrect
378	>	k = j;
379	>	tmp = w[k];
380	>	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
381	>	if (w[i] >= tmp) {                   // why exchage if same?
382	>	k = i;
383	>	tmp = w[k];
384	>	}
385	>	}
386	>	if (k != j) {
387	>	w[k] = w[j];
388	>	w[j] = tmp;
389	>	for (i=0; i<n; i++) {
390	>	tmp = v(i, j);
391	>	v(i, j) = v(i, k);
392	>	v(i, k) = tmp;
393	>	}
394	>	}
395	>	}
396	>	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
397	>	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
398	>	// reek havoc in hyperstreamline/other stuff. We will select the most
399	>	// positive eigenvector.
400	>	int ceil_half_n = (n >> 1) + (n & 1);
401	>	for (j=0; j<n; j++) {
402	>	for (numPos=0, i=0; i<n; i++) {
403	>	if ( v(i, j) >= 0.0 ) {
404	>	numPos++;
405	>	}
406	>	}
407	>	//    if ( numPos < ceil(RealType(n)/RealType(2.0)) )
408	>	if ( numPos < ceil_half_n) {
409	>	for (i=0; i<n; i++) {
410	>	v(i, j) *= -1.0;
411	>	}
412	>	}
413	>	}
414
415	<	if (n > 4) {
416	<	delete [] b;
417	<	delete [] z;
349	<	}
350	<	return 1;
415	>	if (n > 4) {
416	>	delete [] b;
417	>	delete [] z;
418		}
419	+	return 1;
420	+	}
421
422
423	+	typedef SquareMatrix<RealType, 6> Mat6x6d;
424		}
425		#endif //MATH_SQUAREMATRIX_HPP
426

Comparing:
trunk/src/math/SquareMatrix.hpp (property svn:keywords), Revision 146 by tim, Fri Oct 22 23:09:57 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (property svn:keywords), Revision 1787 by gezelter, Wed Aug 29 18:13:11 2012 UTC

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