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Revision 113 by tim, Tue Oct 19 23:01:03 2004 UTC vs.
Revision 385 by tim, Tue Mar 1 20:10:14 2005 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.
1 > /*
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. 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
19 + *    notice, this list of conditions and the following disclaimer.
20 + *
21 + * 3. Redistributions in binary form must reproduce the above copyright
22 + *    notice, this list of conditions and the following disclaimer in the
23 + *    documentation and/or other materials provided with the
24 + *    distribution.
25 + *
26 + * This software is provided "AS IS," without a warranty of any
27 + * kind. All express or implied conditions, representations and
28 + * warranties, including any implied warranty of merchantability,
29 + * fitness for a particular purpose or non-infringement, are hereby
30 + * excluded.  The University of Notre Dame and its licensors shall not
31 + * be liable for any damages suffered by licensee as a result of
32 + * using, modifying or distributing the software or its
33 + * derivatives. In no event will the University of Notre Dame or its
34 + * licensors be liable for any lost revenue, profit or data, or for
35 + * direct, indirect, special, consequential, incidental or punitive
36 + * damages, however caused and regardless of the theory of liability,
37 + * arising out of the use of or inability to use software, even if the
38 + * University of Notre Dame has been advised of the possibility of
39 + * such damages.
40   */
41 <
41 >
42   /**
43   * @file SquareMatrix3.hpp
44   * @author Teng Lin
45   * @date 10/11/2004
46   * @version 1.0
47   */
48 < #ifndef MATH_SQUAREMATRIX3_HPP
48 > #ifndef MATH_SQUAREMATRIX3_HPP
49   #define  MATH_SQUAREMATRIX3_HPP
50  
51   #include "Quaternion.hpp"
# Line 41 | Line 57 | namespace oopse {
57      template<typename Real>
58      class SquareMatrix3 : public SquareMatrix<Real, 3> {
59          public:
60 +
61 +            typedef Real ElemType;
62 +            typedef Real* ElemPoinerType;
63              
64              /** default constructor */
65              SquareMatrix3() : SquareMatrix<Real, 3>() {
66              }
67  
68 +            /** Constructs and initializes every element of this matrix to a scalar */
69 +            SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
70 +            }
71 +
72 +            /** Constructs and initializes from an array */
73 +            SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
74 +            }
75 +
76 +
77              /** copy  constructor */
78              SquareMatrix3(const SquareMatrix<Real, 3>& m)  : SquareMatrix<Real, 3>(m) {
79              }
80 <
80 >            
81              SquareMatrix3( const Vector3<Real>& eulerAngles) {
82                  setupRotMat(eulerAngles);
83              }
# Line 75 | Line 103 | namespace oopse {
103                   return *this;
104              }
105  
106 +
107 +            SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
108 +                this->setupRotMat(q);
109 +                return *this;
110 +            }
111 +
112              /**
113               * Sets this matrix to a rotation matrix by three euler angles
114               * @ param euler
# Line 100 | Line 134 | namespace oopse {
134                  ctheta = cos(theta);
135                  cpsi = cos(psi);
136  
137 <                data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
138 <                data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
139 <                data_[0][2] = spsi * stheta;
137 >                this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
138 >                this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
139 >                this->data_[0][2] = spsi * stheta;
140                  
141 <                data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
142 <                data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
143 <                data_[1][2] = cpsi * stheta;
141 >                this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
142 >                this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
143 >                this->data_[1][2] = cpsi * stheta;
144  
145 <                data_[2][0] = stheta * sphi;
146 <                data_[2][1] = -stheta * cphi;
147 <                data_[2][2] = ctheta;
145 >                this->data_[2][0] = stheta * sphi;
146 >                this->data_[2][1] = -stheta * cphi;
147 >                this->data_[2][2] = ctheta;
148              }
149  
150  
# Line 143 | Line 177 | namespace oopse {
177                  Quaternion<Real> q;
178                  Real t, s;
179                  Real ad1, ad2, ad3;    
180 <                t = data_[0][0] + data_[1][1] + data_[2][2] + 1.0;
180 >                t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0;
181  
182                  if( t > 0.0 ){
183  
184                      s = 0.5 / sqrt( t );
185                      q[0] = 0.25 / s;
186 <                    q[1] = (data_[1][2] - data_[2][1]) * s;
187 <                    q[2] = (data_[2][0] - data_[0][2]) * s;
188 <                    q[3] = (data_[0][1] - data_[1][0]) * s;
186 >                    q[1] = (this->data_[1][2] - this->data_[2][1]) * s;
187 >                    q[2] = (this->data_[2][0] - this->data_[0][2]) * s;
188 >                    q[3] = (this->data_[0][1] - this->data_[1][0]) * s;
189                  } else {
190  
191 <                    ad1 = fabs( data_[0][0] );
192 <                    ad2 = fabs( data_[1][1] );
193 <                    ad3 = fabs( data_[2][2] );
191 >                    ad1 = fabs( this->data_[0][0] );
192 >                    ad2 = fabs( this->data_[1][1] );
193 >                    ad3 = fabs( this->data_[2][2] );
194  
195                      if( ad1 >= ad2 && ad1 >= ad3 ){
196  
197 <                        s = 2.0 * sqrt( 1.0 + data_[0][0] - data_[1][1] - data_[2][2] );
198 <                        q[0] = (data_[1][2] + data_[2][1]) / s;
197 >                        s = 2.0 * sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] );
198 >                        q[0] = (this->data_[1][2] + this->data_[2][1]) / s;
199                          q[1] = 0.5 / s;
200 <                        q[2] = (data_[0][1] + data_[1][0]) / s;
201 <                        q[3] = (data_[0][2] + data_[2][0]) / s;
200 >                        q[2] = (this->data_[0][1] + this->data_[1][0]) / s;
201 >                        q[3] = (this->data_[0][2] + this->data_[2][0]) / s;
202                      } else if ( ad2 >= ad1 && ad2 >= ad3 ) {
203 <                        s = sqrt( 1.0 + data_[1][1] - data_[0][0] - data_[2][2] ) * 2.0;
204 <                        q[0] = (data_[0][2] + data_[2][0]) / s;
205 <                        q[1] = (data_[0][1] + data_[1][0]) / s;
203 >                        s = sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] ) * 2.0;
204 >                        q[0] = (this->data_[0][2] + this->data_[2][0]) / s;
205 >                        q[1] = (this->data_[0][1] + this->data_[1][0]) / s;
206                          q[2] = 0.5 / s;
207 <                        q[3] = (data_[1][2] + data_[2][1]) / s;
207 >                        q[3] = (this->data_[1][2] + this->data_[2][1]) / s;
208                      } else {
209  
210 <                        s = sqrt( 1.0 + data_[2][2] - data_[0][0] - data_[1][1] ) * 2.0;
211 <                        q[0] = (data_[0][1] + data_[1][0]) / s;
212 <                        q[1] = (data_[0][2] + data_[2][0]) / s;
213 <                        q[2] = (data_[1][2] + data_[2][1]) / s;
210 >                        s = sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] ) * 2.0;
211 >                        q[0] = (this->data_[0][1] + this->data_[1][0]) / s;
212 >                        q[1] = (this->data_[0][2] + this->data_[2][0]) / s;
213 >                        q[2] = (this->data_[1][2] + this->data_[2][1]) / s;
214                          q[3] = 0.5 / s;
215                      }
216                  }            
# Line 197 | Line 231 | namespace oopse {
231              */            
232              Vector3<Real> toEulerAngles() {
233                  Vector3<Real> myEuler;
234 <                Real phi,theta,psi,eps;
235 <                Real ctheta,stheta;
234 >                Real phi;
235 >                Real theta;
236 >                Real psi;
237 >                Real ctheta;
238 >                Real stheta;
239                  
240                  // set the tolerance for Euler angles and rotation elements
241  
242 <                theta = acos(std::min(1.0, std::max(-1.0,data_[2][2])));
243 <                ctheta = data_[2][2];
242 >                theta = acos(std::min(1.0, std::max(-1.0,this->data_[2][2])));
243 >                ctheta = this->data_[2][2];
244                  stheta = sqrt(1.0 - ctheta * ctheta);
245  
246                  // when sin(theta) is close to 0, we need to consider singularity
# Line 216 | Line 253 | namespace oopse {
253  
254                  if (fabs(stheta) <= oopse::epsilon){
255                      psi = 0.0;
256 <                    phi = atan2(-data_[1][0], data_[0][0]);  
256 >                    phi = atan2(-this->data_[1][0], this->data_[0][0]);  
257                  }
258                  // we only have one unique solution
259                  else{    
260 <                    phi = atan2(data_[2][0], -data_[2][1]);
261 <                    psi = atan2(data_[0][2], data_[1][2]);
260 >                    phi = atan2(this->data_[2][0], -this->data_[2][1]);
261 >                    psi = atan2(this->data_[0][2], this->data_[1][2]);
262                  }
263  
264                  //wrap phi and psi, make sure they are in the range from 0 to 2*Pi
# Line 242 | Line 279 | namespace oopse {
279              Real determinant() const {
280                  Real x,y,z;
281  
282 <                x = data_[0][0] * (data_[1][1] * data_[2][2] - data_[1][2] * data_[2][1]);
283 <                y = data_[0][1] * (data_[1][2] * data_[2][0] - data_[1][0] * data_[2][2]);
284 <                z = data_[0][2] * (data_[1][0] * data_[2][1] - data_[1][1] * data_[2][0]);
282 >                x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]);
283 >                y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]);
284 >                z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]);
285  
286                  return(x + y + z);
287              }            
288 +
289 +            /** Returns the trace of this matrix. */
290 +            Real trace() const {
291 +                return this->data_[0][0] + this->data_[1][1] + this->data_[2][2];
292 +            }
293              
294              /**
295               * Sets the value of this matrix to  the inversion of itself.
296               * @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
297               * implementation of inverse in SquareMatrix class
298               */
299 <            SquareMatrix3<Real>  inverse() {
299 >            SquareMatrix3<Real>  inverse() const {
300                  SquareMatrix3<Real> m;
301                  double det = determinant();
302                  if (fabs(det) <= oopse::epsilon) {
# Line 262 | Line 304 | namespace oopse {
304                  //"This is a runtime or a programming error in your application.");
305                  }
306  
307 <                m(0, 0) = data_[1][1]*data_[2][2] - data_[1][2]*data_[2][1];
308 <                m(1, 0) = data_[1][2]*data_[2][0] - data_[1][0]*data_[2][2];
309 <                m(2, 0) = data_[1][0]*data_[2][1] - data_[1][1]*data_[2][0];
310 <                m(0, 1) = data_[2][1]*data_[0][2] - data_[2][2]*data_[0][1];
311 <                m(1, 1) = data_[2][2]*data_[0][0] - data_[2][0]*data_[0][2];
312 <                m(2, 1) = data_[2][0]*data_[0][1] - data_[2][1]*data_[0][0];
313 <                m(0, 2) = data_[0][1]*data_[1][2] - data_[0][2]*data_[1][1];
314 <                m(1, 2) = data_[0][2]*data_[1][0] - data_[0][0]*data_[1][2];
315 <                m(2, 2) = data_[0][0]*data_[1][1] - data_[0][1]*data_[1][0];
307 >                m(0, 0) = this->data_[1][1]*this->data_[2][2] - this->data_[1][2]*this->data_[2][1];
308 >                m(1, 0) = this->data_[1][2]*this->data_[2][0] - this->data_[1][0]*this->data_[2][2];
309 >                m(2, 0) = this->data_[1][0]*this->data_[2][1] - this->data_[1][1]*this->data_[2][0];
310 >                m(0, 1) = this->data_[2][1]*this->data_[0][2] - this->data_[2][2]*this->data_[0][1];
311 >                m(1, 1) = this->data_[2][2]*this->data_[0][0] - this->data_[2][0]*this->data_[0][2];
312 >                m(2, 1) = this->data_[2][0]*this->data_[0][1] - this->data_[2][1]*this->data_[0][0];
313 >                m(0, 2) = this->data_[0][1]*this->data_[1][2] - this->data_[0][2]*this->data_[1][1];
314 >                m(1, 2) = this->data_[0][2]*this->data_[1][0] - this->data_[0][0]*this->data_[1][2];
315 >                m(2, 2) = this->data_[0][0]*this->data_[1][1] - this->data_[0][1]*this->data_[1][0];
316  
317                  m /= det;
318                  return m;
319              }
320 +            /**
321 +             * Extract the eigenvalues and eigenvectors from a 3x3 matrix.
322 +             * The eigenvectors (the columns of V) will be normalized.
323 +             * The eigenvectors are aligned optimally with the x, y, and z
324 +             * axes respectively.
325 +             * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
326 +             *     overwritten            
327 +             * @param w will contain the eigenvalues of the matrix On return of this function
328 +             * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
329 +             *    normalized and mutually orthogonal.              
330 +             * @warning a will be overwritten
331 +             */
332 +            static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v);
333 +    };
334 + /*=========================================================================
335  
336 <            void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v) {
337 <                int i,j,k,maxI;
281 <                Real tmp, maxVal;
282 <                Vector3<Real> v_maxI, v_k, v_j;
336 >  Program:   Visualization Toolkit
337 >  Module:    $RCSfile: SquareMatrix3.hpp,v $
338  
339 <                // diagonalize using Jacobi
340 <                jacobi(a, w, v);
339 >  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
340 >  All rights reserved.
341 >  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
342  
343 <                // if all the eigenvalues are the same, return identity matrix
344 <                if (w[0] == w[1] && w[0] == w[2] ) {
345 <                      v = SquareMatrix3<Real>::identity();
346 <                      return;
343 >     This software is distributed WITHOUT ANY WARRANTY; without even
344 >     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
345 >     PURPOSE.  See the above copyright notice for more information.
346 >
347 > =========================================================================*/
348 >    template<typename Real>
349 >    void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w,
350 >                                                                           SquareMatrix3<Real>& v) {
351 >        int i,j,k,maxI;
352 >        Real tmp, maxVal;
353 >        Vector3<Real> v_maxI, v_k, v_j;
354 >
355 >        // diagonalize using Jacobi
356 >        jacobi(a, w, v);
357 >        // if all the eigenvalues are the same, return identity matrix
358 >        if (w[0] == w[1] && w[0] == w[2] ) {
359 >              v = SquareMatrix3<Real>::identity();
360 >              return;
361 >        }
362 >
363 >        // transpose temporarily, it makes it easier to sort the eigenvectors
364 >        v = v.transpose();
365 >        
366 >        // if two eigenvalues are the same, re-orthogonalize to optimally line
367 >        // up the eigenvectors with the x, y, and z axes
368 >        for (i = 0; i < 3; i++) {
369 >            if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
370 >            // find maximum element of the independant eigenvector
371 >            maxVal = fabs(v(i, 0));
372 >            maxI = 0;
373 >            for (j = 1; j < 3; j++) {
374 >                if (maxVal < (tmp = fabs(v(i, j)))){
375 >                    maxVal = tmp;
376 >                    maxI = j;
377                  }
378 +            }
379 +            
380 +            // swap the eigenvector into its proper position
381 +            if (maxI != i) {
382 +                tmp = w(maxI);
383 +                w(maxI) = w(i);
384 +                w(i) = tmp;
385  
386 <                // transpose temporarily, it makes it easier to sort the eigenvectors
387 <                v = v.transpose();
388 <                
389 <                // if two eigenvalues are the same, re-orthogonalize to optimally line
390 <                // up the eigenvectors with the x, y, and z axes
391 <                for (i = 0; i < 3; i++) {
392 <                    if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
393 <                    // find maximum element of the independant eigenvector
301 <                    maxVal = fabs(v(i, 0));
302 <                    maxI = 0;
303 <                    for (j = 1; j < 3; j++) {
304 <                        if (maxVal < (tmp = fabs(v(i, j)))){
305 <                            maxVal = tmp;
306 <                            maxI = j;
307 <                        }
308 <                    }
309 <                    
310 <                    // swap the eigenvector into its proper position
311 <                    if (maxI != i) {
312 <                        tmp = w(maxI);
313 <                        w(maxI) = w(i);
314 <                        w(i) = tmp;
386 >                v.swapRow(i, maxI);
387 >            }
388 >            // maximum element of eigenvector should be positive
389 >            if (v(maxI, maxI) < 0) {
390 >                v(maxI, 0) = -v(maxI, 0);
391 >                v(maxI, 1) = -v(maxI, 1);
392 >                v(maxI, 2) = -v(maxI, 2);
393 >            }
394  
395 <                        v.swapRow(i, maxI);
396 <                    }
397 <                    // maximum element of eigenvector should be positive
319 <                    if (v(maxI, maxI) < 0) {
320 <                        v(maxI, 0) = -v(maxI, 0);
321 <                        v(maxI, 1) = -v(maxI, 1);
322 <                        v(maxI, 2) = -v(maxI, 2);
323 <                    }
395 >            // re-orthogonalize the other two eigenvectors
396 >            j = (maxI+1)%3;
397 >            k = (maxI+2)%3;
398  
399 <                    // re-orthogonalize the other two eigenvectors
400 <                    j = (maxI+1)%3;
401 <                    k = (maxI+2)%3;
399 >            v(j, 0) = 0.0;
400 >            v(j, 1) = 0.0;
401 >            v(j, 2) = 0.0;
402 >            v(j, j) = 1.0;
403  
404 <                    v(j, 0) = 0.0;
405 <                    v(j, 1) = 0.0;
406 <                    v(j, 2) = 0.0;
407 <                    v(j, j) = 1.0;
404 >            /** @todo */
405 >            v_maxI = v.getRow(maxI);
406 >            v_j = v.getRow(j);
407 >            v_k = cross(v_maxI, v_j);
408 >            v_k.normalize();
409 >            v_j = cross(v_k, v_maxI);
410 >            v.setRow(j, v_j);
411 >            v.setRow(k, v_k);
412  
334 –                    /** @todo */
335 –                    v_maxI = v.getRow(maxI);
336 –                    v_j = v.getRow(j);
337 –                    v_k = cross(v_maxI, v_j);
338 –                    v_k.normalize();
339 –                    v_j = cross(v_k, v_maxI);
340 –                    v.setRow(j, v_j);
341 –                    v.setRow(k, v_k);
413  
414 +            // transpose vectors back to columns
415 +            v = v.transpose();
416 +            return;
417 +            }
418 +        }
419  
420 <                    // transpose vectors back to columns
421 <                    v = v.transpose();
346 <                    return;
347 <                    }
348 <                }
420 >        // the three eigenvalues are different, just sort the eigenvectors
421 >        // to align them with the x, y, and z axes
422  
423 <                // the three eigenvalues are different, just sort the eigenvectors
424 <                // to align them with the x, y, and z axes
423 >        // find the vector with the largest x element, make that vector
424 >        // the first vector
425 >        maxVal = fabs(v(0, 0));
426 >        maxI = 0;
427 >        for (i = 1; i < 3; i++) {
428 >            if (maxVal < (tmp = fabs(v(i, 0)))) {
429 >                maxVal = tmp;
430 >                maxI = i;
431 >            }
432 >        }
433  
434 <                // find the vector with the largest x element, make that vector
435 <                // the first vector
436 <                maxVal = fabs(v(0, 0));
437 <                maxI = 0;
438 <                for (i = 1; i < 3; i++) {
439 <                    if (maxVal < (tmp = fabs(v(i, 0)))) {
440 <                        maxVal = tmp;
441 <                        maxI = i;
442 <                    }
443 <                }
434 >        // swap eigenvalue and eigenvector
435 >        if (maxI != 0) {
436 >            tmp = w(maxI);
437 >            w(maxI) = w(0);
438 >            w(0) = tmp;
439 >            v.swapRow(maxI, 0);
440 >        }
441 >        // do the same for the y element
442 >        if (fabs(v(1, 1)) < fabs(v(2, 1))) {
443 >            tmp = w(2);
444 >            w(2) = w(1);
445 >            w(1) = tmp;
446 >            v.swapRow(2, 1);
447 >        }
448  
449 <                // swap eigenvalue and eigenvector
450 <                if (maxI != 0) {
451 <                    tmp = w(maxI);
452 <                    w(maxI) = w(0);
453 <                    w(0) = tmp;
454 <                    v.swapRow(maxI, 0);
455 <                }
456 <                // do the same for the y element
372 <                if (fabs(v(1, 1)) < fabs(v(2, 1))) {
373 <                    tmp = w(2);
374 <                    w(2) = w(1);
375 <                    w(1) = tmp;
376 <                    v.swapRow(2, 1);
377 <                }
449 >        // ensure that the sign of the eigenvectors is correct
450 >        for (i = 0; i < 2; i++) {
451 >            if (v(i, i) < 0) {
452 >                v(i, 0) = -v(i, 0);
453 >                v(i, 1) = -v(i, 1);
454 >                v(i, 2) = -v(i, 2);
455 >            }
456 >        }
457  
458 <                // ensure that the sign of the eigenvectors is correct
459 <                for (i = 0; i < 2; i++) {
460 <                    if (v(i, i) < 0) {
461 <                        v(i, 0) = -v(i, 0);
462 <                        v(i, 1) = -v(i, 1);
463 <                        v(i, 2) = -v(i, 2);
385 <                    }
386 <                }
458 >        // set sign of final eigenvector to ensure that determinant is positive
459 >        if (v.determinant() < 0) {
460 >            v(2, 0) = -v(2, 0);
461 >            v(2, 1) = -v(2, 1);
462 >            v(2, 2) = -v(2, 2);
463 >        }
464  
465 <                // set sign of final eigenvector to ensure that determinant is positive
466 <                if (v.determinant() < 0) {
467 <                    v(2, 0) = -v(2, 0);
468 <                    v(2, 1) = -v(2, 1);
392 <                    v(2, 2) = -v(2, 2);
393 <                }
465 >        // transpose the eigenvectors back again
466 >        v = v.transpose();
467 >        return ;
468 >    }
469  
470 <                // transpose the eigenvectors back again
471 <                v = v.transpose();
472 <                return ;
470 >    /**
471 >    * Return the multiplication of two matrixes  (m1 * m2).
472 >    * @return the multiplication of two matrixes
473 >    * @param m1 the first matrix
474 >    * @param m2 the second matrix
475 >    */
476 >    template<typename Real>
477 >    inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) {
478 >        SquareMatrix3<Real> result;
479 >
480 >            for (unsigned int i = 0; i < 3; i++)
481 >                for (unsigned int j = 0; j < 3; j++)
482 >                    for (unsigned int k = 0; k < 3; k++)
483 >                        result(i, j)  += m1(i, k) * m2(k, j);                
484 >
485 >        return result;
486 >    }
487 >
488 >    template<typename Real>
489 >    inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
490 >        SquareMatrix3<Real> result;
491 >
492 >            for (unsigned int i = 0; i < 3; i++) {
493 >                for (unsigned int j = 0; j < 3; j++) {
494 >                        result(i, j)  = v1[i] * v2[j];                
495 >                }
496              }
497 <    };
497 >            
498 >        return result;        
499 >    }
500  
501 +    
502      typedef SquareMatrix3<double> Mat3x3d;
503      typedef SquareMatrix3<double> RotMat3x3d;
504  
505   } //namespace oopse
506   #endif // MATH_SQUAREMATRIX_HPP
507 +

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