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trunk/src/math/SquareMatrix3.hpp (file contents), Revision 70 by tim, Wed Oct 13 06:51:09 2004 UTC vs.
branches/development/src/math/SquareMatrix3.hpp (file contents), Revision 1753 by gezelter, Tue Jun 12 13:20:28 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 SquareMatrix3.hpp
45		* @author Teng Lin
46		* @date 10/11/2004
47		* @version 1.0
48		*/
49	<	#ifndef MATH_SQUAREMATRIX#_HPP
50	<	#define  MATH_SQUAREMATRIX#_HPP
51	<
49	>	#ifndef MATH_SQUAREMATRIX3_HPP
50	>	#define  MATH_SQUAREMATRIX3_HPP
51	>	#include <vector>
52	>	#include "Quaternion.hpp"
53		#include "SquareMatrix.hpp"
54	<	namespace oopse {
54	>	#include "Vector3.hpp"
55	>	#include "utils/NumericConstant.hpp"
56	>	namespace OpenMD {
57
58	<	template<typename Real>
59	<	class SquareMatrix3 : public SquareMatrix<Real, 3> {
60	<	public:
58	>	template<typename Real>
59	>	class SquareMatrix3 : public SquareMatrix<Real, 3> {
60	>	public:
61	>
62	>	typedef Real ElemType;
63	>	typedef Real* ElemPoinerType;
64
65	<	/** default constructor */
66	<	SquareMatrix3() : SquareMatrix<Real, 3>() {
67	<	}
65	>	/** default constructor */
66	>	SquareMatrix3() : SquareMatrix<Real, 3>() {
67	>	}
68
69	<	/** copy  constructor */
70	<	SquareMatrix3(const SquareMatrix<Real, 3>& m)  : SquareMatrix<Real, 3>(m) {
71	<	}
69	>	/** Constructs and initializes every element of this matrix to a scalar */
70	>	SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
71	>	}
72
73	<	/** copy assignment operator */
74	<	SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
75	<	if (this == &m)
76	<	return *this;
77	<	SquareMatrix<Real, 3>::operator=(m);
78	<	}
73	>	/** Constructs and initializes from an array */
74	>	SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
75	>	}
76	>
77	>
78	>	/** copy  constructor */
79	>	SquareMatrix3(const SquareMatrix<Real, 3>& m)  : SquareMatrix<Real, 3>(m) {
80	>	}
81
82	<	/**
83	<	* Sets the value of this matrix to  the inversion of itself.
84	<	* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
60	<	* implementation of inverse in SquareMatrix class
61	<	*/
62	<	void  inverse();
82	>	SquareMatrix3( const Vector3<Real>& eulerAngles) {
83	>	setupRotMat(eulerAngles);
84	>	}
85
86	<	/**
87	<	* Sets the value of this matrix to  the inversion of other matrix.
88	<	* @ param m the source matrix
67	<	*/
68	<	void inverse(const SquareMatrix<Real, Dim>& m);
86	>	SquareMatrix3(Real phi, Real theta, Real psi) {
87	>	setupRotMat(phi, theta, psi);
88	>	}
89
90	+	SquareMatrix3(const Quaternion<Real>& q) {
91	+	setupRotMat(q);
92	+
93		}
94
95	<	};
95	>	SquareMatrix3(Real w, Real x, Real y, Real z) {
96	>	setupRotMat(w, x, y, z);
97	>	}
98	>
99	>	/** copy assignment operator */
100	>	SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
101	>	if (this == &m)
102	>	return *this;
103	>	SquareMatrix<Real, 3>::operator=(m);
104	>	return *this;
105	>	}
106
107	<	}
108	<	#endif // MATH_SQUAREMATRIX#_HPP
107	>
108	>	SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
109	>	this->setupRotMat(q);
110	>	return *this;
111	>	}
112	>
113	>
114	>	/**
115	>	* Sets this matrix to a rotation matrix by three euler angles
116	>	* @ param euler
117	>	*/
118	>	void setupRotMat(const Vector3<Real>& eulerAngles) {
119	>	setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
120	>	}
121	>
122	>	/**
123	>	* Sets this matrix to a rotation matrix by three euler angles
124	>	* @param phi
125	>	* @param theta
126	>	* @psi theta
127	>	*/
128	>	void setupRotMat(Real phi, Real theta, Real psi) {
129	>	Real sphi, stheta, spsi;
130	>	Real cphi, ctheta, cpsi;
131	>
132	>	sphi = sin(phi);
133	>	stheta = sin(theta);
134	>	spsi = sin(psi);
135	>	cphi = cos(phi);
136	>	ctheta = cos(theta);
137	>	cpsi = cos(psi);
138	>
139	>	this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
140	>	this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
141	>	this->data_[0][2] = spsi * stheta;
142	>
143	>	this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
144	>	this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
145	>	this->data_[1][2] = cpsi * stheta;
146	>
147	>	this->data_[2][0] = stheta * sphi;
148	>	this->data_[2][1] = -stheta * cphi;
149	>	this->data_[2][2] = ctheta;
150	>	}
151	>
152	>
153	>	/**
154	>	* Sets this matrix to a rotation matrix by quaternion
155	>	* @param quat
156	>	*/
157	>	void setupRotMat(const Quaternion<Real>& quat) {
158	>	setupRotMat(quat.w(), quat.x(), quat.y(), quat.z());
159	>	}
160	>
161	>	/**
162	>	* Sets this matrix to a rotation matrix by quaternion
163	>	* @param w the first element
164	>	* @param x the second element
165	>	* @param y the third element
166	>	* @param z the fourth element
167	>	*/
168	>	void setupRotMat(Real w, Real x, Real y, Real z) {
169	>	Quaternion<Real> q(w, x, y, z);
170	>	*this = q.toRotationMatrix3();
171	>	}
172	>
173	>	void setupSkewMat(Vector3<Real> v) {
174	>	setupSkewMat(v[0], v[1], v[2]);
175	>	}
176	>
177	>	void setupSkewMat(Real v1, Real v2, Real v3) {
178	>	this->data_[0][0] = 0;
179	>	this->data_[0][1] = -v3;
180	>	this->data_[0][2] = v2;
181	>	this->data_[1][0] = v3;
182	>	this->data_[1][1] = 0;
183	>	this->data_[1][2] = -v1;
184	>	this->data_[2][0] = -v2;
185	>	this->data_[2][1] = v1;
186	>	this->data_[2][2] = 0;
187	>
188	>
189	>	}
190	>
191	>
192	>	/**
193	>	* Returns the quaternion from this rotation matrix
194	>	* @return the quaternion from this rotation matrix
195	>	* @exception invalid rotation matrix
196	>	*/
197	>	Quaternion<Real> toQuaternion() {
198	>	Quaternion<Real> q;
199	>	Real t, s;
200	>	Real ad1, ad2, ad3;
201	>	t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0;
202	>
203	>	if( t > NumericConstant::epsilon ){
204	>
205	>	s = 0.5 / sqrt( t );
206	>	q[0] = 0.25 / s;
207	>	q[1] = (this->data_[1][2] - this->data_[2][1]) * s;
208	>	q[2] = (this->data_[2][0] - this->data_[0][2]) * s;
209	>	q[3] = (this->data_[0][1] - this->data_[1][0]) * s;
210	>	} else {
211	>
212	>	ad1 = this->data_[0][0];
213	>	ad2 = this->data_[1][1];
214	>	ad3 = this->data_[2][2];
215	>
216	>	if( ad1 >= ad2 && ad1 >= ad3 ){
217	>
218	>	s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] );
219	>	q[0] = (this->data_[1][2] - this->data_[2][1]) * s;
220	>	q[1] = 0.25 / s;
221	>	q[2] = (this->data_[0][1] + this->data_[1][0]) * s;
222	>	q[3] = (this->data_[0][2] + this->data_[2][0]) * s;
223	>	} else if ( ad2 >= ad1 && ad2 >= ad3 ) {
224	>	s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] );
225	>	q[0] = (this->data_[2][0] - this->data_[0][2] ) * s;
226	>	q[1] = (this->data_[0][1] + this->data_[1][0]) * s;
227	>	q[2] = 0.25 / s;
228	>	q[3] = (this->data_[1][2] + this->data_[2][1]) * s;
229	>	} else {
230	>
231	>	s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] );
232	>	q[0] = (this->data_[0][1] - this->data_[1][0]) * s;
233	>	q[1] = (this->data_[0][2] + this->data_[2][0]) * s;
234	>	q[2] = (this->data_[1][2] + this->data_[2][1]) * s;
235	>	q[3] = 0.25 / s;
236	>	}
237	>	}
238	>
239	>	return q;
240	>
241	>	}
242	>
243	>	/**
244	>	* Returns the euler angles from this rotation matrix
245	>	* @return the euler angles in a vector
246	>	* @exception invalid rotation matrix
247	>	* We use so-called "x-convention", which is the most common definition.
248	>	* In this convention, the rotation given by Euler angles (phi, theta,
249	>	* psi), where the first rotation is by an angle phi about the z-axis,
250	>	* the second is by an angle theta (0 <= theta <= 180) about the x-axis,
251	>	* and the third is by an angle psi about the z-axis (again).
252	>	*/
253	>	Vector3<Real> toEulerAngles() {
254	>	Vector3<Real> myEuler;
255	>	Real phi;
256	>	Real theta;
257	>	Real psi;
258	>	Real ctheta;
259	>	Real stheta;
260	>
261	>	// set the tolerance for Euler angles and rotation elements
262	>
263	>	theta = acos(std::min((RealType)1.0, std::max((RealType)-1.0,this->data_[2][2])));
264	>	ctheta = this->data_[2][2];
265	>	stheta = sqrt(1.0 - ctheta * ctheta);
266	>
267	>	// when sin(theta) is close to 0, we need to consider
268	>	// singularity In this case, we can assign an arbitary value to
269	>	// phi (or psi), and then determine the psi (or phi) or
270	>	// vice-versa. We'll assume that phi always gets the rotation,
271	>	// and psi is 0 in cases of singularity.
272	>	// we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
273	>	// Since 0 <= theta <= 180, sin(theta) will be always
274	>	// non-negative. Therefore, it will never change the sign of both of
275	>	// the parameters passed to atan2.
276	>
277	>	if (fabs(stheta) < 1e-6){
278	>	psi = 0.0;
279	>	phi = atan2(-this->data_[1][0], this->data_[0][0]);
280	>	}
281	>	// we only have one unique solution
282	>	else{
283	>	phi = atan2(this->data_[2][0], -this->data_[2][1]);
284	>	psi = atan2(this->data_[0][2], this->data_[1][2]);
285	>	}
286	>
287	>	//wrap phi and psi, make sure they are in the range from 0 to 2*Pi
288	>	if (phi < 0)
289	>	phi += 2.0 * M_PI;
290	>
291	>	if (psi < 0)
292	>	psi += 2.0 * M_PI;
293	>
294	>	myEuler[0] = phi;
295	>	myEuler[1] = theta;
296	>	myEuler[2] = psi;
297	>
298	>	return myEuler;
299	>	}
300	>
301	>	/** Returns the determinant of this matrix. */
302	>	Real determinant() const {
303	>	Real x,y,z;
304	>
305	>	x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]);
306	>	y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]);
307	>	z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]);
308	>
309	>	return(x + y + z);
310	>	}
311	>
312	>	/** Returns the trace of this matrix. */
313	>	Real trace() const {
314	>	return this->data_[0][0] + this->data_[1][1] + this->data_[2][2];
315	>	}
316	>
317	>	/**
318	>	* Sets the value of this matrix to  the inversion of itself.
319	>	* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
320	>	* implementation of inverse in SquareMatrix class
321	>	*/
322	>	SquareMatrix3<Real>  inverse() const {
323	>	SquareMatrix3<Real> m;
324	>	RealType det = determinant();
325	>	if (fabs(det) <= OpenMD::epsilon) {
326	>	//"The method was called on a matrix with |determinant| <= 1e-6.",
327	>	//"This is a runtime or a programming error in your application.");
328	>	std::vector<int> zeroDiagElementIndex;
329	>	for (int i =0; i < 3; ++i) {
330	>	if (fabs(this->data_[i][i]) <= OpenMD::epsilon) {
331	>	zeroDiagElementIndex.push_back(i);
332	>	}
333	>	}
334	>
335	>	if (zeroDiagElementIndex.size() == 2) {
336	>	int index = zeroDiagElementIndex[0];
337	>	m(index, index) = 1.0 / this->data_[index][index];
338	>	}else if (zeroDiagElementIndex.size() == 1) {
339	>
340	>	int a = (zeroDiagElementIndex[0] + 1) % 3;
341	>	int b = (zeroDiagElementIndex[0] + 2) %3;
342	>	RealType denom = this->data_[a][a] * this->data_[b][b] - this->data_[b][a]*this->data_[a][b];
343	>	m(a, a) = this->data_[b][b] /denom;
344	>	m(b, a) = -this->data_[b][a]/denom;
345	>
346	>	m(a,b) = -this->data_[a][b]/denom;
347	>	m(b, b) = this->data_[a][a]/denom;
348	>
349	>	}
350	>
351	>	/*
352	>	for(std::vector<int>::iterator iter = zeroDiagElementIndex.begin(); iter != zeroDiagElementIndex.end() ++iter) {
353	>	if (this->data_[*iter][0] > OpenMD::epsilon || this->data_[*iter][1] ||this->data_[*iter][2] ||
354	>	this->data_[0][*iter] > OpenMD::epsilon || this->data_[1][*iter] ||this->data_[2][*iter] ) {
355	>	std::cout << "can not inverse matrix" << std::endl;
356	>	}
357	>	}
358	>	*/
359	>	} else {
360	>
361	>	m(0, 0) = this->data_[1][1]*this->data_[2][2] - this->data_[1][2]*this->data_[2][1];
362	>	m(1, 0) = this->data_[1][2]*this->data_[2][0] - this->data_[1][0]*this->data_[2][2];
363	>	m(2, 0) = this->data_[1][0]*this->data_[2][1] - this->data_[1][1]*this->data_[2][0];
364	>	m(0, 1) = this->data_[2][1]*this->data_[0][2] - this->data_[2][2]*this->data_[0][1];
365	>	m(1, 1) = this->data_[2][2]*this->data_[0][0] - this->data_[2][0]*this->data_[0][2];
366	>	m(2, 1) = this->data_[2][0]*this->data_[0][1] - this->data_[2][1]*this->data_[0][0];
367	>	m(0, 2) = this->data_[0][1]*this->data_[1][2] - this->data_[0][2]*this->data_[1][1];
368	>	m(1, 2) = this->data_[0][2]*this->data_[1][0] - this->data_[0][0]*this->data_[1][2];
369	>	m(2, 2) = this->data_[0][0]*this->data_[1][1] - this->data_[0][1]*this->data_[1][0];
370	>
371	>	m /= det;
372	>	}
373	>	return m;
374	>	}
375	>
376	>	SquareMatrix3<Real> transpose() const{
377	>	SquareMatrix3<Real> result;
378	>
379	>	for (unsigned int i = 0; i < 3; i++)
380	>	for (unsigned int j = 0; j < 3; j++)
381	>	result(j, i) = this->data_[i][j];
382	>
383	>	return result;
384	>	}
385	>	/**
386	>	* Extract the eigenvalues and eigenvectors from a 3x3 matrix.
387	>	* The eigenvectors (the columns of V) will be normalized.
388	>	* The eigenvectors are aligned optimally with the x, y, and z
389	>	* axes respectively.
390	>	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
391	>	*     overwritten
392	>	* @param w will contain the eigenvalues of the matrix On return of this function
393	>	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
394	>	*    normalized and mutually orthogonal.
395	>	* @warning a will be overwritten
396	>	*/
397	>	static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v);
398	>	};
399	>	/*=========================================================================
400	>
401	>	Program:   Visualization Toolkit
402	>	Module:    $RCSfile: SquareMatrix3.hpp,v $
403	>
404	>	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
405	>	All rights reserved.
406	>	See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
407	>
408	>	This software is distributed WITHOUT ANY WARRANTY; without even
409	>	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
410	>	PURPOSE.  See the above copyright notice for more information.
411	>
412	>	=========================================================================*/
413	>	template<typename Real>
414	>	void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w,
415	>	SquareMatrix3<Real>& v) {
416	>	int i,j,k,maxI;
417	>	Real tmp, maxVal;
418	>	Vector3<Real> v_maxI, v_k, v_j;
419	>
420	>	// diagonalize using Jacobi
421	>	SquareMatrix3<Real>::jacobi(a, w, v);
422	>	// if all the eigenvalues are the same, return identity matrix
423	>	if (w[0] == w[1] && w[0] == w[2] ) {
424	>	v = SquareMatrix3<Real>::identity();
425	>	return;
426	>	}
427	>
428	>	// transpose temporarily, it makes it easier to sort the eigenvectors
429	>	v = v.transpose();
430	>
431	>	// if two eigenvalues are the same, re-orthogonalize to optimally line
432	>	// up the eigenvectors with the x, y, and z axes
433	>	for (i = 0; i < 3; i++) {
434	>	if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
435	>	// find maximum element of the independant eigenvector
436	>	maxVal = fabs(v(i, 0));
437	>	maxI = 0;
438	>	for (j = 1; j < 3; j++) {
439	>	if (maxVal < (tmp = fabs(v(i, j)))){
440	>	maxVal = tmp;
441	>	maxI = j;
442	>	}
443	>	}
444	>
445	>	// swap the eigenvector into its proper position
446	>	if (maxI != i) {
447	>	tmp = w(maxI);
448	>	w(maxI) = w(i);
449	>	w(i) = tmp;
450	>
451	>	v.swapRow(i, maxI);
452	>	}
453	>	// maximum element of eigenvector should be positive
454	>	if (v(maxI, maxI) < 0) {
455	>	v(maxI, 0) = -v(maxI, 0);
456	>	v(maxI, 1) = -v(maxI, 1);
457	>	v(maxI, 2) = -v(maxI, 2);
458	>	}
459	>
460	>	// re-orthogonalize the other two eigenvectors
461	>	j = (maxI+1)%3;
462	>	k = (maxI+2)%3;
463	>
464	>	v(j, 0) = 0.0;
465	>	v(j, 1) = 0.0;
466	>	v(j, 2) = 0.0;
467	>	v(j, j) = 1.0;
468	>
469	>	/** @todo */
470	>	v_maxI = v.getRow(maxI);
471	>	v_j = v.getRow(j);
472	>	v_k = cross(v_maxI, v_j);
473	>	v_k.normalize();
474	>	v_j = cross(v_k, v_maxI);
475	>	v.setRow(j, v_j);
476	>	v.setRow(k, v_k);
477	>
478	>
479	>	// transpose vectors back to columns
480	>	v = v.transpose();
481	>	return;
482	>	}
483	>	}
484	>
485	>	// the three eigenvalues are different, just sort the eigenvectors
486	>	// to align them with the x, y, and z axes
487	>
488	>	// find the vector with the largest x element, make that vector
489	>	// the first vector
490	>	maxVal = fabs(v(0, 0));
491	>	maxI = 0;
492	>	for (i = 1; i < 3; i++) {
493	>	if (maxVal < (tmp = fabs(v(i, 0)))) {
494	>	maxVal = tmp;
495	>	maxI = i;
496	>	}
497	>	}
498	>
499	>	// swap eigenvalue and eigenvector
500	>	if (maxI != 0) {
501	>	tmp = w(maxI);
502	>	w(maxI) = w(0);
503	>	w(0) = tmp;
504	>	v.swapRow(maxI, 0);
505	>	}
506	>	// do the same for the y element
507	>	if (fabs(v(1, 1)) < fabs(v(2, 1))) {
508	>	tmp = w(2);
509	>	w(2) = w(1);
510	>	w(1) = tmp;
511	>	v.swapRow(2, 1);
512	>	}
513	>
514	>	// ensure that the sign of the eigenvectors is correct
515	>	for (i = 0; i < 2; i++) {
516	>	if (v(i, i) < 0) {
517	>	v(i, 0) = -v(i, 0);
518	>	v(i, 1) = -v(i, 1);
519	>	v(i, 2) = -v(i, 2);
520	>	}
521	>	}
522	>
523	>	// set sign of final eigenvector to ensure that determinant is positive
524	>	if (v.determinant() < 0) {
525	>	v(2, 0) = -v(2, 0);
526	>	v(2, 1) = -v(2, 1);
527	>	v(2, 2) = -v(2, 2);
528	>	}
529	>
530	>	// transpose the eigenvectors back again
531	>	v = v.transpose();
532	>	return ;
533	>	}
534	>
535	>	/**
536	>	* Return the multiplication of two matrixes  (m1 * m2).
537	>	* @return the multiplication of two matrixes
538	>	* @param m1 the first matrix
539	>	* @param m2 the second matrix
540	>	*/
541	>	template<typename Real>
542	>	inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) {
543	>	SquareMatrix3<Real> result;
544	>
545	>	for (unsigned int i = 0; i < 3; i++)
546	>	for (unsigned int j = 0; j < 3; j++)
547	>	for (unsigned int k = 0; k < 3; k++)
548	>	result(i, j)  += m1(i, k) * m2(k, j);
549	>
550	>	return result;
551	>	}
552	>
553	>	template<typename Real>
554	>	inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
555	>	SquareMatrix3<Real> result;
556	>
557	>	for (unsigned int i = 0; i < 3; i++) {
558	>	for (unsigned int j = 0; j < 3; j++) {
559	>	result(i, j)  = v1[i] * v2[j];
560	>	}
561	>	}
562	>
563	>	return result;
564	>	}
565	>
566	>
567	>	typedef SquareMatrix3<RealType> Mat3x3d;
568	>	typedef SquareMatrix3<RealType> RotMat3x3d;
569	>
570	>	} //namespace OpenMD
571	>	#endif // MATH_SQUAREMATRIX_HPP
572	>

Comparing:
trunk/src/math/SquareMatrix3.hpp (property svn:keywords), Revision 70 by tim, Wed Oct 13 06:51:09 2004 UTC vs.
branches/development/src/math/SquareMatrix3.hpp (property svn:keywords), Revision 1753 by gezelter, Tue Jun 12 13:20:28 2012 UTC

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