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trunk/src/math/SquareMatrix.hpp (file contents), Revision 101 by tim, Mon Oct 18 23:13:23 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
#	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	>	* @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	<	}
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;
82	<
71	<	for (unsigned int i = 0; i < Dim; i++)
72	<	for (unsigned int j = 0; j < Dim; j++)
73	<	if (i == j)
74	<	m(i, j) = 1.0;
75	<	else
76	<	m(i, j) = 0.0;
80	>	/** Constructs and initializes from an array */
81	>	SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
82	>	}
83
78	–	return m;
79	–	}
84
85	<	/**
86	<	* Retunrs  the inversion of this matrix.
87	<	* @todo
88	<	*/
89	<	SquareMatrix<Real, Dim>  inverse() {
90	<	SquareMatrix<Real, Dim> result;
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	>	}
94	>
95	>	/** Retunrs  an identity matrix*/
96
97	<	return result;
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	<	* Returns the determinant of this matrix.
93	<	* @todo
94	<	*/
95	<	double determinant() const {
96	<	double det;
97	<	return det;
98	<	}
107	>	return m;
108	>	}
109
110	<	/** Returns the trace of this matrix. */
111	<	double trace() const {
112	<	double tmp = 0;
113	<
114	<	for (unsigned int i = 0; i < Dim ; i++)
115	<	tmp += data_[i][i];
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 tmp;
118	<	}
117	>	return result;
118	>	}
119
120	<	/** Tests if this matrix is symmetrix. */
121	<	bool isSymmetric() const {
122	<	for (unsigned int i = 0; i < Dim - 1; i++)
123	<	for (unsigned int j = i; j < Dim; j++)
124	<	if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
125	<	return false;
126	<
127	<	return true;
118	<	}
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	<	/** Tests if this matrix is orthogonal. */
130	<	bool isOrthogonal() {
131	<	SquareMatrix<Real, Dim> tmp;
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	<	tmp = *this * transpose();
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	<	return tmp.isDiagonal();
158	<	}
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	>	}
166
167	<	/** Tests if this matrix is diagonal. */
168	<	bool isDiagonal() const {
169	<	for (unsigned int i = 0; i < Dim ; i++)
132	<	for (unsigned int j = 0; j < Dim; j++)
133	<	if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
134	<	return false;
135	<
136	<	return true;
137	<	}
167	>	/** Tests if this matrix is orthogonal. */
168	>	bool isOrthogonal() {
169	>	SquareMatrix<Real, Dim> tmp;
170
171	<	/** Tests if this matrix is the unit matrix. */
140	<	bool isUnitMatrix() const {
141	<	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;
147	<
148	<	return true;
149	<	}
171	>	tmp = *this * transpose();
172
173	<	/** @todo need implement */
174	<	void diagonalize() {
153	<	//jacobi(m, eigenValues, ortMat);
154	<	}
173	>	return tmp.isDiagonal();
174	>	}
175
176	<	/**
177	<	* Finds the eigenvalues and eigenvectors of a symmetric matrix
178	<	* @param eigenvals a reference to a vector3 where the
179	<	* eigenvalues will be stored. The eigenvalues are ordered so
180	<	* that eigenvals[0] <= eigenvals[1] <= eigenvals[2].
181	<	* @return an orthogonal matrix whose ith column is an
182	<	* eigenvector for the eigenvalue eigenvals[i]
183	<	*/
164	<	SquareMatrix<Real, Dim>  findEigenvectors(Vector<Real, Dim>& eigenValues) {
165	<	SquareMatrix<Real, Dim> ortMat;
166	<
167	<	if ( !isSymmetric()){
168	<	throw();
169	<	}
170	<
171	<	SquareMatrix<Real, Dim> m(*this);
172	<	jacobi(m, eigenValues, ortMat);
173	<
174	<	return ortMat;
175	<	}
176	<	/**
177	<	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
178	<	* real symmetric matrix
179	<	*
180	<	* @return true if success, otherwise return false
181	<	* @param a source matrix
182	<	* @param w output eigenvalues
183	<	* @param v output eigenvectors
184	<	*/
185	<	bool jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
186	<	SquareMatrix<Real, Dim>& v);
187	<	};//end SquareMatrix
188	<
189	<
190	<	#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)
191	<	#define MAX_ROTATIONS 60
192	<
193	<	template<typename Real, int Dim>
194	<	bool SquareMatrix<Real, Dim>::jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
195	<	SquareMatrix<Real, Dim>& v) {
196	<	const int N = Dim;
197	<	int i, j, k, iq, ip;
198	<	double tresh, theta, tau, t, sm, s, h, g, c;
199	<	double tmp;
200	<	Vector<Real, Dim> b, z;
201	<
202	<	// initialize
203	<	for (ip=0; ip<N; ip++) {
204	<	for (iq=0; iq<N; iq++)
205	<	v(ip, iq) = 0.0;
206	<	v(ip, ip) = 1.0;
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		}
185	<
186	<	for (ip=0; ip<N; ip++) {
187	<	b(ip) = w(ip) = a(ip, ip);
188	<	z(ip) = 0.0;
185	>
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	<	// begin rotation sequence
200	<	for (i=0; i<MAX_ROTATIONS; i++) {
201	<	sm = 0.0;
202	<	for (ip=0; ip<2; ip++) {
203	<	for (iq=ip+1; iq<N; iq++)
204	<	sm += fabs(a(ip, iq));
205	<	}
206	<
207	<	if (sm == 0.0)
208	<	break;
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(this->data_[i][i] - 1) > epsilon)
206	>	return false;
207	>
208	>	return true;
209	>	}
210
211	<	if (i < 4)
212	<	tresh = 0.2*sm/(9);
213	<	else
214	<	tresh = 0.0;
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	<	for (ip=0; ip<2; ip++) {
220	<	for (iq=ip+1; iq<N; iq++) {
221	<	g = 100.0*fabs(a(ip, iq));
222	<	if (i > 4 && (fabs(w(ip))+g) == fabs(w(ip))
223	<	&& (fabs(w(iq))+g) == fabs(w(iq))) {
224	<	a(ip, iq) = 0.0;
225	<	} else if (fabs(a(ip, iq)) > tresh) {
237	<	h = w(iq) - w(ip);
238	<	if ( (fabs(h)+g) == fabs(h)) {
239	<	t = (a(ip, iq)) / h;
240	<	} else {
241	<	theta = 0.5*h / (a(ip, iq));
242	<	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
219	>	return result;
220	>	}
221	>
222	>	/** @todo need implementation */
223	>	void diagonalize() {
224	>	//jacobi(m, eigenValues, ortMat);
225	>	}
226
227	<	if (theta < 0.0)
228	<	t = -t;
229	<	}
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
242
248	–	c = 1.0 / sqrt(1+t*t);
249	–	s = t*c;
250	–	tau = s/(1.0+c);
251	–	h = t*a(ip, iq);
252	–	z(ip) -= h;
253	–	z(iq) += h;
254	–	w(ip) -= h;
255	–	w(iq) += h;
256	–	a(ip, iq)=0.0;
257	–
258	–	for (j=0;j<ip-1;j++)
259	–	ROT(a,j,ip,j,iq);
243
244	<	for (j=ip+1;j<iq-1;j++)
262	<	ROT(a,ip,j,j,iq);
244	>	/*=========================================================================
245
246	<	for (j=iq+1; j<N; j++)
247	<	ROT(a,ip,j,iq,j);
266	<
267	<	for (j=0; j<N; j++)
268	<	ROT(v,j,ip,j,iq);
269	<	}
270	<	}
271	<	}//for (ip=0; ip<2; ip++)
246	>	Program:   Visualization Toolkit
247	>	Module:    $RCSfile: SquareMatrix.hpp,v $
248
249	<	for (ip=0; ip<N; ip++) {
250	<	b(ip) += z(ip);
251	<	w(ip) = b(ip);
276	<	z(ip) = 0.0;
277	<	}
278	<
279	<	} // end for (i=0; i<MAX_ROTATIONS; i++)
249	>	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
250	>	All rights reserved.
251	>	See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
252
253	<	if ( i >= MAX_ROTATIONS )
254	<	return false;
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	<	// sort eigenfunctions
258	<	for (j=0; j<N; j++) {
259	<	k = j;
260	<	tmp = w(k);
261	<	for (i=j; i<N; i++) {
262	<	if (w(i) >= tmp) {
263	<	k = i;
264	<	tmp = w(k);
265	<	}
266	<	}
267	<
268	<	if (k != j) {
269	<	w(k) = w(j);
270	<	w(j) = tmp;
271	<	for (i=0; i<N; i++)  {
272	<	tmp = v(i, j);
273	<	v(i, j) = v(i, k);
274	<	v(i, k) = tmp;
275	<	}
276	<	}
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)
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;
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		}
284
285	<	//    insure eigenvector consistency (i.e., Jacobi can compute
286	<	//    vectors that are negative of one another (.707,.707,0) and
287	<	//    (-.707,-.707,0). This can reek havoc in
288	<	//    hyperstreamline/other stuff. We will select the most
289	<	//    positive eigenvector.
290	<	int numPos;
312	<	for (j=0; j<N; j++) {
313	<	for (numPos=0, i=0; i<N; i++) if ( v(i, j) >= 0.0 ) numPos++;
314	<	if ( numPos < 2 ) for(i=0; i<N; i++) v(i, j) *= -1.0;
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	<	return true;
298	<	}
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	<	#undef ROT
310	<	#undef MAX_ROTATIONS
309	>	if (i < 3) {                                // first 3 sweeps
310	>	tresh = 0.2*sm/(n*n);
311	>	} else {
312	>	tresh = 0.0;
313	>	}
314
315	<	}
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;
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	+	}
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	+	}
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	+	}
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(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;
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 101 by tim, Mon Oct 18 23:13:23 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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