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root/OpenMD/trunk/src/math/SquareMatrix.hpp

Comparing trunk/src/math/SquareMatrix.hpp (file contents):
Revision 93 by tim, Sun Oct 17 01:19:11 2004 UTC vs.
Revision 1924 by gezelter, Mon Aug 5 21:46:11 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
#	Line 33 | Line 50
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	<	/** Retunrs  the inversion of this matrix. */
108	<	SquareMatrix<Real, Dim>  inverse() {
83	<	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	<	/** Returns the determinant of this matrix. */
118	<	double determinant() const {
90	<	double det;
91	<	return det;
92	<	}
117	>	return result;
118	>	}
119
120	<	/** Returns the trace of this matrix. */
121	<	double trace() const {
122	<	double 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	<	/** Tests if this matrix is symmetrix. */
140	<	bool isSymmetric() const {
141	<	for (unsigned int i = 0; i < Dim - 1; i++)
142	<	for (unsigned int j = i; j < Dim; j++)
143	<	if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
144	<	return false;
145	<
146	<	return true;
147	<	}
139	>	/** Tests if this matrix is symmetrix. */
140	>	bool isSymmetric() const {
141	>	for (unsigned int i = 0; i < Dim - 1; i++)
142	>	for (unsigned int j = i; j < Dim; j++)
143	>	if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon)
144	>	return false;
145	>
146	>	return true;
147	>	}
148
149	<	/** Tests if this matrix is orthogonal. */
150	<	bool isOrthogonal() {
151	<	SquareMatrix<Real, Dim> tmp;
149	>	/** Tests if this matrix is orthogonal. */
150	>	bool isOrthogonal() {
151	>	SquareMatrix<Real, Dim> tmp;
152
153	<	tmp = *this * transpose();
153	>	tmp = *this * transpose();
154
155	<	return tmp.isDiagonal();
156	<	}
155	>	return tmp.isDiagonal();
156	>	}
157
158	<	/** Tests if this matrix is diagonal. */
159	<	bool isDiagonal() const {
160	<	for (unsigned int i = 0; i < Dim ; i++)
161	<	for (unsigned int j = 0; j < Dim; j++)
162	<	if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
163	<	return false;
158	>	/** Tests if this matrix is diagonal. */
159	>	bool isDiagonal() const {
160	>	for (unsigned int i = 0; i < Dim ; i++)
161	>	for (unsigned int j = 0; j < Dim; j++)
162	>	if (i !=j && fabs(this->data_[i][j]) > epsilon)
163	>	return false;
164	>
165	>	return true;
166	>	}
167	>
168	>	/**
169	>	* Returns a column vector that contains the elements from the
170	>	* diagonal of m in the order R(0) = m(0,0), R(1) = m(1,1), and so
171	>	* on.
172	>	*/
173	>	Vector<Real, Dim> diagonals() const {
174	>	Vector<Real, Dim> result;
175	>	for (unsigned int i = 0; i < Dim; i++) {
176	>	result(i) = this->data_[i][i];
177	>	}
178	>	return result;
179	>	}
180	>
181	>	/** Tests if this matrix is the unit matrix. */
182	>	bool isUnitMatrix() const {
183	>	if (!isDiagonal())
184	>	return false;
185	>
186	>	for (unsigned int i = 0; i < Dim ; i++)
187	>	if (fabs(this->data_[i][i] - 1) > epsilon)
188	>	return false;
189
190	<	return true;
191	<	}
190	>	return true;
191	>	}
192
193	<	/** Tests if this matrix is the unit matrix. */
194	<	bool isUnitMatrix() const {
195	<	if (!isDiagonal())
136	<	return false;
137	<
138	<	for (unsigned int i = 0; i < Dim ; i++)
139	<	if (fabs(data_[i][i] - 1) > oopse::epsilon)
140	<	return false;
193	>	/** Return the transpose of this matrix */
194	>	SquareMatrix<Real,  Dim> transpose() const{
195	>	SquareMatrix<Real,  Dim> result;
196
197	<	return true;
198	<	}
197	>	for (unsigned int i = 0; i < Dim; i++)
198	>	for (unsigned int j = 0; j < Dim; j++)
199	>	result(j, i) = this->data_[i][j];
200
201	<	void diagonalize() {
202	<	jacobi(m, eigenValues, ortMat);
147	<	}
148	<
149	<	/**
150	<	* Finds the eigenvalues and eigenvectors of a symmetric matrix
151	<	* @param eigenvals a reference to a vector3 where the
152	<	* eigenvalues will be stored. The eigenvalues are ordered so
153	<	* that eigenvals[0] <= eigenvals[1] <= eigenvals[2].
154	<	* @return an orthogonal matrix whose ith column is an
155	<	* eigenvector for the eigenvalue eigenvals[i]
156	<	*/
157	<	SquareMatrix<Real, Dim>  findEigenvectors(Vector<Real, Dim>& eigenValues) {
158	<	SquareMatrix<Real, Dim> ortMat;
201	>	return result;
202	>	}
203
204	<	if ( !isSymmetric()){
205	<	throw();
206	<	}
207	<
164	<	SquareMatrix<Real, Dim> m(*this);
165	<	jacobi(m, eigenValues, ortMat);
204	>	/** @todo need implementation */
205	>	void diagonalize() {
206	>	//jacobi(m, eigenValues, ortMat);
207	>	}
208
209	<	return ortMat;
210	<	}
211	<	/**
212	<	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
213	<	* real symmetric matrix
214	<	*
215	<	* @return true if success, otherwise return false
216	<	* @param a source matrix
217	<	* @param w output eigenvalues
218	<	* @param v output eigenvectors
219	<	*/
220	<	bool jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
221	<	SquareMatrix<Real, Dim>& v);
222	<	};//end SquareMatrix
209	>	/**
210	>	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
211	>	* real symmetric matrix
212	>	*
213	>	* @return true if success, otherwise return false
214	>	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
215	>	*     overwritten
216	>	* @param d will contain the eigenvalues of the matrix On return of this function
217	>	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
218	>	*    normalized and mutually orthogonal.
219	>	*/
220	>
221	>	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
222	>	SquareMatrix<Real, Dim>& v);
223	>	};//end SquareMatrix
224
225
226	<	#define ROT(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);a(k, l)=h+s*(g-h*tau)
184	<	#define MAX_ROTATIONS 60
226	>	/*=========================================================================
227
228	<	template<typename Real, int Dim>
229	<	bool SquareMatrix<Real, Dim>::jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
188	<	SquareMatrix<Real, Dim>& v) {
189	<	const int N = Dim;
190	<	int i, j, k, iq, ip;
191	<	double tresh, theta, tau, t, sm, s, h, g, c;
192	<	double tmp;
193	<	Vector<Real, Dim> b, z;
228	>	Program:   Visualization Toolkit
229	>	Module:    $RCSfile: SquareMatrix.hpp,v $
230
231	+	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
232	+	All rights reserved.
233	+	See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
234	+
235	+	This software is distributed WITHOUT ANY WARRANTY; without even
236	+	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
237	+	PURPOSE.  See the above copyright notice for more information.
238	+
239	+	=========================================================================*/
240	+
241	+	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \
242	+	a(k, l)=h+s*(g-h*tau)
243	+
244	+	#define VTK_MAX_ROTATIONS 20
245	+
246	+	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
247	+	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
248	+	// output eigenvalues in w; and output eigenvectors in v. Resulting
249	+	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
250	+	// normalized.
251	+	template<typename Real, int Dim>
252	+	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
253	+	SquareMatrix<Real, Dim>& v) {
254	+	const int n = Dim;
255	+	int i, j, k, iq, ip, numPos;
256	+	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
257	+	Real bspace[4], zspace[4];
258	+	Real *b = bspace;
259	+	Real *z = zspace;
260	+
261	+	// only allocate memory if the matrix is large
262	+	if (n > 4) {
263	+	b = new Real[n];
264	+	z = new Real[n];
265	+	}
266	+
267		// initialize
268	<	for (ip=0; ip<N; ip++) {
269	<	for (iq=0; iq<N; iq++)
270	<	v(ip, iq) = 0.0;
271	<	v(ip, ip) = 1.0;
268	>	for (ip=0; ip<n; ip++) {
269	>	for (iq=0; iq<n; iq++) {
270	>	v(ip, iq) = 0.0;
271	>	}
272	>	v(ip, ip) = 1.0;
273		}
274	<
275	<	for (ip=0; ip<N; ip++) {
276	<	b(ip) = w(ip) = a(ip, ip);
204	<	z(ip) = 0.0;
274	>	for (ip=0; ip<n; ip++) {
275	>	b[ip] = w[ip] = a(ip, ip);
276	>	z[ip] = 0.0;
277		}
278
279		// begin rotation sequence
280	<	for (i=0; i<MAX_ROTATIONS; i++) {
281	<	sm = 0.0;
282	<	for (ip=0; ip<2; ip++) {
283	<	for (iq=ip+1; iq<N; iq++)
284	<	sm += fabs(a(ip, iq));
285	<	}
286	<
287	<	if (sm == 0.0)
288	<	break;
280	>	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
281	>	sm = 0.0;
282	>	for (ip=0; ip<n-1; ip++) {
283	>	for (iq=ip+1; iq<n; iq++) {
284	>	sm += fabs(a(ip, iq));
285	>	}
286	>	}
287	>	if (sm == 0.0) {
288	>	break;
289	>	}
290
291	<	if (i < 4)
292	<	tresh = 0.2*sm/(9);
293	<	else
294	<	tresh = 0.0;
291	>	if (i < 3) {                                // first 3 sweeps
292	>	tresh = 0.2*sm/(n*n);
293	>	} else {
294	>	tresh = 0.0;
295	>	}
296
297	<	for (ip=0; ip<2; ip++) {
298	<	for (iq=ip+1; iq<N; iq++) {
299	<	g = 100.0*fabs(a(ip, iq));
226	<	if (i > 4 && (fabs(w(ip))+g) == fabs(w(ip))
227	<	&& (fabs(w(iq))+g) == fabs(w(iq))) {
228	<	a(ip, iq) = 0.0;
229	<	} else if (fabs(a(ip, iq)) > tresh) {
230	<	h = w(iq) - w(ip);
231	<	if ( (fabs(h)+g) == fabs(h)) {
232	<	t = (a(ip, iq)) / h;
233	<	} else {
234	<	theta = 0.5*h / (a(ip, iq));
235	<	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
297	>	for (ip=0; ip<n-1; ip++) {
298	>	for (iq=ip+1; iq<n; iq++) {
299	>	g = 100.0*fabs(a(ip, iq));
300
301	<	if (theta < 0.0)
302	<	t = -t;
303	<	}
301	>	// after 4 sweeps
302	>	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
303	>	&& (fabs(w[iq])+g) == fabs(w[iq])) {
304	>	a(ip, iq) = 0.0;
305	>	} else if (fabs(a(ip, iq)) > tresh) {
306	>	h = w[iq] - w[ip];
307	>	if ( (fabs(h)+g) == fabs(h)) {
308	>	t = (a(ip, iq)) / h;
309	>	} else {
310	>	theta = 0.5*h / (a(ip, iq));
311	>	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
312	>	if (theta < 0.0) {
313	>	t = -t;
314	>	}
315	>	}
316	>	c = 1.0 / sqrt(1+t*t);
317	>	s = t*c;
318	>	tau = s/(1.0+c);
319	>	h = t*a(ip, iq);
320	>	z[ip] -= h;
321	>	z[iq] += h;
322	>	w[ip] -= h;
323	>	w[iq] += h;
324	>	a(ip, iq)=0.0;
325
326	<	c = 1.0 / sqrt(1+t*t);
327	<	s = t*c;
328	<	tau = s/(1.0+c);
329	<	h = t*a(ip, iq);
330	<	z(ip) -= h;
331	<	z(iq) += h;
332	<	w(ip) -= h;
333	<	w(iq) += h;
334	<	a(ip, iq)=0.0;
335	<
336	<	for (j=0;j<ip-1;j++)
337	<	ROT(a,j,ip,j,iq);
326	>	// ip already shifted left by 1 unit
327	>	for (j = 0;j <= ip-1;j++) {
328	>	VTK_ROTATE(a,j,ip,j,iq);
329	>	}
330	>	// ip and iq already shifted left by 1 unit
331	>	for (j = ip+1;j <= iq-1;j++) {
332	>	VTK_ROTATE(a,ip,j,j,iq);
333	>	}
334	>	// iq already shifted left by 1 unit
335	>	for (j=iq+1; j<n; j++) {
336	>	VTK_ROTATE(a,ip,j,iq,j);
337	>	}
338	>	for (j=0; j<n; j++) {
339	>	VTK_ROTATE(v,j,ip,j,iq);
340	>	}
341	>	}
342	>	}
343	>	}
344
345	<	for (j=ip+1;j<iq-1;j++)
346	<	ROT(a,ip,j,j,iq);
345	>	for (ip=0; ip<n; ip++) {
346	>	b[ip] += z[ip];
347	>	w[ip] = b[ip];
348	>	z[ip] = 0.0;
349	>	}
350	>	}
351
352	<	for (j=iq+1; j<N; j++)
353	<	ROT(a,ip,j,iq,j);
354	<	for (j=0; j<N; j++)
355	<	ROT(v,j,ip,j,iq);
356	<	}
357	<	}
358	<	}//for (ip=0; ip<2; ip++)
352	>	//// this is NEVER called
353	>	if ( i >= VTK_MAX_ROTATIONS ) {
354	>	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
355	>	if (n > 4) {
356	>	delete[] b;
357	>	delete[] z;
358	>	}
359	>	return 0;
360	>	}
361
362	<	for (ip=0; ip<N; ip++) {
363	<	b(ip) += z(ip);
364	<	w(ip) = b(ip);
365	<	z(ip) = 0.0;
366	<	}
367	<
368	<	} // end for (i=0; i<MAX_ROTATIONS; i++)
369	<
370	<	if ( i >= MAX_ROTATIONS )
371	<	return false;
372	<
373	<	// sort eigenfunctions
374	<	for (j=0; j<N; j++) {
375	<	k = j;
376	<	tmp = w(k);
377	<	for (i=j; i<N; i++) {
378	<	if (w(i) >= tmp) {
379	<	k = i;
380	<	tmp = w(k);
284	<	}
285	<	}
286	<
287	<	if (k != j) {
288	<	w(k) = w(j);
289	<	w(j) = tmp;
290	<	for (i=0; i<N; i++)  {
291	<	tmp = v(i, j);
292	<	v(i, j) = v(i, k);
293	<	v(i, k) = tmp;
294	<	}
295	<	}
362	>	// sort eigenfunctions                 these changes do not affect accuracy
363	>	for (j=0; j<n-1; j++) {                  // boundary incorrect
364	>	k = j;
365	>	tmp = w[k];
366	>	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
367	>	if (w[i] >= tmp) {                   // why exchage if same?
368	>	k = i;
369	>	tmp = w[k];
370	>	}
371	>	}
372	>	if (k != j) {
373	>	w[k] = w[j];
374	>	w[j] = tmp;
375	>	for (i=0; i<n; i++) {
376	>	tmp = v(i, j);
377	>	v(i, j) = v(i, k);
378	>	v(i, k) = tmp;
379	>	}
380	>	}
381		}
382	+	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
383	+	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
384	+	// reek havoc in hyperstreamline/other stuff. We will select the most
385	+	// positive eigenvector.
386	+	int ceil_half_n = (n >> 1) + (n & 1);
387	+	for (j=0; j<n; j++) {
388	+	for (numPos=0, i=0; i<n; i++) {
389	+	if ( v(i, j) >= 0.0 ) {
390	+	numPos++;
391	+	}
392	+	}
393	+	//    if ( numPos < ceil(RealType(n)/RealType(2.0)) )
394	+	if ( numPos < ceil_half_n) {
395	+	for (i=0; i<n; i++) {
396	+	v(i, j) *= -1.0;
397	+	}
398	+	}
399	+	}
400
401	<	//    insure eigenvector consistency (i.e., Jacobi can compute
402	<	//    vectors that are negative of one another (.707,.707,0) and
403	<	//    (-.707,-.707,0). This can reek havoc in
301	<	//    hyperstreamline/other stuff. We will select the most
302	<	//    positive eigenvector.
303	<	int numPos;
304	<	for (j=0; j<N; j++) {
305	<	for (numPos=0, i=0; i<N; i++) if ( v(i, j) >= 0.0 ) numPos++;
306	<	if ( numPos < 2 ) for(i=0; i<N; i++) v(i, j) *= -1.0;
401	>	if (n > 4) {
402	>	delete [] b;
403	>	delete [] z;
404		}
405	+	return 1;
406	+	}
407
309	–	return true;
310	–	}
408
409	<	#undef ROT
313	<	#undef MAX_ROTATIONS
314	<
409	>	typedef SquareMatrix<RealType, 6> Mat6x6d;
410		}
316	–
411		#endif //MATH_SQUAREMATRIX_HPP
412	+

Comparing trunk/src/math/SquareMatrix.hpp (property svn:keywords):
Revision 93 by tim, Sun Oct 17 01:19:11 2004 UTC vs.
Revision 1924 by gezelter, Mon Aug 5 21:46:11 2013 UTC

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