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Revision 101 by tim, Mon Oct 18 23:13:23 2004 UTC vs.
Revision 1360 by cli2, Mon Sep 7 16:31:51 2009 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. 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
# Line 31 | Line 47
47   */
48   #ifndef MATH_SQUAREMATRIX3_HPP
49   #define  MATH_SQUAREMATRIX3_HPP
50 <
50 > #include <vector>
51   #include "Quaternion.hpp"
52   #include "SquareMatrix.hpp"
53   #include "Vector3.hpp"
54 <
54 > #include "utils/NumericConstant.hpp"
55   namespace oopse {
56  
57 <    template<typename Real>
58 <    class SquareMatrix3 : public SquareMatrix<Real, 3> {
59 <        public:
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 <            }
64 >    /** default constructor */
65 >    SquareMatrix3() : SquareMatrix<Real, 3>() {
66 >    }
67  
68 <            /** copy  constructor */
69 <            SquareMatrix3(const SquareMatrix<Real, 3>& m)  : SquareMatrix<Real, 3>(m) {
70 <            }
68 >    /** Constructs and initializes every element of this matrix to a scalar */
69 >    SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
70 >    }
71  
72 <            SquareMatrix3( const Vector3<Real>& eulerAngles) {
73 <                setupRotMat(eulerAngles);
74 <            }
56 <            
57 <            SquareMatrix3(Real phi, Real theta, Real psi) {
58 <                setupRotMat(phi, theta, psi);
59 <            }
72 >    /** Constructs and initializes from an array */
73 >    SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
74 >    }
75  
61 –            SquareMatrix3(const Quaternion<Real>& q) {
62 –                *this = q.toRotationMatrix3();
63 –            }
76  
77 <            SquareMatrix3(Real w, Real x, Real y, Real z) {
78 <                Quaternion<Real> q(w, x, y, z);
79 <                *this = q.toRotationMatrix3();
68 <            }
77 >    /** copy  constructor */
78 >    SquareMatrix3(const SquareMatrix<Real, 3>& m)  : SquareMatrix<Real, 3>(m) {
79 >    }
80              
81 <            /** copy assignment operator */
82 <            SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
83 <                if (this == &m)
84 <                    return *this;
85 <                 SquareMatrix<Real, 3>::operator=(m);
86 <                 return *this;
87 <            }
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 <            /**
90 <             * Sets this matrix to a rotation matrix by three euler angles
80 <             * @ param euler
81 <             */
82 <            void setupRotMat(const Vector3<Real>& eulerAngles) {
83 <                setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
84 <            }
89 >    SquareMatrix3(const Quaternion<Real>& q) {
90 >      setupRotMat(q);
91  
92 <            /**
87 <             * Sets this matrix to a rotation matrix by three euler angles
88 <             * @param phi
89 <             * @param theta
90 <             * @psi theta
91 <             */
92 <            void setupRotMat(Real phi, Real theta, Real psi) {
93 <                Real sphi, stheta, spsi;
94 <                Real cphi, ctheta, cpsi;
92 >    }
93  
94 <                sphi = sin(phi);
95 <                stheta = sin(theta);
96 <                spsi = sin(psi);
97 <                cphi = cos(phi);
98 <                ctheta = cos(theta);
99 <                cpsi = cos(psi);
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  
103 –                data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
104 –                data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
105 –                data_[0][2] = spsi * stheta;
106 –                
107 –                data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
108 –                data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
109 –                data_[1][2] = cpsi * stheta;
106  
107 <                data_[2][0] = stheta * sphi;
108 <                data_[2][1] = -stheta * cphi;
109 <                data_[2][2] = ctheta;
110 <            }
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 Vector3<Real>& eulerAngles) {
117 +      setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
118 +    }
119  
120 <            /**
121 <             * Sets this matrix to a rotation matrix by quaternion
122 <             * @param quat
123 <            */
124 <            void setupRotMat(const Quaternion<Real>& quat) {
125 <                *this = quat.toRotationMatrix3();
126 <            }
120 >    /**
121 >     * Sets this matrix to a rotation matrix by three euler angles
122 >     * @param phi
123 >     * @param theta
124 >     * @psi theta
125 >     */
126 >    void setupRotMat(Real phi, Real theta, Real psi) {
127 >      Real sphi, stheta, spsi;
128 >      Real cphi, ctheta, cpsi;
129  
130 <            /**
131 <             * Sets this matrix to a rotation matrix by quaternion
132 <             * @param w the first element
133 <             * @param x the second element
134 <             * @param y the third element
135 <             * @param z the fourth element
131 <            */
132 <            void setupRotMat(Real w, Real x, Real y, Real z) {
133 <                Quaternion<Real> q(w, x, y, z);
134 <                *this = q.toRotationMatrix3();
135 <            }
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 <            /**
138 <             * Returns the quaternion from this rotation matrix
139 <             * @return the quaternion from this rotation matrix
140 <             * @exception invalid rotation matrix
141 <            */            
142 <            Quaternion<Real> toQuaternion() {
143 <                Quaternion<Real> q;
144 <                Real t, s;
145 <                Real ad1, ad2, ad3;    
146 <                t = data_[0][0] + data_[1][1] + data_[2][2] + 1.0;
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 <                if( t > 0.0 ){
145 >      this->data_[2][0] = stheta * sphi;
146 >      this->data_[2][1] = -stheta * cphi;
147 >      this->data_[2][2] = ctheta;
148 >    }
149  
150 –                    s = 0.5 / sqrt( t );
151 –                    q[0] = 0.25 / s;
152 –                    q[1] = (data_[1][2] - data_[2][1]) * s;
153 –                    q[2] = (data_[2][0] - data_[0][2]) * s;
154 –                    q[3] = (data_[0][1] - data_[1][0]) * s;
155 –                } else {
150  
151 <                    ad1 = fabs( data_[0][0] );
152 <                    ad2 = fabs( data_[1][1] );
153 <                    ad3 = fabs( data_[2][2] );
151 >    /**
152 >     * Sets this matrix to a rotation matrix by quaternion
153 >     * @param quat
154 >     */
155 >    void setupRotMat(const Quaternion<Real>& quat) {
156 >      setupRotMat(quat.w(), quat.x(), quat.y(), quat.z());
157 >    }
158  
159 <                    if( ad1 >= ad2 && ad1 >= ad3 ){
159 >    /**
160 >     * Sets this matrix to a rotation matrix by quaternion
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(Real w, Real x, Real y, Real z) {
167 >      Quaternion<Real> q(w, x, y, z);
168 >      *this = q.toRotationMatrix3();
169 >    }
170  
171 <                        s = 2.0 * sqrt( 1.0 + data_[0][0] - data_[1][1] - data_[2][2] );
172 <                        q[0] = (data_[1][2] + data_[2][1]) / s;
173 <                        q[1] = 0.5 / s;
166 <                        q[2] = (data_[0][1] + data_[1][0]) / s;
167 <                        q[3] = (data_[0][2] + data_[2][0]) / s;
168 <                    } else if ( ad2 >= ad1 && ad2 >= ad3 ) {
169 <                        s = sqrt( 1.0 + data_[1][1] - data_[0][0] - data_[2][2] ) * 2.0;
170 <                        q[0] = (data_[0][2] + data_[2][0]) / s;
171 <                        q[1] = (data_[0][1] + data_[1][0]) / s;
172 <                        q[2] = 0.5 / s;
173 <                        q[3] = (data_[1][2] + data_[2][1]) / s;
174 <                    } else {
171 >    void setupSkewMat(Vector3<Real> v) {
172 >        setupSkewMat(v[0], v[1], v[2]);
173 >    }
174  
175 <                        s = sqrt( 1.0 + data_[2][2] - data_[0][0] - data_[1][1] ) * 2.0;
176 <                        q[0] = (data_[0][1] + data_[1][0]) / s;
177 <                        q[1] = (data_[0][2] + data_[2][0]) / s;
178 <                        q[2] = (data_[1][2] + data_[2][1]) / s;
179 <                        q[3] = 0.5 / s;
180 <                    }
181 <                }            
175 >    void setupSkewMat(Real v1, Real v2, Real v3) {
176 >        this->data_[0][0] = 0;
177 >        this->data_[0][1] = -v3;
178 >        this->data_[0][2] = v2;
179 >        this->data_[1][0] = v3;
180 >        this->data_[1][1] = 0;
181 >        this->data_[1][2] = -v1;
182 >        this->data_[2][0] = -v2;
183 >        this->data_[2][1] = v1;
184 >        this->data_[2][2] = 0;
185 >        
186 >        
187 >    }
188  
189 <                return q;
189 >
190 >
191 >    /**
192 >     * Returns the quaternion from this rotation matrix
193 >     * @return the quaternion from this rotation matrix
194 >     * @exception invalid rotation matrix
195 >     */            
196 >    Quaternion<Real> toQuaternion() {
197 >      Quaternion<Real> q;
198 >      Real t, s;
199 >      Real ad1, ad2, ad3;    
200 >      t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0;
201 >
202 >      if( t > NumericConstant::epsilon ){
203 >
204 >        s = 0.5 / sqrt( t );
205 >        q[0] = 0.25 / s;
206 >        q[1] = (this->data_[1][2] - this->data_[2][1]) * s;
207 >        q[2] = (this->data_[2][0] - this->data_[0][2]) * s;
208 >        q[3] = (this->data_[0][1] - this->data_[1][0]) * s;
209 >      } else {
210 >
211 >        ad1 = this->data_[0][0];
212 >        ad2 = this->data_[1][1];
213 >        ad3 = this->data_[2][2];
214 >
215 >        if( ad1 >= ad2 && ad1 >= ad3 ){
216 >
217 >          s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] );
218 >          q[0] = (this->data_[1][2] - this->data_[2][1]) * s;
219 >          q[1] = 0.25 / s;
220 >          q[2] = (this->data_[0][1] + this->data_[1][0]) * s;
221 >          q[3] = (this->data_[0][2] + this->data_[2][0]) * s;
222 >        } else if ( ad2 >= ad1 && ad2 >= ad3 ) {
223 >          s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] );
224 >          q[0] = (this->data_[2][0] - this->data_[0][2] ) * s;
225 >          q[1] = (this->data_[0][1] + this->data_[1][0]) * s;
226 >          q[2] = 0.25 / s;
227 >          q[3] = (this->data_[1][2] + this->data_[2][1]) * s;
228 >        } else {
229 >
230 >          s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] );
231 >          q[0] = (this->data_[0][1] - this->data_[1][0]) * s;
232 >          q[1] = (this->data_[0][2] + this->data_[2][0]) * s;
233 >          q[2] = (this->data_[1][2] + this->data_[2][1]) * s;
234 >          q[3] = 0.25 / s;
235 >        }
236 >      }            
237 >
238 >      return q;
239                  
240 <            }
240 >    }
241  
242 <            /**
243 <             * Returns the euler angles from this rotation matrix
244 <             * @return the euler angles in a vector
245 <             * @exception invalid rotation matrix
246 <             * We use so-called "x-convention", which is the most common definition.
247 <             * In this convention, the rotation given by Euler angles (phi, theta, psi), where the first
248 <             * rotation is by an angle phi about the z-axis, the second is by an angle  
249 <             * theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the
250 <             * z-axis (again).
251 <            */            
252 <            Vector3<Real> toEulerAngles() {
253 <                Vector<Real> myEuler;
254 <                Real phi,theta,psi,eps;
255 <                Real ctheta,stheta;
242 >    /**
243 >     * Returns the euler angles from this rotation matrix
244 >     * @return the euler angles in a vector
245 >     * @exception invalid rotation matrix
246 >     * We use so-called "x-convention", which is the most common definition.
247 >     * In this convention, the rotation given by Euler angles (phi, theta,
248 >     * psi), where the first rotation is by an angle phi about the z-axis,
249 >     * the second is by an angle theta (0 <= theta <= 180) about the x-axis,
250 >     * and the third is by an angle psi about the z-axis (again).
251 >     */            
252 >    Vector3<Real> toEulerAngles() {
253 >      Vector3<Real> myEuler;
254 >      Real phi;
255 >      Real theta;
256 >      Real psi;
257 >      Real ctheta;
258 >      Real stheta;
259                  
260 <                // set the tolerance for Euler angles and rotation elements
260 >      // set the tolerance for Euler angles and rotation elements
261  
262 <                theta = acos(min(1.0,max(-1.0,data_[2][2])));
263 <                ctheta = data_[2][2];
264 <                stheta = sqrt(1.0 - ctheta * ctheta);
262 >      theta = acos(std::min((RealType)1.0, std::max((RealType)-1.0,this->data_[2][2])));
263 >      ctheta = this->data_[2][2];
264 >      stheta = sqrt(1.0 - ctheta * ctheta);
265  
266 <                // when sin(theta) is close to 0, we need to consider singularity
267 <                // In this case, we can assign an arbitary value to phi (or psi), and then determine
268 <                // the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0
269 <                // in cases of singularity.  
270 <                // we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
271 <                // Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never
272 <                // change the sign of both of the parameters passed to atan2.
266 >      // when sin(theta) is close to 0, we need to consider
267 >      // singularity In this case, we can assign an arbitary value to
268 >      // phi (or psi), and then determine the psi (or phi) or
269 >      // vice-versa. We'll assume that phi always gets the rotation,
270 >      // and psi is 0 in cases of singularity.
271 >      // we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
272 >      // Since 0 <= theta <= 180, sin(theta) will be always
273 >      // non-negative. Therefore, it will never change the sign of both of
274 >      // the parameters passed to atan2.
275  
276 <                if (fabs(stheta) <= oopse::epsilon){
277 <                    psi = 0.0;
278 <                    phi = atan2(-data_[1][0], data_[0][0]);  
279 <                }
280 <                // we only have one unique solution
281 <                else{    
282 <                    phi = atan2(data_[2][0], -data_[2][1]);
283 <                    psi = atan2(data_[0][2], data_[1][2]);
284 <                }
276 >      if (fabs(stheta) < 1e-6){
277 >        psi = 0.0;
278 >        phi = atan2(-this->data_[1][0], this->data_[0][0]);  
279 >      }
280 >      // we only have one unique solution
281 >      else{    
282 >        phi = atan2(this->data_[2][0], -this->data_[2][1]);
283 >        psi = atan2(this->data_[0][2], this->data_[1][2]);
284 >      }
285  
286 <                //wrap phi and psi, make sure they are in the range from 0 to 2*Pi
287 <                if (phi < 0)
288 <                  phi += M_PI;
286 >      //wrap phi and psi, make sure they are in the range from 0 to 2*Pi
287 >      if (phi < 0)
288 >        phi += 2.0 * M_PI;
289  
290 <                if (psi < 0)
291 <                  psi += M_PI;
290 >      if (psi < 0)
291 >        psi += 2.0 * M_PI;
292  
293 <                myEuler[0] = phi;
294 <                myEuler[1] = theta;
295 <                myEuler[2] = psi;
296 <
297 <                return myEuler;
298 <            }
293 >      myEuler[0] = phi;
294 >      myEuler[1] = theta;
295 >      myEuler[2] = psi;
296 >
297 >      return myEuler;
298 >    }
299              
300 <            /** Returns the determinant of this matrix. */
301 <            Real determinant() const {
302 <                Real x,y,z;
300 >    /** Returns the determinant of this matrix. */
301 >    Real determinant() const {
302 >      Real x,y,z;
303  
304 <                x = data_[0][0] * (data_[1][1] * data_[2][2] - data_[1][2] * data_[2][1]);
305 <                y = data_[0][1] * (data_[1][2] * data_[2][0] - data_[1][0] * data_[2][2]);
306 <                z = data_[0][2] * (data_[1][0] * data_[2][1] - data_[1][1] * data_[2][0]);
304 >      x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]);
305 >      y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]);
306 >      z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]);
307  
308 <                return(x + y + z);
309 <            }            
308 >      return(x + y + z);
309 >    }            
310 >
311 >    /** Returns the trace of this matrix. */
312 >    Real trace() const {
313 >      return this->data_[0][0] + this->data_[1][1] + this->data_[2][2];
314 >    }
315              
316 <            /**
317 <             * Sets the value of this matrix to  the inversion of itself.
318 <             * @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
319 <             * implementation of inverse in SquareMatrix class
320 <             */
321 <            SquareMatrix3<Real>  inverse() {
322 <                SquareMatrix3<Real> m;
323 <                double det = determinant();
324 <                if (fabs(det) <= oopse::epsilon) {
325 <                //"The method was called on a matrix with |determinant| <= 1e-6.",
326 <                //"This is a runtime or a programming error in your application.");
327 <                }
316 >    /**
317 >     * Sets the value of this matrix to  the inversion of itself.
318 >     * @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
319 >     * implementation of inverse in SquareMatrix class
320 >     */
321 >    SquareMatrix3<Real>  inverse() const {
322 >      SquareMatrix3<Real> m;
323 >      RealType det = determinant();
324 >      if (fabs(det) <= oopse::epsilon) {
325 >        //"The method was called on a matrix with |determinant| <= 1e-6.",
326 >        //"This is a runtime or a programming error in your application.");
327 >        std::vector<int> zeroDiagElementIndex;
328 >        for (int i =0; i < 3; ++i) {
329 >            if (fabs(this->data_[i][i]) <= oopse::epsilon) {
330 >                zeroDiagElementIndex.push_back(i);
331 >            }
332 >        }
333  
334 <                m(0, 0) = data_[1][1]*data_[2][2] - data_[1][2]*data_[2][1];
335 <                m(1, 0) = data_[1][2]*data_[2][0] - data_[1][0]*data_[2][2];
336 <                m(2, 0) = data_[1][0]*data_[2][1] - data_[1][1]*data_[2][0];
337 <                m(0, 1) = data_[2][1]*data_[0][2] - data_[2][2]*data_[0][1];
269 <                m(1, 1) = data_[2][2]*data_[0][0] - data_[2][0]*data_[0][2];
270 <                m(2, 1) = data_[2][0]*data_[0][1] - data_[2][1]*data_[0][0];
271 <                m(0, 2) = data_[0][1]*data_[1][2] - data_[0][2]*data_[1][1];
272 <                m(1, 2) = data_[0][2]*data_[1][0] - data_[0][0]*data_[1][2];
273 <                m(2, 2) = data_[0][0]*data_[1][1] - data_[0][1]*data_[1][0];
334 >        if (zeroDiagElementIndex.size() == 2) {
335 >            int index = zeroDiagElementIndex[0];
336 >            m(index, index) = 1.0 / this->data_[index][index];
337 >        }else if (zeroDiagElementIndex.size() == 1) {
338  
339 <                m /= det;
340 <                return m;
339 >            int a = (zeroDiagElementIndex[0] + 1) % 3;
340 >            int b = (zeroDiagElementIndex[0] + 2) %3;
341 >            RealType denom = this->data_[a][a] * this->data_[b][b] - this->data_[b][a]*this->data_[a][b];
342 >            m(a, a) = this->data_[b][b] /denom;
343 >            m(b, a) = -this->data_[b][a]/denom;
344 >
345 >            m(a,b) = -this->data_[a][b]/denom;
346 >            m(b, b) = this->data_[a][a]/denom;
347 >                
348 >        }
349 >      
350 > /*
351 >        for(std::vector<int>::iterator iter = zeroDiagElementIndex.begin(); iter != zeroDiagElementIndex.end() ++iter) {
352 >            if (this->data_[*iter][0] > oopse::epsilon || this->data_[*iter][1] ||this->data_[*iter][2] ||
353 >                this->data_[0][*iter] > oopse::epsilon || this->data_[1][*iter] ||this->data_[2][*iter] ) {
354 >                std::cout << "can not inverse matrix" << std::endl;
355              }
356 +        }
357 + */
358 +      } else {
359  
360 <            void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v) {
361 <                int i,j,k,maxI;
362 <                Real tmp, maxVal;
363 <                Vector3<Real> v_maxI, v_k, v_j;
360 >          m(0, 0) = this->data_[1][1]*this->data_[2][2] - this->data_[1][2]*this->data_[2][1];
361 >          m(1, 0) = this->data_[1][2]*this->data_[2][0] - this->data_[1][0]*this->data_[2][2];
362 >          m(2, 0) = this->data_[1][0]*this->data_[2][1] - this->data_[1][1]*this->data_[2][0];
363 >          m(0, 1) = this->data_[2][1]*this->data_[0][2] - this->data_[2][2]*this->data_[0][1];
364 >          m(1, 1) = this->data_[2][2]*this->data_[0][0] - this->data_[2][0]*this->data_[0][2];
365 >          m(2, 1) = this->data_[2][0]*this->data_[0][1] - this->data_[2][1]*this->data_[0][0];
366 >          m(0, 2) = this->data_[0][1]*this->data_[1][2] - this->data_[0][2]*this->data_[1][1];
367 >          m(1, 2) = this->data_[0][2]*this->data_[1][0] - this->data_[0][0]*this->data_[1][2];
368 >          m(2, 2) = this->data_[0][0]*this->data_[1][1] - this->data_[0][1]*this->data_[1][0];
369  
370 <                // diagonalize using Jacobi
371 <                jacobi(a, w, v);
370 >          m /= det;
371 >        }
372 >      return m;
373 >    }
374  
375 <                // if all the eigenvalues are the same, return identity matrix
376 <                if (w[0] == w[1] && w[0] == w[2] ){
289 <                      v = SquareMatrix3<Real>::identity();
290 <                      return
291 <                }
292 <
293 <                // transpose temporarily, it makes it easier to sort the eigenvectors
294 <                v = v.tanspose();
375 >    SquareMatrix3<Real> transpose() const{
376 >      SquareMatrix3<Real> result;
377                  
378 <                // if two eigenvalues are the same, re-orthogonalize to optimally line
379 <                // up the eigenvectors with the x, y, and z axes
380 <                for (i = 0; i < 3; i++) {
299 <                    if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
300 <                    // 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;
378 >      for (unsigned int i = 0; i < 3; i++)
379 >        for (unsigned int j = 0; j < 3; j++)              
380 >          result(j, i) = this->data_[i][j];
381  
382 <                        v.swapRow(i, maxI);
383 <                    }
384 <                    // maximum element of eigenvector should be positive
385 <                    if (v(maxI, maxI) < 0) {
386 <                        v(maxI, 0) = -v(maxI, 0);
387 <                        v(maxI, 1) = -v(maxI, 1);
388 <                        v(maxI, 2) = -v(maxI, 2);
389 <                    }
382 >      return result;
383 >    }
384 >    /**
385 >     * Extract the eigenvalues and eigenvectors from a 3x3 matrix.
386 >     * The eigenvectors (the columns of V) will be normalized.
387 >     * The eigenvectors are aligned optimally with the x, y, and z
388 >     * axes respectively.
389 >     * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
390 >     *     overwritten            
391 >     * @param w will contain the eigenvalues of the matrix On return of this function
392 >     * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
393 >     *    normalized and mutually orthogonal.              
394 >     * @warning a will be overwritten
395 >     */
396 >    static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v);
397 >  };
398 >  /*=========================================================================
399  
400 <                    // re-orthogonalize the other two eigenvectors
401 <                    j = (maxI+1)%3;
327 <                    k = (maxI+2)%3;
400 >  Program:   Visualization Toolkit
401 >  Module:    $RCSfile: SquareMatrix3.hpp,v $
402  
403 <                    v(j, 0) = 0.0;
404 <                    v(j, 1) = 0.0;
405 <                    v(j, 2) = 0.0;
332 <                    v(j, j) = 1.0;
403 >  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
404 >  All rights reserved.
405 >  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
406  
407 <                    /** @todo */
408 <                    v_maxI = v.getRow(maxI);
409 <                    v_j = v.getRow(j);
337 <                    v_k = cross(v_maxI, v_j);
338 <                    v_k.normailze();
339 <                    v_j = cross(v_k, v_maxI);
340 <                    v.setRow(j, v_j);
341 <                    v.setRow(k, v_k);
407 >  This software is distributed WITHOUT ANY WARRANTY; without even
408 >  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
409 >  PURPOSE.  See the above copyright notice for more information.
410  
411 +  =========================================================================*/
412 +  template<typename Real>
413 +  void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w,
414 +                                        SquareMatrix3<Real>& v) {
415 +    int i,j,k,maxI;
416 +    Real tmp, maxVal;
417 +    Vector3<Real> v_maxI, v_k, v_j;
418  
419 <                    // transpose vectors back to columns
420 <                    v = v.transpose();
421 <                    return;
422 <                    }
423 <                }
419 >    // diagonalize using Jacobi
420 >    jacobi(a, w, v);
421 >    // if all the eigenvalues are the same, return identity matrix
422 >    if (w[0] == w[1] && w[0] == w[2] ) {
423 >      v = SquareMatrix3<Real>::identity();
424 >      return;
425 >    }
426  
427 <                // the three eigenvalues are different, just sort the eigenvectors
428 <                // to align them with the x, y, and z axes
427 >    // transpose temporarily, it makes it easier to sort the eigenvectors
428 >    v = v.transpose();
429 >        
430 >    // if two eigenvalues are the same, re-orthogonalize to optimally line
431 >    // up the eigenvectors with the x, y, and z axes
432 >    for (i = 0; i < 3; i++) {
433 >      if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
434 >        // find maximum element of the independant eigenvector
435 >        maxVal = fabs(v(i, 0));
436 >        maxI = 0;
437 >        for (j = 1; j < 3; j++) {
438 >          if (maxVal < (tmp = fabs(v(i, j)))){
439 >            maxVal = tmp;
440 >            maxI = j;
441 >          }
442 >        }
443 >            
444 >        // swap the eigenvector into its proper position
445 >        if (maxI != i) {
446 >          tmp = w(maxI);
447 >          w(maxI) = w(i);
448 >          w(i) = tmp;
449  
450 <                // find the vector with the largest x element, make that vector
451 <                // the first vector
452 <                maxVal = fabs(v(0, 0));
453 <                maxI = 0;
454 <                for (i = 1; i < 3; i++) {
455 <                    if (maxVal < (tmp = fabs(v(i, 0)))) {
456 <                        maxVal = tmp;
457 <                        maxI = i;
361 <                    }
362 <                }
450 >          v.swapRow(i, maxI);
451 >        }
452 >        // maximum element of eigenvector should be positive
453 >        if (v(maxI, maxI) < 0) {
454 >          v(maxI, 0) = -v(maxI, 0);
455 >          v(maxI, 1) = -v(maxI, 1);
456 >          v(maxI, 2) = -v(maxI, 2);
457 >        }
458  
459 <                // swap eigenvalue and eigenvector
460 <                if (maxI != 0) {
461 <                    tmp = w(maxI);
367 <                    w(maxI) = w(0);
368 <                    w(0) = tmp;
369 <                    v.swapRow(maxI, 0);
370 <                }
371 <                // 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 <                }
459 >        // re-orthogonalize the other two eigenvectors
460 >        j = (maxI+1)%3;
461 >        k = (maxI+2)%3;
462  
463 <                // ensure that the sign of the eigenvectors is correct
464 <                for (i = 0; i < 2; i++) {
465 <                    if (v(i, i) < 0) {
466 <                        v(i, 0) = -v(i, 0);
383 <                        v(i, 1) = -v(i, 1);
384 <                        v(i, 2) = -v(i, 2);
385 <                    }
386 <                }
463 >        v(j, 0) = 0.0;
464 >        v(j, 1) = 0.0;
465 >        v(j, 2) = 0.0;
466 >        v(j, j) = 1.0;
467  
468 <                // set sign of final eigenvector to ensure that determinant is positive
469 <                if (determinant(v) < 0) {
470 <                    v(2, 0) = -v(2, 0);
471 <                    v(2, 1) = -v(2, 1);
472 <                    v(2, 2) = -v(2, 2);
473 <                }
468 >        /** @todo */
469 >        v_maxI = v.getRow(maxI);
470 >        v_j = v.getRow(j);
471 >        v_k = cross(v_maxI, v_j);
472 >        v_k.normalize();
473 >        v_j = cross(v_k, v_maxI);
474 >        v.setRow(j, v_j);
475 >        v.setRow(k, v_k);
476  
395 –                // transpose the eigenvectors back again
396 –                v = v.transpose();
397 –                return ;
398 –            }
399 –    };
477  
478 <    typedef SquareMatrix3<double> Mat3x3d;
479 <    typedef SquareMatrix3<double> RotMat3x3d;
478 >        // transpose vectors back to columns
479 >        v = v.transpose();
480 >        return;
481 >      }
482 >    }
483  
484 +    // the three eigenvalues are different, just sort the eigenvectors
485 +    // to align them with the x, y, and z axes
486 +
487 +    // find the vector with the largest x element, make that vector
488 +    // the first vector
489 +    maxVal = fabs(v(0, 0));
490 +    maxI = 0;
491 +    for (i = 1; i < 3; i++) {
492 +      if (maxVal < (tmp = fabs(v(i, 0)))) {
493 +        maxVal = tmp;
494 +        maxI = i;
495 +      }
496 +    }
497 +
498 +    // swap eigenvalue and eigenvector
499 +    if (maxI != 0) {
500 +      tmp = w(maxI);
501 +      w(maxI) = w(0);
502 +      w(0) = tmp;
503 +      v.swapRow(maxI, 0);
504 +    }
505 +    // do the same for the y element
506 +    if (fabs(v(1, 1)) < fabs(v(2, 1))) {
507 +      tmp = w(2);
508 +      w(2) = w(1);
509 +      w(1) = tmp;
510 +      v.swapRow(2, 1);
511 +    }
512 +
513 +    // ensure that the sign of the eigenvectors is correct
514 +    for (i = 0; i < 2; i++) {
515 +      if (v(i, i) < 0) {
516 +        v(i, 0) = -v(i, 0);
517 +        v(i, 1) = -v(i, 1);
518 +        v(i, 2) = -v(i, 2);
519 +      }
520 +    }
521 +
522 +    // set sign of final eigenvector to ensure that determinant is positive
523 +    if (v.determinant() < 0) {
524 +      v(2, 0) = -v(2, 0);
525 +      v(2, 1) = -v(2, 1);
526 +      v(2, 2) = -v(2, 2);
527 +    }
528 +
529 +    // transpose the eigenvectors back again
530 +    v = v.transpose();
531 +    return ;
532 +  }
533 +
534 +  /**
535 +   * Return the multiplication of two matrixes  (m1 * m2).
536 +   * @return the multiplication of two matrixes
537 +   * @param m1 the first matrix
538 +   * @param m2 the second matrix
539 +   */
540 +  template<typename Real>
541 +  inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) {
542 +    SquareMatrix3<Real> result;
543 +
544 +    for (unsigned int i = 0; i < 3; i++)
545 +      for (unsigned int j = 0; j < 3; j++)
546 +        for (unsigned int k = 0; k < 3; k++)
547 +          result(i, j)  += m1(i, k) * m2(k, j);                
548 +
549 +    return result;
550 +  }
551 +
552 +  template<typename Real>
553 +  inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
554 +    SquareMatrix3<Real> result;
555 +
556 +    for (unsigned int i = 0; i < 3; i++) {
557 +      for (unsigned int j = 0; j < 3; j++) {
558 +        result(i, j)  = v1[i] * v2[j];                
559 +      }
560 +    }
561 +            
562 +    return result;        
563 +  }
564 +
565 +    
566 +  typedef SquareMatrix3<RealType> Mat3x3d;
567 +  typedef SquareMatrix3<RealType> RotMat3x3d;
568 +
569   } //namespace oopse
570   #endif // MATH_SQUAREMATRIX_HPP
571 +

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