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Revision 76 by tim, Thu Oct 14 23:28:09 2004 UTC vs.
Revision 385 by tim, Tue Mar 1 20:10:14 2005 UTC

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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_SQUAREMATRIX#_HPP
49 < #define  MATH_SQUAREMATRIX#_HPP
48 > #ifndef MATH_SQUAREMATRIX3_HPP
49 > #define  MATH_SQUAREMATRIX3_HPP
50  
51 + #include "Quaternion.hpp"
52   #include "SquareMatrix.hpp"
53 + #include "Vector3.hpp"
54 +
55   namespace oopse {
56  
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 +            
81 +            SquareMatrix3( const Vector3<Real>& eulerAngles) {
82 +                setupRotMat(eulerAngles);
83 +            }
84 +            
85 +            SquareMatrix3(Real phi, Real theta, Real psi) {
86 +                setupRotMat(phi, theta, psi);
87 +            }
88  
89 +            SquareMatrix3(const Quaternion<Real>& q) {
90 +                setupRotMat(q);
91 +
92 +            }
93 +
94 +            SquareMatrix3(Real w, Real x, Real y, Real z) {
95 +                setupRotMat(w, x, y, z);
96 +            }
97 +            
98              /** copy assignment operator */
99              SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
100                  if (this == &m)
101                      return *this;
102                   SquareMatrix<Real, 3>::operator=(m);
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
115               */
116 <            void setupRotMat(const Vector3d& euler);
116 >            void setupRotMat(const Vector3<Real>& eulerAngles) {
117 >                setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
118 >            }
119  
120              /**
121               * Sets this matrix to a rotation matrix by three euler angles
# Line 66 | Line 123 | namespace oopse {
123               * @param theta
124               * @psi theta
125               */
126 <            void setupRotMat(double phi, double theta, double psi);
126 >            void setupRotMat(Real phi, Real theta, Real psi) {
127 >                Real sphi, stheta, spsi;
128 >                Real cphi, ctheta, cpsi;
129  
130 +                sphi = sin(phi);
131 +                stheta = sin(theta);
132 +                spsi = sin(psi);
133 +                cphi = cos(phi);
134 +                ctheta = cos(theta);
135 +                cpsi = cos(psi);
136  
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 +                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 +                this->data_[2][0] = stheta * sphi;
146 +                this->data_[2][1] = -stheta * cphi;
147 +                this->data_[2][2] = ctheta;
148 +            }
149 +
150 +
151              /**
152               * Sets this matrix to a rotation matrix by quaternion
153               * @param quat
154              */
155 <            void setupRotMat(const Vector4d& quat);
155 >            void setupRotMat(const Quaternion<Real>& quat) {
156 >                setupRotMat(quat.w(), quat.x(), quat.y(), quat.z());
157 >            }
158  
159              /**
160               * Sets this matrix to a rotation matrix by quaternion
161 <             * @param q0
162 <             * @param q1
163 <             * @param q2
164 <             * @parma q3
161 >             * @param w the first element
162 >             * @param x the second element
163 >             * @param y the third element
164 >             * @param z the fourth element
165              */
166 <            void setupRotMat(double q0, double q1, double q2, double q4);
166 >            void setupRotMat(Real w, Real x, Real y, Real z) {
167 >                Quaternion<Real> q(w, x, y, z);
168 >                *this = q.toRotationMatrix3();
169 >            }
170  
171              /**
172               * Returns the quaternion from this rotation matrix
173               * @return the quaternion from this rotation matrix
174               * @exception invalid rotation matrix
175              */            
176 <            Quaternion rotMatToQuat();
176 >            Quaternion<Real> toQuaternion() {
177 >                Quaternion<Real> q;
178 >                Real t, s;
179 >                Real ad1, ad2, ad3;    
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] = (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( 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 + 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] = (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 + 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] = (this->data_[1][2] + this->data_[2][1]) / s;
208 +                    } else {
209 +
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 +                }            
217 +
218 +                return q;
219 +                
220 +            }
221 +
222              /**
223               * Returns the euler angles from this rotation matrix
224 <             * @return the quaternion from this rotation matrix
224 >             * @return the euler angles in a vector
225               * @exception invalid rotation matrix
226 +             * We use so-called "x-convention", which is the most common definition.
227 +             * In this convention, the rotation given by Euler angles (phi, theta, psi), where the first
228 +             * rotation is by an angle phi about the z-axis, the second is by an angle  
229 +             * theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the
230 +             * z-axis (again).
231              */            
232 <            Vector3d rotMatToEuler();
232 >            Vector3<Real> toEulerAngles() {
233 >                Vector3<Real> myEuler;
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,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
247 >                // In this case, we can assign an arbitary value to phi (or psi), and then determine
248 >                // the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0
249 >                // in cases of singularity.  
250 >                // we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
251 >                // Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never
252 >                // change the sign of both of the parameters passed to atan2.
253 >
254 >                if (fabs(stheta) <= oopse::epsilon){
255 >                    psi = 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(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
265 >                if (phi < 0)
266 >                  phi += M_PI;
267 >
268 >                if (psi < 0)
269 >                  psi += M_PI;
270 >
271 >                myEuler[0] = phi;
272 >                myEuler[1] = theta;
273 >                myEuler[2] = psi;
274 >
275 >                return myEuler;
276 >            }
277              
278 +            /** Returns the determinant of this matrix. */
279 +            Real determinant() const {
280 +                Real x,y,z;
281 +
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 <            void  inverse();
299 >            SquareMatrix3<Real>  inverse() const {
300 >                SquareMatrix3<Real> m;
301 >                double det = determinant();
302 >                if (fabs(det) <= oopse::epsilon) {
303 >                //"The method was called on a matrix with |determinant| <= 1e-6.",
304 >                //"This is a runtime or a programming error in your application.");
305 >                }
306  
307 <            void diagonalize();
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 +  Program:   Visualization Toolkit
337 +  Module:    $RCSfile: SquareMatrix3.hpp,v $
338 +
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 +     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 +                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 +            // re-orthogonalize the other two eigenvectors
396 +            j = (maxI+1)%3;
397 +            k = (maxI+2)%3;
398 +
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 +            /** @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 +
413 +
414 +            // transpose vectors back to columns
415 +            v = v.transpose();
416 +            return;
417 +            }
418 +        }
419 +
420 +        // the three eigenvalues are different, just sort the eigenvectors
421 +        // to align them with the x, y, and z axes
422 +
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 +        // 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 +        // 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 +        // 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 +        // transpose the eigenvectors back again
466 +        v = v.transpose();
467 +        return ;
468      }
469  
470 <    };
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 < }
481 < #endif // MATH_SQUAREMATRIX#_HPP
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 >            
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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